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https://resolver.caltech.edu/CaltechAUTHORS:20160127-073148263
Authors: {'items': [{'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'K.'}, 'orcid': '0000-0003-2908-5469'}]}
Year: 1991
DOI: 10.1098/rspa.1991.0108
A version of the Korn's inequality valid for a weakly convergent sequence of deformations is given.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/tt243-pzq23Wedge-like microstructure in martensites
https://resolver.caltech.edu/CaltechAUTHORS:20160126-130553661
Authors: {'items': [{'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'K.'}, 'orcid': '0000-0003-2908-5469'}]}
Year: 1991
DOI: 10.1016/0956-7151(91)90023-T
The wedge-like microstructure commonly seen in martensites, especially in shape-memory alloys, is an important mechanism for thermoelastic austenite-martensite transformation. This microstructure is analyzed using a suitable energy minimization principle. The Hadamard jump condition is used to characterize coherent interfaces. The crystallographic theory of martensite follows as a consequence of this. It is shown that only very special materials whose lattice parameters satisfy certain highly restrictive conditions can form the wedge-like microstructure. The lattice parameters of common shape-memory alloys satisfy these relations and their morphology shows good agreement with the predictions. This suggests that the microstructure and consequently the macroscopic behavior of martensites may depend very delicately on the lattice parameters.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/4jkwh-m7e66Effective behavior of polycrystals that undergo martensitic phase transformation
https://resolver.caltech.edu/CaltechAUTHORS:20180709-153925415
Authors: {'items': [{'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'Kaushik'}, 'orcid': '0000-0003-2908-5469'}, {'id': 'Kohn-R-V', 'name': {'family': 'Kohn', 'given': 'Robert V.'}}]}
Year: 1993
DOI: 10.1117/12.148412
The shape-memory effect is the ability of a material to recover, on heating, apparently plastic deformations that it suffers below a critical temperature. These apparently plastic strains are not caused by slip or dislocation, but by deformation twinning and the formation of other coherent microstructures by the symmetry-related variants of martensite. In single crystals, these strains depend on the transformation strain and can be quite large. However, in polycrystals made up of a large number of randomly oriented grains, the various grains may not deform cooperatively. Consequently, these recoverable strains depend on the texture and may be severely reduced or even eliminated. Thus, the shape-memory behavior of polycrystals may be significantly different from that of a single crystal. We address this issue by studying some model problems in the setting of anti-plane shear.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/nc8b8-t0911Restrictions on microstructure
https://resolver.caltech.edu/CaltechAUTHORS:20160127-093548090
Authors: {'items': [{'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'Kaushik'}, 'orcid': '0000-0003-2908-5469'}, {'id': 'Firoozye-N-B', 'name': {'family': 'Firoozye', 'given': 'Nikan B.'}}, {'id': 'James-R-D', 'name': {'family': 'James', 'given': 'Richard D.'}, 'orcid': '0000-0001-6019-6613'}, {'id': 'Kohn-R-V', 'name': {'family': 'Kohn', 'given': 'Robert V.'}}]}
Year: 1994
DOI: 10.1017/S0308210500022381
We consider the following question: given a set of matrices ⊁ with no rank-one connections, does it support a nontrivial Young measure limit of gradients? Our main results are these: (a) a Young measure can be supported on four incompatible matrices; (b) in two space dimensions, a Young measure cannot be supported on finitely many incompatible elastic wells; (c) in three or more space dimensions, a Young measure can be supported on three incompatible elastic wells; and (d) if ⊁ supports a nontrivial Young measure with mean value 0, then the linear span of ⊁ must contain a matrix of rank one.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/edc8b-dd224Recoverable Strains in Shape-Memory Polycrystals
https://resolver.caltech.edu/CaltechAUTHORS:20160127-092842919
Authors: {'items': [{'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'K.'}, 'orcid': '0000-0003-2908-5469'}, {'id': 'Kohn-R-V', 'name': {'family': 'Kohn', 'given': 'R. V.'}}]}
Year: 1995
DOI: 10.1051/jp4:1995836
Many alloys display the shape-memory effect in single crystal form, however the degree to which they retain this effect in polycrystalline form varies widely. We propose a theoretical explanation for this difference, showing that the recoverable strain of a polycrystal depends on the texture of the polycrystal, the transformation strain of the underlying martensitic transformation and especially critically on the change of symmetry during the underlying transformation. Roughly, we find that the greater the change in symmetry during transformation, the greater the recoverable strain. Our results agree with experimental observations, and provide guidance for the improvement of the shape-memory effect in polycrystals.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/2z0yn-km645Symmetry, texture and the recoverable strain of shape-memory polycrystals
https://resolver.caltech.edu/CaltechAUTHORS:20160126-133506833
Authors: {'items': [{'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'K.'}, 'orcid': '0000-0003-2908-5469'}, {'id': 'Kohn-R-V', 'name': {'family': 'Kohn', 'given': 'R. V.'}}]}
Year: 1996
DOI: 10.1016/1359-6454(95)00198-0
Shape-memory behavior is the ability of certain materials to recover, on heating, apparently plastic deformation sustained below a critical temperature. Some materials have good shape-memory behavior as single crystals but little or none as polycrystals, while others display good shape-memory behavior even as polycrystals. In this paper, we propose a theoretical explanation for this difference: we show that the recoverable strain in a polycrystal depends on the texture of the polycrystal, the transformation strain of the underlying martensitic transformation and especially on the change of symmetry during the underlying transformation. Roughly, we find that the greater the change in symmetry during transformation, the greater the recoverable strain. We include an extensive survey of the experimental literature and show that our results agree with these observations. We make recommendations for improved shape-memory effect in polycrystals.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/afsjt-b9y56A Theory of Shape-Memory Thin Films with Applications
https://resolver.caltech.edu/CaltechAUTHORS:20160127-091313224
Authors: {'items': [{'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'K.'}, 'orcid': '0000-0003-2908-5469'}, {'id': 'James-R-D', 'name': {'family': 'James', 'given': 'R. D.'}, 'orcid': '0000-0001-6019-6613'}]}
Year: 1996
DOI: 10.1557/PROC-459-311
Shape-memory alloys have the largest energy output per unit volume per cycle of known actuator systems [1]. Unfortunately, they are temperature activated and hence, their frequency is limited in bulk specimens. However, this is overcome in thin films; and hence shape-memory alloys are ideal actuator materials in micromachines. The heart of the shape-memory effect lies in a martensitic phase transformation and the resulting microstructure. It is well-known that microstructure can be significantly different in thin films as compared to bulk materials. In this paper, we report on a theory of single crystal martensitic this films. We show that single crystal films of shape memory material offer interesting possibilities for producing very large deformations, at small scales.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/wqvm7-5pq08Kinematics of Crossing Twins
https://resolver.caltech.edu/CaltechAUTHORS:20160127-081030087
Authors: {'items': [{'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'K.'}, 'orcid': '0000-0003-2908-5469'}]}
Year: 1997
Twins are commonly observed in crystalline solids that undergo martensitic phase transformation. In many materials the twins are also seen to cross each other. This is surprising in view of the severe kinematic restrictions that such crossings impose. This paper presents a sufficient condition for satisfying these restrictions. It
turns out that this condition is automatically satisfied as a consequence of material symmetry in many common martensitic materials. This explains the common observation
of crossing twins. The result is also applied to the magnetostrictive material Terfenol.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/p07ke-5fs22Elastic Energy Minimization and the Recoverable Strains of Polycrystalline Shape-Memory Materials
https://resolver.caltech.edu/CaltechAUTHORS:20131007-131619635
Authors: {'items': [{'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'Kaushik'}, 'orcid': '0000-0003-2908-5469'}, {'id': 'Kohn-R-V', 'name': {'family': 'Kohn', 'given': 'Robert V.'}}]}
Year: 1997
DOI: 10.1007/s002050050049
Shape‐memory behavior is the ability of certain materials to recover, on heating, apparently plastic deformation sustained below a critical temperature. Some materials have good shape‐memory behavior as single crystals but little or none as polycrystals, while others have good shape‐memory behavior even as polycrystals. We propose a method for explaining the difference.
Our approach is based on elastic energy minimization. It leads to a special class of nonlinear homogenization problems, involving integrands that are degenerate near the origin. We explore the behavior of these problems through various examples and bounds. The elementary "Taylor bound" and the newer "translation method" are central to our analysis.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/qfnt6-0et66Equilibrium conditions at corners and edges of an interface in a multiphase solid
https://resolver.caltech.edu/CaltechAUTHORS:20131007-094847359
Authors: {'items': [{'id': 'Simha-N-K', 'name': {'family': 'Simha', 'given': 'N. K.'}}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'K.'}, 'orcid': '0000-0003-2908-5469'}]}
Year: 1997
DOI: 10.1016/S0921-5093(97)00431-0
In various situations such as coherent precipitation, martensitic transformation, recrystallization, and grain growth the kinetics of phase boundaries play a crucial role in determining the microstructure and the resulting macroscopic properties. By performing a variational calculation in a two dimensional setting, we find the equilibrium conditions at corners, where two interfaces meet, and at edges, where an interface meets the boundary of a finite body. We allow for possible singularities in the bulk stress at corners and edges. The general case considers elastic energy for the bulk and anisotropic energies for the surfaces. Special cases treated are: (i) constant bulk energy or purely surface case; (ii) purely elastic case or zero surface energy; and (iii) constant surface energy.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/1mzxh-0b587Relaxation in shape-memory alloys—Part II. Thermo-mechanical model and proposed experiments
https://resolver.caltech.edu/CaltechAUTHORS:20131008-113053878
Authors: {'items': [{'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'K.'}, 'orcid': '0000-0003-2908-5469'}, {'id': 'James-R-D', 'name': {'family': 'James', 'given': 'R. D.'}, 'orcid': '0000-0001-6019-6613'}, {'id': 'Swart-P-J', 'name': {'family': 'Swart', 'given': 'P. J.'}}]}
Year: 1997
DOI: 10.1016/S1359-6454(97)00125-0
A variety of relaxation phenomena such as stabilization of martensite, rubber-like behavior, evolving hysteresis loops and stabilization of interfaces have been observed in various shape-memory alloys. These effects adversely impact technological applications. In Part I of this paper we proposed a phenomenological, but predictive, model of the mechanical behavior of these materials. We showed that this model reproduces the experimental observations. In this part, we extend this model to include the effects of temperature and the austenite-martensite transformation. Once again, the predictions from this extended model agree with experimental observations. We can therefore conclude that the basic phenomenological ideas combined with a few easily measured material parameters is sufficient to predict the behavior of these materials. Finally, we propose new experiments in order to probe longstanding issues concerning the mechanism responsible for the relaxation.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/sx1tk-hs155Relaxation in shape-memory alloys—Part I. Mechanical model
https://resolver.caltech.edu/CaltechAUTHORS:20131008-090814329
Authors: {'items': [{'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'K.'}, 'orcid': '0000-0003-2908-5469'}, {'id': 'James-R-D', 'name': {'family': 'James', 'given': 'R. D.'}, 'orcid': '0000-0001-6019-6613'}, {'id': 'Swart-P-J', 'name': {'family': 'Swart', 'given': 'P. J.'}}]}
Year: 1997
DOI: 10.1016/S1359-6454(97)00124-9
A variety of relaxation phenomena such as the stabilization of martensite, rubber-like behavior, evolving hysteresis loops and stabilization of interfaces have been observed in various shape-memory alloys. These effects adversely impact technological applications. Despite a great deal of experimental evidence, there is no consensus on the mechanism. However, there is universal agreement on certain fundamental aspects of these phenomena. Based on these areas of agreement, we propose a phenomenological, but predictive, model in this paper. This model is based on the framework of thermoelasticity augmented with an internal variable. In this part, we discuss the basic mechanical model and show that it reproduces the experimental observations remarkably well. In Part II of this paper, we extend this model to include thermal effects and use these models to propose new experiments in order to clarify longstanding issues.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/8kr7j-3fm07The Taylor Estimate of Recoverable Strains in Shape-Memory Polycrystals
https://resolver.caltech.edu/CaltechAUTHORS:20160126-121928408
Authors: {'items': [{'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'K.'}, 'orcid': '0000-0003-2908-5469'}, {'id': 'Kohn-R-V', 'name': {'family': 'Kohn', 'given': 'R. V.'}}, {'id': 'Shu-Y-C', 'name': {'family': 'Shu', 'given': 'Y. C.'}}]}
Year: 1998
DOI: 10.1007/0-306-46935-9_9
Shape-memory behavior ls the ability of ccrwin materials to recover, on heating, apparently plastic deformation sustained below a critical temperature. Some materials have good shape-memory behavior as single crystals but little or none as polycrystals, while others have good shape-memory behavior even as polycrystals. Bhattacharya and Kohn (1996. 1997) have proposed a framework to understand this difference. They use energy minimization and the Taylor estimate to argue that the recoverable strains in a polycrystal depend not only on the texture of the polycrystal and the transformation, but critically on the change in symmetry during the underlying martensitic phase transformation. Their results agree with the experimental observations. Shu and Bhattacharya (1997) have also used the
Taylor estimate to study the effect of texture in polycrys- tals of Nickel-Titanium and Copper based shape-memory alloys. The use of the Taylor estimate was evaluated in some detail in Bhattacharya and Kohn ( 1997) and more recently in Shu and Bhattacharya (1997) and Shu (1997). In this short report, we summarize the model of recoverable strain and discuss some results that allow us to evaluate the Taylor estimate.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/mt9x9-7x492The influence of texture on the shape-memory effect in polycrystals
https://resolver.caltech.edu/CaltechAUTHORS:20131007-095506660
Authors: {'items': [{'id': 'Shu-Y-C', 'name': {'family': 'Shu', 'given': 'Y. C.'}}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'K.'}, 'orcid': '0000-0003-2908-5469'}]}
Year: 1998
DOI: 10.1016/S1359-6454(98)00184-0
A model is developed to show that texture is a crucial factor in determining the shape-memory effect in polycrystals. In particular, it is established that texture is the reason why the strains recoverable in Ti–Ni are so much larger than those in Cu-based shape-memory alloys in rolled, extruded and drawn specimens. Further, it is shown that both these materials recover relatively small strains in sputter-deposited thin films due to unfavorable texture. It is found that even the qualitative behavior of combined tension–torsion can critically depend on the texture. The results are in good agreement with experimental observations. Finally, textures are suggested for improved shape-memory effect.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/6nvev-x9716Energy-based model of compressive splitting in heterogeneous brittle solids
https://resolver.caltech.edu/CaltechAUTHORS:20131007-083528747
Authors: {'items': [{'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'K.'}, 'orcid': '0000-0003-2908-5469'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}, {'id': 'Ravichandran-G', 'name': {'family': 'Ravichandran', 'given': 'G.'}, 'orcid': '0000-0002-2912-0001'}]}
Year: 1998
DOI: 10.1016/S0022-5096(98)00026-X
Confined heterogeneous brittle solids loaded under far-field uniaxial compression are often observed to split along the loading axis. We develop a theory which accords this phenomenon an energetic interpretation : the solid splits because in so doing it reduces its total energy, defined as the sum of bulk strain energy and surface energy. The heterogeneous microstructure gives rise to a complex stress distribution in the intact solid. We show that the change in energy due to the release of the microstructural stresses may exceed the cost in fracture energy. Critical conditions for splitting are formulated for polycrystalline solids as a function of readily measurable material properties and applied stresses. The predictions of the theory are found to be in remarkably good agreement with experimental observations in ceramics and rocks.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/pxcgk-t0x90Kinetics of phase boundaries with edges and junctions
https://resolver.caltech.edu/CaltechAUTHORS:20131004-085837547
Authors: {'items': [{'id': 'Simha-N-K', 'name': {'family': 'Simha', 'given': 'N. K.'}}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'K.'}, 'orcid': '0000-0003-2908-5469'}]}
Year: 1998
DOI: 10.1016/S0022-5096(98)00008-8
In this paper we study the propagation of a phase boundary which meets the boundary of the body at an edge or meets other phase boundaries at a junction. We show that it is necessary to provide kinetic relations for the edges and junctions in addition to the kinetic relation of the phase boundary. We derive thermodynamically consistent forms for these additional kinetic relations and show that they have a profound effect on the evolution of the phase boundary.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/4dwdp-q3a95Energy minimization and nonlinear problems in polycrystalline solids
https://resolver.caltech.edu/CaltechAUTHORS:20160126-095640051
Authors: {'items': [{'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'Kaushik'}, 'orcid': '0000-0003-2908-5469'}]}
Year: 1999
Common engineering structural materials -- metallic alloys and ceramics -- are polycrystalline. They are made up of a very large number of grins which have identical crystal structure, but which are oriented differently. The properties of the material depend critically on the texture, by which one means the size, the shape and the orientation distributions of the different grains. If we can systematically understand this dependence, we can identify textures which provide the best possible properties and then try to design a processing technique which gives rise to the texture.
Linear properties -- elastic moduli, conductivity etc. -- have received much attention and there are by now many sophisticated methods to study them (see [1] for a recent example). Some nonlinear properties have also been studied extensively -- for example, there has been much work in polycrystal plasticity beginning with the pioneering work of Taylor [2] -- though in general much less is known here.
This paper highlights some recent successes in modelling the behavior of polycrystalline solids using energy minimization. Two examples -- the splitting of ceramics subjected to compressive loads and shape-memory polycrystals -- are described.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/09na0-3ex49Crystallographic attributes of a shape-memory alloy
https://resolver.caltech.edu/CaltechAUTHORS:20131008-112919537
Authors: {'items': [{'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'Kaushik'}, 'orcid': '0000-0003-2908-5469'}]}
Year: 1999
DOI: 10.1115/1.2816005
Shape-memory Alloys are attractive for many potential applications. In an attempt to provide ideas and guidelines for the development of new shape-memory alloys, this paper reports on a series of investigations that examine the reasons in the crystallography that make (i) shape-memory alloys special amongst martensites and (ii) Nickel-Titanium special among shape-memory alloys.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/1fh9j-y9r67Some examples of nonlinear homogenization involving nearly degenerate energies
https://resolver.caltech.edu/CaltechAUTHORS:20131008-135432675
Authors: {'items': [{'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'K.'}, 'orcid': '0000-0003-2908-5469'}, {'id': 'Kohn-R-V', 'name': {'family': 'Kohn', 'given': 'R. V.'}}, {'id': 'Kozlov-S', 'name': {'family': 'Kozlov', 'given': 'S.'}}]}
Year: 1999
We consider a specific class of nonlinear homogenization problems. The microstructure is a sort of checkerboard polycrystal, and the energy of the basic crystal is degenerate in one direction. We give matching upper and lower bounds for the homogenized energy. The motivation for this problem lies in the recent work of Bhattacharya &
Kohn on shape-memory polycrystals. Our results show that a bound proved therein is nearly sharp.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/yjp53-2a748Phase boundary propagation in a heterogeneous body
https://resolver.caltech.edu/CaltechAUTHORS:20131008-135459071
Authors: {'items': [{'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'Kaushik'}, 'orcid': '0000-0003-2908-5469'}]}
Year: 1999
DOI: 10.1098/rspa.1999.0333
This paper shows that microscopic obstacles can have a profound effect on the motion
of a phase boundary and endow it with some crucial and characteristic experimentally
observed features.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/mjhxc-5r552A theory of thin films of martensitic materials with applications to microactuators
https://resolver.caltech.edu/CaltechAUTHORS:20131008-080907937
Authors: {'items': [{'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'K.'}, 'orcid': '0000-0003-2908-5469'}, {'id': 'James-R-D', 'name': {'family': 'James', 'given': 'R. D.'}, 'orcid': '0000-0001-6019-6613'}]}
Year: 1999
DOI: 10.1016/S0022-5096(98)00043-X
A direct derivation is given of a theory for single crystal thin films, starting from three dimensional nonlinear elasticity theory augmented by a term for interfacial energy. The derivation involves no a priori choice of asymptotic expansion or ansatz. It yields a frame-indifferent Cosserat membrane theory with one Cosserat vector field. The theory is applied to multi-well energy functions appropriate to martensitic materials. It is found that, unlike in bulk materials, which generally only support finely twinned austenite/martensite interfaces as energy minimizing states, the thin film theory predicts the existence of exact, untwined austenite/martensite interfaces. These are used to construct some simple energy minimizing deformations—"tents" and "tunnels"—that could possibly be the basis of simple large-deformation microactuators. Explicit results are given for martensitic materials in the systems NiMnGa, NiTi,NiTiCu, and NiAl. A certain alloy of precise composition Ni_(30.5) Ti_(49.5) Cu_(20.0) is predicted to support a four-sided "tent" on an (001) film, which furthermore is predicted to collapse to the substrate upon heating. A formal derivation is given of higher order theories, which yields two additional Cosserat vectors and an explicit form of the bending energy. The derivation indicates an approach to plate-shell-thin film theories that is rather different from the ones usually followed.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/p4sq7-dyv34The mathematics of microstructure and the design of new materials
https://resolver.caltech.edu/CaltechAUTHORS:20131008-103853023
Authors: {'items': [{'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'K.'}, 'orcid': '0000-0003-2908-5469'}, {'id': 'Friesecke-G', 'name': {'family': 'Friesecke', 'given': 'G.'}}, {'id': 'James-R-D', 'name': {'family': 'James', 'given': 'R. D.'}, 'orcid': '0000-0001-6019-6613'}]}
Year: 1999
DOI: 10.1073/pnas.96.15.8332
PMCID: PMC33624
The "pathological" energy function E(u) = u^2 for u ≠ 0, E(0) = 1, has no minimizer. As u decreases to 0, the energy also decreases, but there is no way to achieve the value 0. Although examples like this might seem to be unimaginably far from scientific thought, they are at the heart of a new approach (1) to understand the complex microstructure and macroscopic response of materials that undergo phase transformations. The free energy of such materials typically has no minimizer, and the observed microstructures (complex, fine-scale patterns of domains of different atomic lattice structure as shown below in a micrograph of CuAlNi by C. Chu and R.D.J.; Fig. 1) have their origin in the material's ultimately futile attempt to find the minimum energy state (2). The lack of a ground state prohibits prediction of the macroscopic response from microscopic data via the standard procedure: determine the free energy, find the minimizing state, and evaluate its macroscopic properties. Emerging mathematical methods, linked to profound work in the 1940s by L. C. Young and recently surveyed in (3), nevertheless deliver well defined macroscopic quantities, obtained via averaging over all low-energy states. One area where predictions obtained in this new way have played a role is the recent synthetization of a new magnetostrictive material (4, 5) whose magnetostrictive strain is 50 times larger than that of giant magnetostrictive materials (formerly those with the largest strain).https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/39gsj-92c81The Simply Laminated Microstructure in Martensitic Crystals that Undergo a Cubic-to-Orthorhombic Phase Transformation
https://resolver.caltech.edu/CaltechAUTHORS:20131009-110131372
Authors: {'items': [{'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'Kaushik'}, 'orcid': '0000-0003-2908-5469'}, {'id': 'Li-Bo', 'name': {'family': 'Li', 'given': 'Bo'}, 'orcid': '0000-0002-8019-8891'}, {'id': 'Luskin-M', 'name': {'family': 'Luskin', 'given': 'Mitchell'}}]}
Year: 1999
DOI: 10.1007/s002050050170
We study simply laminated microstructures of a martensitic crystal capable of undergoing a cubic‐to‐orthorhombic transformation of type P^((432))→P^((222))′ . The free energy density modeling such a crystal is minimized on six energy wells that are pairwise rank‐one connected. We consider the energy minimization problem with Dirichlet boundary data compatible with an arbitrary but fixed simple laminate. We first show that for all but a few isolated values of transformation strains, this problem has a unique Young measure solution solely characterized by the boundary data that represents the simply laminated microstructure. We then present a theory of stability for such a microstructure, and apply it to the conforming finite element approximation to obtain the corresponding error estimates for the finite element energy minimizers.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/qasb4-ksm26A three-dimensional model of step flow mediated crystal growth under the combined influences of stress and diffusion
https://resolver.caltech.edu/CaltechAUTHORS:20131008-143238571
Authors: {'items': [{'id': 'Kukta-R-V', 'name': {'family': 'Kukta', 'given': 'R. V.'}}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'K.'}, 'orcid': '0000-0003-2908-5469'}]}
Year: 1999
DOI: 10.1016/S0040-6090(99)00471-X
This paper presents a three-dimensional model of step flow mediated crystal growth which carefully accounts for both stress and terrace diffusion. Two regularization schemes are proposed to deal with the primary difficulty, an infinite elastic self-interaction force on a curved step. The merger of impinging islands and the dynamics of step bunching in a step train are studied numerically using a two-dimensional version of this model.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/er9c3-n0990A multispecies step-flow model of growth of compound thin films by MOCVD
https://resolver.caltech.edu/CaltechAUTHORS:20131008-110352649
Authors: {'items': [{'id': 'Jabbour-M', 'name': {'family': 'Jabbour', 'given': 'M.'}}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'K.'}, 'orcid': '0000-0003-2908-5469'}]}
Year: 1999
DOI: 10.1016/S0040-6090(99)00469-1
This paper presents a model of step-flow-mediated growth of a multispecies stoichiometric compound in the setting of MOCVD. The gas phase delivers adatoms of the different species to the terraces; these adatoms diffuse along the terraces until they reach the steps where they react to form the compound which is incorporated into the film. The model shows that possible blocking of open sites on the terrace and non-linear kinetics at the steps give rise to an unusual dependence of the deposition flux (growth rate) on the gas phase composition. A methodology for coupling this step-flow model to reactor-scale gas phase models is also proposed, and shown to be linearly stable.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/pmn02-p6855Tents and tunnels on martensitic films
https://resolver.caltech.edu/CaltechAUTHORS:20131008-100811678
Authors: {'items': [{'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'K.'}, 'orcid': '0000-0003-2908-5469'}, {'id': 'DeSimone-A', 'name': {'family': 'DeSimone', 'given': 'A.'}}, {'id': 'Hane-K-F', 'name': {'family': 'Hane', 'given': 'K. F.'}}, {'id': 'James-R-D', 'name': {'family': 'James', 'given': 'R. D.'}, 'orcid': '0000-0001-6019-6613'}, {'id': 'Palmstrøm-C-J', 'name': {'family': 'Palmstrøm', 'given': 'C. J.'}}]}
Year: 1999
DOI: 10.1016/S0921-5093(99)00397-4
In this paper we outline a strategy for producing certain deformable structures — tents and tunnels — on epitaxially grown
martensitic single crystal films. These structures are intended to be the basic building blocks of micropumps and microactuators.
We give specific predictions for the systems Ni_2MnGa, PbTiO_3 and Cu-Zn-Al.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/dnv7j-jr056Edge effects on the propagation of phase boundaries
https://resolver.caltech.edu/CaltechAUTHORS:20131008-095857788
Authors: {'items': [{'id': 'Simha-N-K', 'name': {'family': 'Simha', 'given': 'N. K.'}}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'K.'}, 'orcid': '0000-0003-2908-5469'}]}
Year: 1999
DOI: 10.1016/S0921-5093(99)00379-2
This paper shows that the kinetics of a phase boundary can be profoundly influenced by the conditions at the edges where it meets other phase boundaries, grain boundaries or the physical boundary of the body.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/0adwa-0yc89Relaxed constitutive relations for phase transforming materials
https://resolver.caltech.edu/CaltechAUTHORS:20131004-140605432
Authors: {'items': [{'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'Kaushik'}, 'orcid': '0000-0003-2908-5469'}, {'id': 'Dolzmann-G', 'name': {'family': 'Dolzmann', 'given': 'Georg'}}]}
Year: 2000
DOI: 10.1016/S0022-5096(99)00093-9
In this paper, we propose relaxed constitutive relations which model the effective behavior of some materials that undergo the martensitic phase transformation and consequently display fine scale microstructure.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/m33rh-4xs77Mechanics of large electrostriction in ferroelectrics
https://resolver.caltech.edu/CaltechAUTHORS:20131004-100114192
Authors: {'items': [{'id': 'Burcsu-E', 'name': {'family': 'Burcsu', 'given': 'Eric'}}, {'id': 'Ravichandran-G', 'name': {'family': 'Ravichandran', 'given': 'G.'}, 'orcid': '0000-0002-2912-0001'}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'K.'}, 'orcid': '0000-0003-2908-5469'}]}
Year: 2000
DOI: 10.1117/12.388214
The complex arrangement of domains observed in ferroelectric crystals is a consequence of multiple energy minima
of the crystal free energy density. Since the total energy is a sum of the free energy, and electrical and mechanical
work, switching between the different energetically equivalent domain states can be achieved by both electrical and
mechanical means. For many ferroelectric materials, this results in an electrostrictive phenomenon resulting from
domain switching. In the current study, the electrostrictive behavior of single crystal ferroelectric perovskites has
been investigated experimentally. Experiments have been performed in which a crystal of barium titanate is exposed
to a constant compressive stress and an oscillating electric field and global deformation is measured. The combined
electromechanical loading results in a cycle of stress and electric field induced 90-degree domain switching. The
domain switching cycle results in a measurable strain response theoretically limited by the crystallographic unit cell
dimensions. Induced strains of more than 0.8% have been measured in barium titanate. Larger strains of up to 5%
are predicted for other materials of the same class.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/g7p4f-bgb71Large strain electrostrictive actuation in barium titanate
https://resolver.caltech.edu/CaltechAUTHORS:BURapl00
Authors: {'items': [{'id': 'Burscu-E', 'name': {'family': 'Burscu', 'given': 'E.'}}, {'id': 'Ravichandran-G', 'name': {'family': 'Ravichandran', 'given': 'G.'}, 'orcid': '0000-0002-2912-0001'}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'K.'}, 'orcid': '0000-0003-2908-5469'}]}
Year: 2000
DOI: 10.1063/1.1308533
Large strain electrostriction in single-crystal ferroelectric materials is investigated. The mode of electrostriction is based on a combined electromechanical loading used to induce cyclic, 90° domain switching. Experiments have been performed on crystals of barium titanate with constant compressive stress and oscillating electric-field input. Induced strains of more than 0.8% have been measured. Strains as large as 5% are predicted for other materials of the same class. The results demonstrate a possible avenue for obtaining large actuation strains in electromechanical devices.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/pfvxa-znm84Kinetics of phase boundaries with edges and junctions in a three-dimensional multi-phase body
https://resolver.caltech.edu/CaltechAUTHORS:20131004-075718615
Authors: {'items': [{'id': 'Simha-N-K', 'name': {'family': 'Simha', 'given': 'N. K.'}}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'K.'}, 'orcid': '0000-0003-2908-5469'}]}
Year: 2000
DOI: 10.1016/S0022-5096(00)00008-9
The propagation of phase boundaries that intersect other phase boundaries at junctions and physical boundaries at edges in a three-dimensional multi-phase body is examined. The driving forces that govern the propagation of these phase boundaries, edges and junctions are calculated, and kinetic relations consistent with the second law of thermodynamics are proposed. This work extends the two-dimensional situation discussed previously (Simha, N.K., Bhattacharya, K., 1998. J. Mech. Phys. Solids, 46, 2323–2359).https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/aqr5y-j3b80Relaxation of some multi-well problems
https://resolver.caltech.edu/CaltechAUTHORS:20131022-085750715
Authors: {'items': [{'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'Kaushik'}, 'orcid': '0000-0003-2908-5469'}, {'id': 'Dolzmann-G', 'name': {'family': 'Dolzmann', 'given': 'Georg'}}]}
Year: 2001
DOI: 10.1017/S0308210500000883
Mathematical models of phase transitions in solids lead to the variational problem, minimize ∫_ΩW (Du) dx, where W has a multi-well structure, i.e. W = 0 on a multi-well set K and W > 0 otherwise. We study this problem in two dimensions in the case of equal determinant, i.e. for K = SO(2)U_1 ∪...∪ SO(2)U_k or K = O(2)U_1 ∪...∪ O(2)Uk for U_1,...,U_k ∈ M^(2×2) with det U_i = δ in three dimensions when the matrices U_i are essentially two-dimensional and also for K = SO(3)Û_1 ∪...∪ SO(3)Û_k for U_1,...,U_k ∈ M^(3×3) with (adj U_i^TU_i)33 = δ^2, which arises in the study of thin films. Here, Û_i denotes the (3×2) matrix formed with the first two columns of U_i. We characterize generalized convex hulls, including the quasiconvex hull, of these sets, prove existence of minimizers and identify conditions for the uniqueness of the minimizing Young measure. Finally, we use the characterization of the quasiconvex hull to propose 'approximate relaxed energies', quasiconvex functions which vanish on the quasiconvex hull of K and grow quadratically away from it.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/5kjg2-9cd26Electromechanical behavior of 90-degree domain motion in barium titanate single crystals
https://resolver.caltech.edu/CaltechAUTHORS:20160126-135845277
Authors: {'items': [{'id': 'Burcsu-E', 'name': {'family': 'Burcsu', 'given': 'Eric'}}, {'id': 'Ravichandran-G', 'name': {'family': 'Ravichandran', 'given': 'G.'}, 'orcid': '0000-0002-2912-0001'}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'Kaushik'}, 'orcid': '0000-0003-2908-5469'}]}
Year: 2001
DOI: 10.1117/12.432748
It is well known that many common ferroelectric materials are also ferroelastic, thus the nonlinear behavior of these materials, as governed by domain motion, is highly affected by stress, as well as electric field. The combined influence of stress and electric field on domain motion and the electrostrictive response of ferroelectric single crystals is investigated. Experiments are performed on (001) and (100) oriented single crystals of barium titanate under combined electro-mechanical loading. The crystal is exposed to a constant compressive stress and an oscillating electric field along the [001] direction. Global deformation and polarization are measured as a function of electric field at different values of compressive stress. The use of semi-transparent electrodes and transmitted illumination allow in situ, real-time microscopic observations of domain motion using a long working-distance, polarizing microscope. The combined electro-mechanical loading results in a cycle of stress and electric field induced 90-degree domain switching. The magnitude of the global deformation increases with stress, with maximum steady state actuation strain of 0.57%.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/gsdnb-2cy80Comments on the spontaneous strain and polarization of polycrystalline ferroelectric ceramics
https://resolver.caltech.edu/CaltechAUTHORS:20160126-134241728
Authors: {'items': [{'id': 'Li-Jiangyu', 'name': {'family': 'Li', 'given': 'Jiangyu'}, 'orcid': '0000-0003-0533-1397'}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'Kaushik'}, 'orcid': '0000-0003-2908-5469'}]}
Year: 2001
DOI: 10.1117/12.432742
A framework to calculate the spontaneous strain and polarization of a polycrystalline ferroelectric is presented, and various applications are discussed.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/hqf9w-6vv57Modeling electromechanical properties of ionic polymers
https://resolver.caltech.edu/CaltechAUTHORS:20160126-141456675
Authors: {'items': [{'id': 'Xiao-Yu', 'name': {'family': 'Xiao', 'given': 'Yu'}}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'Kaushik'}, 'orcid': '0000-0003-2908-5469'}]}
Year: 2001
DOI: 10.1117/12.432658
We present a multi-scale approach to modeling the electro-mechanical behavior of ionic polymers. We start with
a detailed elasto-electro-chemical model which allows for finite deformation. We reduce it to one space dimension
appropriate for the commonly used sheet configuration, and demonstrate that steady state solutions display an
important boundary layer effect. We conclude with a macroscopic model of a strip of ionic-polymer-metal-composite.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/ykfwd-1r618Domain Patterns, Texture and Macroscopic Electro-mechanical Behavior of Ferroelectrics
https://resolver.caltech.edu/CaltechAUTHORS:20111116-115029667
Authors: {'items': [{'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'Kaushik'}, 'orcid': '0000-0003-2908-5469'}, {'id': 'Li-Jiang-Yu', 'name': {'family': 'Li', 'given': 'Jiang Yu'}}]}
Year: 2001
DOI: 10.1063/1.1399691
This paper examines the domain patterns and its relation to the macroscopic electromechanical behavior of ferroelectric solids using a theory based on homogenization and energy minimization. The domain patterns in different crystalline systems are classified, the spontaneous strain and polarization for single crystals and polycrystals are characterized, and the optimal texture of polycrystals for high-strain actuation is identified. The results also reveal why it is easy to pole PZT at compositions close to the 'morphotropic phase boundary'.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/bqwwv-zrz35Domain patterns and macroscopic behaviour of ferroelectric materials
https://resolver.caltech.edu/CaltechAUTHORS:20131004-082951362
Authors: {'items': [{'id': 'Shu-Y-C', 'name': {'family': 'Shu', 'given': 'Y. C.'}}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'K.'}, 'orcid': '0000-0003-2908-5469'}]}
Year: 2001
DOI: 10.1080/13642810108208556
This paper examines the domain patterns and the macroscopic behaviour of single crystals of ferroelectric material using a theory based on energy minimization. A low-energy path is identified for domain switching and a novel configuration that yields very large electrostriction is identified.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/d73g7-2v421Observation of Domain Motion in Single-Crystal Barium Titanate under Combined Electromechanical Loading Conditions
https://resolver.caltech.edu/CaltechAUTHORS:20160127-085635071
Authors: {'items': [{'id': 'Burcsu-E', 'name': {'family': 'Burcsu', 'given': 'E.'}}, {'id': 'Ravichandran-G', 'name': {'family': 'Ravichandran', 'given': 'G.'}, 'orcid': '0000-0002-2912-0001'}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'K.'}, 'orcid': '0000-0003-2908-5469'}]}
Year: 2002
DOI: 10.1007/978-94-017-0069-6_8
The nonlinear electromechanical behavior of ferroelectric materials is governed by the motion of domains. Since many common ferroelectric materials, such as barium titanate and PZT, are also ferroelastic, the domain motion is highly affected by stress as well as electric field. Experiments are performed on (001) and (100) oriented single crystals of barium titanate under combined electromechanical loading conditions. The crystal is subjected to a constant compressive stress (dead load) and an oscillating electric field along the [001] direction. Global deformation and polarization are measured as a function of electric field at different values of compressive stress. The use of semi-transparent electrodes and transmitted illumination allows in situ, real-time microscopic observations of domain patterns using a long working-distance, polarizing microscope. The combined electromechanical loading results in a cycle of stress and electric field induced 90° domain switching. This is an electrostrictive behavior with measured strains of up to 0.9%.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/ypr41-9rp58An Asymptotic Study of the Debonding of Thin Films
https://resolver.caltech.edu/CaltechAUTHORS:20131017-151943131
Authors: {'items': [{'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'Kaushik'}, 'orcid': '0000-0003-2908-5469'}, {'id': 'Fonseca-I', 'name': {'family': 'Fonseca', 'given': 'Irene'}}, {'id': 'Francfort-G', 'name': {'family': 'Francfort', 'given': 'Gilles'}}]}
Year: 2002
DOI: 10.1007/s002050100177
We examine the asymptotic behavior of a bilayer thin film using the notion of Γ-convergence. We allow for debonding at the interface, but penalize it using an interfacial energy; thus the functional we consider consists of the elastic energy of the two layers and the interfacial energy with penalized debonding. We show that the asymptotic theory or Γ-limit depends on the particular form of the interfacial energy, and derive detailed results for both the cohesive and the brittle interface.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/zbta5-by951A micromechanical model of surface steps
https://resolver.caltech.edu/CaltechAUTHORS:20131004-082434919
Authors: {'items': [{'id': 'Kukta-R-V', 'name': {'family': 'Kukta', 'given': 'R. V.'}}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'K.'}, 'orcid': '0000-0003-2908-5469'}]}
Year: 2002
DOI: 10.1016/S0022-5096(01)00079-5
The surface of an epitaxial thin film typically consists of terraces separated by steps of atomic height and it evolves largely by the motion of steps. Steps are sources of stress that interact with other residual stress fields, and these interactions have a profound effect on surface evolution. A model of the elastic field arising from a two-dimensional step is presented as a departure from the commonly used half-plane point-multipole model. The field is calculated asymptotically for small step height up to second order in terms of 'structural' parameters that can be determined from empirical data or atomistic calculations. Effects of a lattice mismatch and surface stress are included. The model is shown to be in remarkable agreement with atomistic predictions. It is demonstrated that second-order terms are necessary for understanding non-trivial step–step interactions, and that these second-order fields cannot be described by point sources on a half-plane.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/h8935-mg114Thin films with many small cracks
https://resolver.caltech.edu/CaltechAUTHORS:20131004-103540402
Authors: {'items': [{'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'Kaushik'}, 'orcid': '0000-0003-2908-5469'}, {'id': 'Braides-A', 'name': {'family': 'Braides', 'given': 'Andrea'}}]}
Year: 2002
DOI: 10.1098/rspa.2001.0821
We show with an example that the limiting theory as thickness goes to zero of a thin
film with many small cracks can be three dimensional rather than two dimensional.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/s4210-z2m97On beams made of a phase-transforming material
https://resolver.caltech.edu/CaltechAUTHORS:20131004-074804695
Authors: {'items': [{'id': 'Purohit-P-K', 'name': {'family': 'Purohit', 'given': 'Prashant K.'}}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'Kaushik'}, 'orcid': '0000-0003-2908-5469'}]}
Year: 2002
DOI: 10.1016/S0020-7683(02)00187-7
This paper presents a theory for the mechanics of beams made of single crystals of shape memory alloys. The behavior of such beams can be quite unexpected and complicated due to the presence and propagation of phase boundaries. It is shown that the usual laws of mechanics do not fully determine the propagation of phase boundaries and that there is a need for additional constitutive information in the form of a kinetic relation. A simple experiment to measure this kinetic relation is proposed. Finally, a strategy to use such beams for propulsion at small scales is presented.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/x4hq9-4vd76A Mesoscopic Electromechanical Theory of Ferroelectric Films and Ceramics
https://resolver.caltech.edu/CaltechAUTHORS:20111026-092923527
Authors: {'items': [{'id': 'Li-Jiangyu', 'name': {'family': 'Li', 'given': 'Jiangyu'}, 'orcid': '0000-0003-0533-1397'}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'Kaushik'}, 'orcid': '0000-0003-2908-5469'}]}
Year: 2002
DOI: 10.1063/1.1499571
We present a multi-scale modelling framework to predict the effective electromechanical behavior of ferroelectric ceramics and thin films. This paper specifically focuses on the mesoscopic scale and models the effects of domains and domain switching taking into account intergranular constraints. Starting from the properties of the single crystal and the pre-poling granular texture, the theory predicts the domain patterns, the post-poling texture, the saturation polarization, saturation strain and the electromechanical moduli. We demonstrate remarkable agreement with experimental data. The theory also explains the superior electromechanical property of PZT at the morphotropic phase boundary. The paper concludes with the application of the theory to predict the optimal texture for enhanced electromechanical coupling factors and high-strain actuation in selected materials.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/ekbmw-1r826Dynamics of strings made of phase-transforming materials
https://resolver.caltech.edu/CaltechAUTHORS:20131007-143329723
Authors: {'items': [{'id': 'Purohit-P-K', 'name': {'family': 'Purohit', 'given': 'Prashant K.'}}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'Kaushik'}, 'orcid': '0000-0003-2908-5469'}]}
Year: 2003
DOI: 10.1016/S0022-5096(02)00097-2
This paper presents a theory to describe the dynamical behavior of a string made of a phase-transforming material like a shape-memory alloy. The study of phase boundaries, the driving force acting on them and the kinetic relation governing their propagation is of central concern. The paper proposes a qualitative experimental test of the notion of a kinetic relation, as well as a simple experimental method for measuring it quantitatively. It presents a numerical method for studying general initial and boundary value problems in strings, and concludes by exploring the use of phase transforming strings to generate motion at very small scales.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/2q133-qk211Homogenization of a Hamilton-Jacobi equation associated with the geometric motion of an interface
https://resolver.caltech.edu/CaltechAUTHORS:20131007-100104548
Authors: {'items': [{'id': 'Craciun-B', 'name': {'family': 'Craciun', 'given': 'Bogdan'}}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'Kaushik'}, 'orcid': '0000-0003-2908-5469'}]}
Year: 2003
DOI: 10.1017/S0308210500002675
This paper studies the overall evolution of fronts propagating with a normal velocity that depends on position, υ_n = f(x), where f is rapidly oscillating and periodic. A level-set formulation is used to rewrite this problem as the periodic homogenization of a Hamilton–Jacobi equation. The paper presents a series of variational characterization (formulae) of the effective Hamiltonian or effective normal velocity. It also examines the situation when f changes sign.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/bbcm8-9vx35Modeling large strain electrostriction of ferroelectrics under combined electromechanical loads
https://resolver.caltech.edu/CaltechAUTHORS:20160127-065852731
Authors: {'items': [{'id': 'Zhang-Wei', 'name': {'family': 'Zhang', 'given': 'Wei'}}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'Kaushik'}, 'orcid': '0000-0003-2908-5469'}]}
Year: 2003
DOI: 10.1117/12.498564
A computational model for investigating domain switching and macroscopic electromechanical properties of ferroelectric materials is developed. Various aspects of domain nucleation and growth, and their effects on macroscopic hysteresis are examined. The model is validated against recent experimental observations. It is thus validated as a design tool to investigate various aspects of a novel thin film ferroelectric microactuator in future work.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/x20qz-19897Mobility of twin and phase boundaries
https://resolver.caltech.edu/CaltechAUTHORS:20160127-080333461
Authors: {'items': [{'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'K.'}, 'orcid': '0000-0003-2908-5469'}, {'id': 'Purohit-P', 'name': {'family': 'Purohit', 'given': 'P.'}}, {'id': 'Craciun-B', 'name': {'family': 'Craciun', 'given': 'B.'}}]}
Year: 2003
DOI: 10.1051/jp4:2003856
This paper reviews some recent advances in understanding the mobility of twin and phase boundaries in martensites, and discusses the design of systematic experiments.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/jexa9-rny97Ferroelectric perovskites for electromechanical actuation
https://resolver.caltech.edu/CaltechAUTHORS:20131007-112842630
Authors: {'items': [{'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'K.'}, 'orcid': '0000-0003-2908-5469'}, {'id': 'Ravichandran-G', 'name': {'family': 'Ravichandran', 'given': 'G.'}, 'orcid': '0000-0002-2912-0001'}]}
Year: 2003
DOI: 10.1016/j.actamat.2003.08.001
There has been a recent surge of activity in ferroelectric materials motivated by the desire for materials capable of large strains for actuator applications. New materials have been developed and systematic attempts to exploit underlying domains have been pursued. New experimental methods have probed the material at the atomistic and domain scales. Significant advances have been made in the theoretical understanding of the origins of ferroelectricity, nature of domain patterns and their overall behavior. Modern methods of synthesis with controlled texture and composition have opened the possibility of exploiting the inherent microscopic features of these materials. This paper provides some snapshots of the recent advances in theory and experiment, and points to open issues and opportunities for the future.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/88mr1-91e44A Continuum Theory of Multispecies Thin Solid Film Growth by Chemical Vapor Deposition
https://resolver.caltech.edu/CaltechAUTHORS:20131007-114059985
Authors: {'items': [{'id': 'Jappour-M-E', 'name': {'family': 'Jabbour', 'given': 'Michel E.'}}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'Kaushik'}, 'orcid': '0000-0003-2908-5469'}]}
Year: 2003
DOI: 10.1023/B:ELAS.0000030018.40095.d5
A continuum theory for the chemical vapor deposition of thin solid films is proposed, in which a flowing, chemically reacting, gaseous mixture is coupled to the bulk of a growing thin film via the equations that govern the morphological evolution of the interface separating them. The vapor-film interface is viewed as a surface of zero thickness capable of sustaining mass and endowed with thermodynamic variables that account for its distinct structure. We consider situations in which species diffusion and heat conduction occur in all three phases (vapor, bulk and surface), with the former mechanism augmented by the convective transport of particles in the gas. Special attention is given to the chemical reactions that occur both in the vapor and on the film surface. Ours is a conceptual framework based on conservation laws for chemical species, momentum and energy, together with a separate balance of configurational forces. These balances are supplemented by an appropriate version of the second law which is used to develop suitable constitutive relations for each of the phases. In particular, we investigate the case of an elastic film, deposited on a rigid substrate and in contact with a reacting, multispecies, ideal vapor, whose surface behaves like an anisotropic, chemically reactive, multicomponent, ideal lattice gas. In addition to recovering the standard equations that describe the behavior of the gas and film phases, we derive the coupled PDE's that govern the interfacial morphological, chemical, and thermal evolution. In particular, the constitutively augmented interfacial configurational force balance provides a "kinetic relation" linking the thermodynamic "driving force" at the film surface to the growth rate. The special cases of (i) negligible interfacial species densities, and (ii) local (mechanical) equilibrium of both multi- and single-species films are investigated.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/maf70-a2j97Crystal symmetry and the reversibility of martensitic transformations
https://resolver.caltech.edu/CaltechAUTHORS:20131007-130456440
Authors: {'items': [{'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'Kaushik'}, 'orcid': '0000-0003-2908-5469'}, {'id': 'Conti-S', 'name': {'family': 'Conti', 'given': 'Sergio'}, 'orcid': '0000-0001-7987-9174'}, {'id': 'Zanzotto-G', 'name': {'family': 'Zanzotto', 'given': 'Giovanni'}}, {'id': 'Zimmer-J', 'name': {'family': 'Zimmer', 'given': 'Johannes'}}]}
Year: 2004
DOI: 10.1038/nature02378
Martensitic transformations are diffusionless, solid-to-solid phase transitions, and have been observed in metals, alloys, ceramics and proteins. They are characterized by a rapid change of crystal structure, accompanied by the development of a rich microstructure. Martensitic transformations can be irreversible, as seen in steels upon quenching, or they can be reversible, such as those observed in shape-memory alloys. In the latter case, the microstructures formed on cooling are easily manipulated by loads and disappear upon reheating. Here, using mathematical theory and numerical simulation, we explain these sharp differences in behaviour on the basis of the change in crystal symmetry during the transition. We find that a necessary condition for reversibility is that the symmetry groups of the parent and product phases be included in a common finite symmetry group. In these cases, the energy barrier to lattice-invariant shear is generically higher than that pertaining to the phase change and, consequently, transformations of this type can occur with virtually no plasticity. Irreversibility is inevitable in all other martensitic transformations, where the energy barrier to plastic deformation (via lattice-invariant shears, as in twinning or slip) is no higher than the barrier to the phase change itself. Various experimental observations confirm the importance of the symmetry of the stable states in determining the macroscopic reversibility of martensitic transformations.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/jm798-y3q15Large electrostrictive actuation of barium titanate single crystals
https://resolver.caltech.edu/CaltechAUTHORS:20131004-084239216
Authors: {'items': [{'id': 'Burcsu-E', 'name': {'family': 'Burcsu', 'given': 'E.'}}, {'id': 'Ravichandran-G', 'name': {'family': 'Ravichandran', 'given': 'G.'}, 'orcid': '0000-0002-2912-0001'}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'K.'}, 'orcid': '0000-0003-2908-5469'}]}
Year: 2004
DOI: 10.1016/j.jmps.2003.08.001
An experimental investigation of the electromechanical behavior of single crystals of the ferroelectric
perovskite barium titanate is presented. An experimental setup has been designed to
investigate large strain actuation in single crystal ferroelectrics subjected to combined electrical
and mechanical loading. Experiments have been performed on initially single domain crystals
of barium titanate with (1 0 0) and (0 0 1) orientation at compressive stresses between 0 and
5 MPa. Global strain and polarization histories have been recorded. The electrostrictive response
is shown to be highly dependent on the level of applied stress with a maximum strain of 0.9%
measured at a compressive stress of about 2 MPa and electric 8eld of about 10 kV/cm. This
level of strain is about 5 times higher than in typical commercial piezoelectric PZT. Polarized
light microscopy has been used to observe the evolution of the domain pattern simultaneously
with the strain and polarization measurement. The observations reveal that the observed large
strain behavior is the result of 90° domain switching.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/hs19r-rps39All-organic dielectric-percolative three-component composite materials with high electromechanical response
https://resolver.caltech.edu/CaltechAUTHORS:HUAapl04a
Authors: {'items': [{'id': 'Huang-Cheng', 'name': {'family': 'Huang', 'given': 'Cheng'}}, {'id': 'Zhang-Q-M', 'name': {'family': 'Zhang', 'given': 'Q. M.'}}, {'id': 'deBotton-G', 'name': {'family': 'deBotton', 'given': 'Gal'}, 'orcid': '0000-0003-3608-1896'}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'Kaushik'}, 'orcid': '0000-0003-2908-5469'}]}
Year: 2004
DOI: 10.1063/1.1757632
By combining the high-dielectric copper phthalocyanine oligomer (PolyCuPc) and conductive polyanline (PANI) within polyurethane (PU) matrix an all-organic three-component dielectric-percolative composite with high dielectric constant is demonstrated. In this three-component composite system, the high-dielectric-constant PolyCuPc particulates enhance the dielectric constant of the PU matrix and this combined two-component dielectric matrix in turn serves as the high-dielectric-constant host for the PANI to realize percolative phenomenon and further enhance the dielectric response. As a result, an electromechanical strain of 9.3% and elastic energy density of 0.4 J/cm(3) under an electric field of 20 V/mum can be induced.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/epsx1-4qd19Transformation yield surface of shape memory alloys
https://resolver.caltech.edu/CaltechAUTHORS:20160127-073934774
Authors: {'items': [{'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'K.'}, 'orcid': '0000-0003-2908-5469'}, {'id': 'Schlömerkemper-A', 'name': {'family': 'Schlömerkemper', 'given': 'A.'}}]}
Year: 2004
DOI: 10.1051/jp4:2004115020
Shape-memory alloys transform under stress, and this stress-induced transformation is useful for various practical applications. The stress at which the alloy transforms depends on the orientation of the stress relative to the specimen, and may be described using a transformation yield surface. This paper provides early results of a theoretical treatment of the transformation yield surface of shape-memory polycrystals with particular emphasis on the influence of texture.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/t2kfn-xd446Effective motion of a curvature-sensitive interface through a
heterogeneous medium
https://resolver.caltech.edu/CaltechAUTHORS:20131008-121754258
Authors: {'items': [{'id': 'Craciun-B', 'name': {'family': 'Craciun', 'given': 'Bogdan'}}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'Kaushik'}, 'orcid': '0000-0003-2908-5469'}]}
Year: 2004
DOI: 10.4171/IFB/95
This paper deals with the evolution of fronts or interfaces propagating with normal velocity v_n=f−cκ where f is a spatially periodic function, c a constant and κ the mean curvature. This study is motivated by the propagation of phase boundaries and dislocation loops through heterogeneous media. We establish a homogenization result when the scale of oscillation of f is small compared to the macroscopic dimensions, and show that the overall front is governed by a geometric law v_n=f(n). We illustrate the results using examples. We also provide an explicit characterization of f in the limit c → ∞.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/fakr0-fbb34Investigation of twin-wall structure at the nanometre scale using atomic force microscopy
https://resolver.caltech.edu/CaltechAUTHORS:20131007-113946664
Authors: {'items': [{'id': 'Shilo-D', 'name': {'family': 'Shilo', 'given': 'Doron'}}, {'id': 'Ravichandran-G', 'name': {'family': 'Ravichandran', 'given': 'Guruswami'}, 'orcid': '0000-0002-2912-0001'}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'Kaushik'}, 'orcid': '0000-0003-2908-5469'}]}
Year: 2004
DOI: 10.1038/nmat1151
The structure of twin walls and their interaction with defects has important implications for the behaviour of a variety of materials including ferroelectric, ferroelastic, co-elastic and superconducting crystals. Here, we present a method for investigating the structure of twin walls with nanometre-scale resolution. In this method, the surface topography measured using atomic force microscopy is compared with candidate displacement fields, and this allows for the determination of the twin-wall thickness and other structural features. Moreover, analysis of both complete area images and individual line-scan profiles provides essential information about local mechanisms of twin-wall broadening, which cannot be obtained by existing experimental methods. The method is demonstrated in the ferroelectric material PbTiO3, and it is shown that the accumulation of point defects is responsible for significant broadening of the twin walls. Such defects are of interest because they contribute to the twin-wall kinetics and hysteresis.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/rvxxq-58r80Interaction of oxygen vacancies with domain walls and its impact on fatigue in ferroelectric thin films
https://resolver.caltech.edu/CaltechAUTHORS:20160127-064923846
Authors: {'items': [{'id': 'Xiao-Yu', 'name': {'family': 'Xiao', 'given': 'Yu'}}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'Kaushik'}, 'orcid': '0000-0003-2908-5469'}]}
Year: 2004
DOI: 10.1117/12.539588
The role of oxygen vacancies in fatigue and dielectric breakdown has been a topic of intense research in ferroelectric perovskites like BaTiO_3. This paper presents a comprehensive model that treats the ferroelectrics as polarizable wide band-gap semiconductors where the oxygen vacancies act as donors. First, a fully coupled nonlinear model is developed with space charges, polarization, electric potential and elastic displacements as variables without making any a priori assumptions on the space charge distribution and the polarization. Second, a Pt/BaTiO_3/Pt structure is considered. Full-field coupled numerical simulations are used to investigate the structure of 180° and 90° domain walls in both perfect and defected crystals. The interactions of oxygen vacancies with domain walls are explored. Numerical results show that there is pronounced charge trapping near 90° domain walls, giving rise to possible domain wall pinning and dielectric breakdown. Third, a simple analytical solution of the potential profile for a metal/ferroelectric semiconductor interface is obtained and the depletion layer width is estimated. These analytical estimates agree with our numerical results and provide a useful tool to discuss the implications of our results.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/n96py-jpy19Thin Films of Active Materials
https://resolver.caltech.edu/CaltechAUTHORS:20160127-083437576
Authors: {'items': [{'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'K.'}, 'orcid': '0000-0003-2908-5469'}]}
Year: 2005
DOI: 10.1007/1-4020-2623-4_2
This paper summarizes some recent developments in the study of the mechanics of thin films motivated by the use of active materials in making microactuators.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/r4jat-6pe58A computational model of ferroelectric domains. Part II: grain boundaries and defect pinning
https://resolver.caltech.edu/CaltechAUTHORS:20131007-154059651
Authors: {'items': [{'id': 'Zhang-W', 'name': {'family': 'Zhang', 'given': 'W.'}}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'K.'}, 'orcid': '0000-0003-2908-5469'}]}
Year: 2005
DOI: 10.1016/j.actamat.2004.09.015
Domain nucleation, domain switching and the hysteretic behavior of ferroelectric polycrystals or ceramics can differ from those in ferroelectric single crystals. This paper extends the model presented in Part I to polycrytals, and uses it to study domain switching in bicrystals that are chosen to model biaxially textured thin films. The results show that the switching behavior in bicrystals is similar to that in single crystals for small misalignment of grains but becomes quite different at larger misalignment.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/ht22z-dtg32A computational model of ferroelectric domains. Part I: model formulation and domain switching
https://resolver.caltech.edu/CaltechAUTHORS:20131004-091710365
Authors: {'items': [{'id': 'Zhang-W', 'name': {'family': 'Zhang', 'given': 'W.'}}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'K.'}, 'orcid': '0000-0003-2908-5469'}]}
Year: 2005
DOI: 10.1016/j.actamat.2004.09.016
A model for studying the domain pattern of ferroelectric materials and its evolution is developed. In a departure from prior work, the electrostatic potential is made explicit, and consequently the model is able to predict the microstructural evolution and the macroscopic behavior of ferroelectrics subjected to realistic electro-mechanical boundary conditions. Nucleation of domains and propagation of domain walls are investigated under combined electro-mechanical loading and compared to recent experiments. The correlation between the microstructural change and macroscopic response provides evidence that the recently observed large strain actuation of ferroelectric materials is due to 90° domain switching.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/ee0tw-xkd59The Material Is the Machine
https://resolver.caltech.edu/CaltechAUTHORS:20141119-075744826
Authors: {'items': [{'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'Kaushik'}, 'orcid': '0000-0003-2908-5469'}, {'id': 'James-R-D', 'name': {'family': 'James', 'given': 'Richard D.'}, 'orcid': '0000-0001-6019-6613'}]}
Year: 2005
DOI: 10.1126/science.1100892
Efforts are under way to manufacture electromechanical devices at ever smaller sizes. However, standard semiconductor technology places limits on how small such machines can be. In their Perspective, Bhattacharya and James explain how martensitic materials--which can distort reversibly without any diffusion taking place--may overcome this problem. Theoretical studies and preliminary experiments suggest that such materials can act as machines themselves, without the need for complicated construction of moving parts in the device.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/t2g71-8me46A model problem concerning recoverable strains of shape-memory polycrystals
https://resolver.caltech.edu/CaltechAUTHORS:20131007-125756465
Authors: {'items': [{'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'K.'}, 'orcid': '0000-0003-2908-5469'}, {'id': 'Suquet-P-M', 'name': {'family': 'Suquet', 'given': 'P. M.'}}]}
Year: 2005
DOI: 10.1098/rspa.2005.1493
This paper addresses a model problem of nonlinear homogenization motivated by the study of the shape-memory effect in polycrystalline media. Specifically, it numerically computes the set of recoverable strains in a polycrystal given the set of recoverable strains of a single crystal in the two-dimensional scalar (or antiplane shear) setting. This problem shares a direct analogy with crystal plasticity. The paper considers typical or random polycrystals where the grains are generated by a Voronoi tesselation of a set of random points and are randomly oriented. The numerical results show that for such microstructures, the Taylor bound appears to be the most accurate (though pessimistic) bound when the anisotropy is moderate, and that recent Kohn–Little–Goldsztein outer bounds overestimate the recoverable strains when the anisotropy is large. The results also show that the stress tends to localize on tortuous paths that traverse (poorly oriented) grains as the polycrystal reaches its limit of recoverable strain.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/wx5dg-jfm21Domain switching in polycrystalline ferroelectric ceramics
https://resolver.caltech.edu/CaltechAUTHORS:20131007-114439370
Authors: {'items': [{'id': 'Li-J-Y', 'name': {'family': 'Li', 'given': 'J. Y.'}}, {'id': 'Rogan-R-C', 'name': {'family': 'Rogan', 'given': 'R. C.'}}, {'id': 'Üstündag-E', 'name': {'family': 'Üstündag', 'given': 'E.'}}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'K.'}, 'orcid': '0000-0003-2908-5469'}]}
Year: 2005
DOI: 10.1038/nmat1485
Ferroelectric ceramics are widely used as sensors and actuators for their electro-mechanical properties, and in electronic applications for their dielectric properties. Domain switching – the phenomenon wherein the ferroelectric material changes from one spontaneously polarized state to another under electrical or mechanical loads – is an important attribute of these materials. However, this is a complex collective process in commercially used polycrystalline ceramics that are agglomerations of a very large number of variously oriented grains. As the domains in one grain attempt to switch, they are constrained by the differently oriented neighbouring grains. Here we use a combined theoretical and experimental approach to establish a relation between crystallographic symmetry and the ability of a ferroelectric polycrystalline ceramic to switch. In particular, we show that equiaxed polycrystals of materials that are either tetragonal or rhombohedral cannot switch; yet polycrystals of materials where these two symmetries co-exist can in fact switch.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/fw5cz-hp069Examples of nonlinear homogenization involving degenerate energies. I. Plane strain
https://resolver.caltech.edu/CaltechAUTHORS:20131008-134246206
Authors: {'items': [{'id': 'Chenchiah-I-V', 'name': {'family': 'Chenchiah', 'given': 'Isaac V.'}}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'Kaushik'}, 'orcid': '0000-0003-2908-5469'}]}
Year: 2005
DOI: 10.1098/rspa.2005.1515
The study of polycrystals of shape-memory alloys and rigid-perfectly plastic materials gives rise to problems of nonlinear homogenization involving degenerate energies. This paper presents a characterization of the stress and strain fields in a class of problems in plane strain, and uses it to study examples including checkerboards and hexagonal microstructures. Consequences for shape-memory alloys and rigid-perfectly plastic materials are discussed.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/kckzd-cqe63Depletion Layers and Domain Walls in Semiconducting Ferroelectric Thin Films
https://resolver.caltech.edu/CaltechAUTHORS:XIAprl05
Authors: {'items': [{'id': 'Xiao-Yu', 'name': {'family': 'Xiao', 'given': 'Yu'}}, {'id': 'Shenoy-V-B', 'name': {'family': 'Shenoy', 'given': 'Vivek B.'}}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'Kaushik'}, 'orcid': '0000-0003-2908-5469'}]}
Year: 2005
DOI: 10.1103/PhysRevLett.95.247603
Commonly used ferroelectric perovskites are also wide-band-gap semiconductors. In such materials, the polarization and the space-charge distribution are intimately coupled, and this Letter studies them simultaneously with no a priori ansatz on either. In particular, we study the structure of domain walls and the depletion layers that form at the metal-ferroelectric interfaces. We find the coupling between polarization and space charges leads to the formation of charge double layers at the 90° domain walls, which, like the depletion layers, are also decorated by defects like oxygen vacancies. In contrast, the 180° domain walls do not interact with the defects or space charges. Implications of these results to domain switching and fatigue in ferroelectric devices are discussed.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/c9tsn-8qr68Characterization of domain walls in BaTiO3 using simultaneous atomic force and piezo response force microscopy
https://resolver.caltech.edu/CaltechAUTHORS:FRAapl06
Authors: {'items': [{'id': 'Franck-C', 'name': {'family': 'Franck', 'given': 'Christian'}}, {'id': 'Ravichandran-G', 'name': {'family': 'Ravichandran', 'given': 'Guruswami'}, 'orcid': '0000-0002-2912-0001'}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'Kaushik'}, 'orcid': '0000-0003-2908-5469'}]}
Year: 2006
DOI: 10.1063/1.2185640
In this letter a method to simultaneously measure the physical and the polarization thickness of a 90° domain wall in a ferroelectric perovskite is presented. This method combines accurate atomic force microscopy and piezoresponse force microscopy scans of the same area with little drift and an analysis of the entire scanned area. It is found that the physical thickness is significantly narrower (about seven and a half times) than the polarization thickness in a 90° domain wall in BaTiO3. Evidence of the trapping of defects at such domain walls is also found.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/pjt1j-w7c49The effect of biaxial texture on the effective electromechanical constants of polycrystalline barium titanate and lead titanate thin films
https://resolver.caltech.edu/CaltechAUTHORS:20131007-140336325
Authors: {'items': [{'id': 'Ruglovsky-J-L', 'name': {'family': 'Ruglovsky', 'given': 'Jennifer L.'}}, {'id': 'Li-Jiangyu', 'name': {'family': 'Li', 'given': 'Jiangyu'}, 'orcid': '0000-0003-0533-1397'}, {'id': 'Diest-K-A', 'name': {'family': 'Diest', 'given': 'Kenneth A.'}}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'Kaushik'}, 'orcid': '0000-0003-2908-5469'}, {'id': 'Atwater-H-A', 'name': {'family': 'Atwater', 'given': 'Harry A.'}, 'orcid': '0000-0001-9435-0201'}]}
Year: 2006
DOI: 10.1016/j.actamat.2006.03.023
Effective electromechanical constants as a function of biaxial crystallographic texture in polycrystalline films are modeled using a self-consistent approach. The film is modeled by assuming Gaussian distributions of two Euler angle textures about perfect orientation with varying spread, or full width at half maximum. We see that independent in-plane texturing has little effect on the piezoelectric displacement tensor. Increased out-of-plane texturing gives rise to an enhanced piezoelectric effect for barium titanate films, but not for lead titanate. Twist texturing about these out-of-plane angles shows a further enhancement in the non-shear components of the piezoelectric displacement tensor for both materials. Finally, we use the effective piezoelectric coupling factor as the primary figure of merit for the effective piezoelectric properties of polycrystal devices, thus utilizing all electromechanical constants of this simulation. This quantity shows a primary dependence on the out-of-plane texture.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/w80my-9qf10Mechanical Characterization of Released Thin Films by Contact Loading
https://resolver.caltech.edu/CaltechAUTHORS:20110411-103722979
Authors: {'items': [{'id': 'Zhang-Rongjing', 'name': {'family': 'Zhang', 'given': 'Rongjing'}}, {'id': 'Shilo-D', 'name': {'family': 'Shilo', 'given': 'Doron'}}, {'id': 'Ravichandran-G', 'name': {'family': 'Ravichandran', 'given': 'Guruswami'}, 'orcid': '0000-0002-2912-0001'}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'Kaushik'}, 'orcid': '0000-0003-2908-5469'}]}
Year: 2006
DOI: 10.1115/1.2166652
The design of reliable micro electro-mechanical systems (MEMS) requires understanding of material properties of devices, especially for free-standing thin structures such as membranes, bridges, and cantilevers. The desired characterization system for obtaining mechanical properties of active materials often requires load control. However, there is no such device among the currently available tools for mechanical characterization of thin films. In this paper, a new technique, which is load-controlled and especially suitable for testing highly fragile free-standing structures, is presented. The instrument developed for this purpose has the capability of measuring both the static and dynamic mechanical response and can be used for electro/magneto/thermo mechanical characterization of actuators or active materials. The capabilities of the technique are demonstrated by studying the behavior of 75 nm thick amorphous silicon nitride (Si_3N_4) membranes. Loading up to very large deflections shows excellent repeatability and complete elastic behavior without significant cracking or mechanical damage. These results indicate the stability of the developed instrument and its ability to avoid local or temporal stress concentration during the entire experimental process. Finite element simulations are used to extract the material properties such as Young's modulus and residual stress of the membranes. These values for Si_3N_4 are in close agreement with values obtained using a different technique, as well as those found in the literature. Potential applications of this technique in studying functional thin film materials, such as shape memory alloys, are also discussed.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/wqfxg-3gh14Kinetics of phase transformations in the peridynamic formulation of continuum mechanics
https://resolver.caltech.edu/CaltechAUTHORS:DAYjmps06
Authors: {'items': [{'id': 'Dayal-K', 'name': {'family': 'Dayal', 'given': 'Kaushik'}, 'orcid': '0000-0002-0516-3066'}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'Kaushik'}, 'orcid': '0000-0003-2908-5469'}]}
Year: 2006
DOI: 10.1016/j.jmps.2006.04.001
We study the kinetics of phase transformations in solids using the peridynamic formulation of continuum mechanics. The peridynamic theory is a nonlocal formulation that does not involve spatial derivatives, and is a powerful tool to study defects such as cracks and interfaces.
We apply the peridynamic formulation to the motion of phase boundaries in one dimension. We show that unlike the classical continuum theory, the peridynamic formulation does not require any extraneous constitutive laws such as the kinetic relation (the relation between the velocity of the interface and the thermodynamic driving force acting across it) or the nucleation criterion (the criterion that determines whether a new phase arises from a single phase). Instead this information is obtained from inside the theory simply by specifying the inter-particle interaction. We derive a nucleation criterion by examining nucleation as a dynamic instability. We find the induced kinetic relation by analyzing the solutions of impact and release problems, and also directly by viewing phase boundaries as traveling waves.
We also study the interaction of a phase boundary with an elastic non-transforming inclusion in two dimensions. We find that phase boundaries remain essentially planar with little bowing. Further, we find a new mechanism whereby acoustic waves ahead of the phase boundary nucleate new phase boundaries at the edges of the inclusion while the original phase boundary slows down or stops. Transformation proceeds as the freshly nucleated phase boundaries propagate leaving behind some untransformed martensite around the inclusion.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/k351c-67k66Graded ferroelectric capacitors with robust temperature characteristics
https://resolver.caltech.edu/CaltechAUTHORS:NAGjap06
Authors: {'items': [{'id': 'El-Naggar-M-Y', 'name': {'family': 'El-Naggar', 'given': 'Mohamed Y.'}}, {'id': 'Dayal-K', 'name': {'family': 'Dayal', 'given': 'Kaushik'}, 'orcid': '0000-0002-0516-3066'}, {'id': 'Goodwin-D-G', 'name': {'family': 'Goodwin', 'given': 'David G.'}}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'Kaushik'}, 'orcid': '0000-0003-2908-5469'}]}
Year: 2006
DOI: 10.1063/1.2369650
Ferroelectric thin films offer the possibility of engineering the dielectric response for tunable components in frequency-agile rf and microwave devices. However, this approach often leads to an undesired temperature sensitivity. Compositionally graded ferroelectric films have been explored as a means of redressing this sensitivity, but experimental observations vary depending on geometry and other details. In this paper, we present a continuum model to calculate the capacitive response of graded ferroelectric films with realistic electrode geometries by accurately accounting for the polarization distribution and long-range electrostatic interactions. We show that graded c-axis poled BaxSr_(1−xT)iO_3 BST parallel plate capacitors are ineffective while graded a-axis poled BST coplanar capacitors with interdigitated electrodes are extremely effective in obtaining high and temperature-stable dielectric properties.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/kzzd8-7cz26Investigation of Twin-Wall Structure at the Nanometer Scale Using Atomic Force Microscopy
https://resolver.caltech.edu/CaltechAUTHORS:20190828-083227549
Authors: {'items': [{'id': 'Shilo-D', 'name': {'family': 'Shilo', 'given': 'Doron'}}, {'id': 'Ravichandran-G', 'name': {'family': 'Ravichandran', 'given': 'Guruswami'}, 'orcid': '0000-0002-2912-0001'}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'Kaushik'}, 'orcid': '0000-0003-2908-5469'}]}
Year: 2007
DOI: 10.1007/978-1-4020-6239-1_191
The structure of twin-walls and their interaction with defects has important implications for the behavior of a variety of materials including ferroelectric, ferroelastic, and co-elastic crystals. One unique characteristic of such crystals is that their physical properties as well as their macroscopic response to electrical, mechanical, and optical loads are strongly related to their microstructural twin patterns. These, in turn, are governed by the atomistic and mesoscale structure of twin-walls and their interaction with other crystal defects.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/byq2z-wba47A theory of anharmonic lattice statics for analysis of defective crystals
https://resolver.caltech.edu/CaltechAUTHORS:20131009-090857631
Authors: {'items': [{'id': 'Yavari-A', 'name': {'family': 'Yavari', 'given': 'Arash'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'Michael'}, 'orcid': '0000-0001-5877-4824'}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'Kaushik'}, 'orcid': '0000-0003-2908-5469'}]}
Year: 2007
DOI: 10.1007/s10659-006-9079-8
This paper develops a theory of anharmonic lattice statics for the analysis of defective complex lattices. This theory differs from the classical treatments of defects in lattice statics in that it does not rely on harmonic and homogenous force constants. Instead, it starts with an interatomic potential, possibly with infinite range as appropriate for situations with electrostatics, and calculates the equilibrium states of defects. In particular, the present theory accounts for the differences in the force constants near defects and in the bulk. The present formulation reduces the analysis of defective crystals to the solution of a system of nonlinear difference equations with appropriate boundary conditions. A harmonic problem is obtained by linearizing the nonlinear equations, and a method for obtaining analytical solutions is described in situations where one can exploit symmetry. It is then extended to the anharmonic problem using modified Newton–Raphson iteration. The method is demonstrated for model problems motivated by domain walls in ferroelectric materials.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/7qryr-3vt64A micromechanics inspired constitutive model for shape-memory alloys: the one-dimensional case
https://resolver.caltech.edu/CaltechAUTHORS:SADsms07
Authors: {'items': [{'id': 'Sadjadpour-A', 'name': {'family': 'Sadjadpour', 'given': 'Amir'}}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'Kaushik'}, 'orcid': '0000-0003-2908-5469'}]}
Year: 2007
DOI: 10.1088/0964-1726/16/1/S06
This paper presents a constitutive model for shape-memory alloys that builds on ideas generated from recent micromechanical studies of the underlying microstructure. The presentation here is in one dimension. It is applicable in a wide temperature range that covers both the shape-memory effect and superelasticity, is valid for a wide range of strain rates and incorporates plasticity. The thermodynamic setting of the model is explained and the model is demonstrated through examples.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/422xf-1np28A model for large electrostrictive actuation in ferroelectric single crystals
https://resolver.caltech.edu/CaltechAUTHORS:20101007-120102984
Authors: {'items': [{'id': 'Shilo-D', 'name': {'family': 'Shilo', 'given': 'D.'}}, {'id': 'Burcsu-E', 'name': {'family': 'Burcsu', 'given': 'E.'}}, {'id': 'Ravichandran-G', 'name': {'family': 'Ravichandran', 'given': 'G.'}, 'orcid': '0000-0002-2912-0001'}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'K.'}, 'orcid': '0000-0003-2908-5469'}]}
Year: 2007
DOI: 10.1016/j.ijsolstr.2006.07.020
A new mode of large electrostrictive actuation, based on 90° domain switching in ferroelectric crystals subjected to combined electromechanical loading, has recently been experimentally demonstrated. In this paper, we develop a model for this phenomenon by assuming a reasonable arrangement of domain walls and formulating equations of motion for these walls. The model captures most of the features observed in the experiments, reveals the significant role of friction at the interfaces between the loading frame and the crystal surfaces, and predicts that a reduction of friction will allow larger strains at lower mechanical loads.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/w0j77-5bh47Quasi-continuum orbital-free density-functional theory: A route to multi-million atom non-periodic DFT calculation
https://resolver.caltech.edu/CaltechAUTHORS:20131007-153105987
Authors: {'items': [{'id': 'Gavini-V', 'name': {'family': 'Gavini', 'given': 'Vikram'}}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'Kaushik'}, 'orcid': '0000-0003-2908-5469'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'Michael'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2007
DOI: 10.1016/j.jmps.2007.01.012
Density-functional theory (DFT) has provided insights into various materials properties in the recent decade. However, its computational complexity has made other aspects, especially those involving defects, beyond reach. Here, we present a method that enables the study of multi-million atom clusters using orbital-free density-functional theory (OFDFT) with no spurious physics or restrictions on geometry. The key ideas are: (i) a real-space formulation; (ii) a nested finite-element implementation of the formulation and (iii) a systematic means of adaptive coarse-graining retaining full resolution where necessary and coarsening elsewhere with no patches, assumptions or structure. We demonstrate the method, its accuracy under modest computational cost and the physical insights it offers by studying one and two vacancies in aluminum crystals consisting of millions of atoms.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/had6d-4zn49Non-periodic finite-element formulation of orbital-free density functional theory
https://resolver.caltech.edu/CaltechAUTHORS:20101213-152730530
Authors: {'items': [{'id': 'Gavini-V', 'name': {'family': 'Gavini', 'given': 'Vikram'}}, {'id': 'Knap-J', 'name': {'family': 'Knap', 'given': 'Jaroslaw'}}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'Kaushik'}, 'orcid': '0000-0003-2908-5469'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'Michael'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2007
DOI: 10.1016/j.jmps.2006.09.011
We propose an approach to perform orbital-free density functional theory calculations in a non-periodic setting using the finite-element method. We consider this a step towards constructing a seamless multi-scale approach for studying defects like vacancies, dislocations and cracks that require quantum mechanical resolution at the core and are sensitive to long range continuum stresses. In this paper, we describe a local real-space variational formulation for orbital-free density functional theory, including the electrostatic terms and prove existence results. We prove the convergence of the finite-element approximation including numerical quadratures for our variational formulation. Finally, we demonstrate our method using examples.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/5p4s5-bkb13A real-space non-local phase-field model of ferroelectric domain patterns in complex geometries
https://resolver.caltech.edu/CaltechAUTHORS:20131008-075822606
Authors: {'items': [{'id': 'Dayal-K', 'name': {'family': 'Dayal', 'given': 'Kaushik'}, 'orcid': '0000-0002-0516-3066'}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'Kaushik'}, 'orcid': '0000-0003-2908-5469'}]}
Year: 2007
DOI: 10.1016/j.actamat.2006.10.049
Ferroelectric perovskites are used in various transducer, memory and optical applications due to their attractive properties. In these applications, the ferroelectric materials often have complex geometries and electrode arrangements, and are subjected to domain switching. Therefore, it is important to understand the domain pattern that forms in these geometries. However, models of domain evolution often make assumptions like periodicity and complete shielding which make them unrealistic for these applications. In this paper, we develop a phase-field approach that can study domain patterns and domain evolution in complex geometries with no a priori assumption on geometry, electrode arrangement, and dielectric properties. The key idea is a boundary element method to resolve the electrostatic fields. We illustrate the method by examining the closure domains that form at a free surface and domain switching under cyclic electric field in a device with interdigitated electrodes.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/kkw75-21870Stress-induced martensitic phase transformation in thin sheets of Nitinol
https://resolver.caltech.edu/CaltechAUTHORS:20131008-082850831
Authors: {'items': [{'id': 'Daly-S', 'name': {'family': 'Daly', 'given': 'S.'}}, {'id': 'Ravichandran-G', 'name': {'family': 'Ravichandran', 'given': 'G.'}, 'orcid': '0000-0002-2912-0001'}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'K.'}, 'orcid': '0000-0003-2908-5469'}]}
Year: 2007
DOI: 10.1016/j.actamat.2007.02.011
Using the in situ optical technique known as digital image correlation (DIC), full-field quantitative strain maps of localization have been experimentally obtained for the first time in thin sheets of Nitinol. The use of DIC provides new information connecting previous observations on the micro- and macro-scales. It shows that the transformation initiates before the formation of localized bands, and the strain inside the bands does not saturate when they nucleate. The effect of rolling texture on the macroscopic stress–strain behavior was observed and it is shown that the resolved stress criterion or Clausius–Clapeyron relation does not hold for polycrystalline Nitinol. Finally, the effect of geometric defects on localization behavior was observed.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/n8xxv-46d40Anharmonic lattice statics analysis of 180º and 90º ferroelectric domain walls in PbTiO_3
https://resolver.caltech.edu/CaltechAUTHORS:20131008-142756092
Authors: {'items': [{'id': 'Yavari-A', 'name': {'family': 'Yavari', 'given': 'A.'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'K.'}, 'orcid': '0000-0003-2908-5469'}]}
Year: 2007
DOI: 10.1080/14786430701418956
This paper presents an anharmonic lattice statics analysis of 180 ° and 90 ° domain walls in tetragonal ferroelectric perovskites. We present all the calculations and numerical examples for the technologically important ferroelectric material PbTiO_3. We use shell potentials that are fitted to quantum mechanics calculations. Our formulation places no restrictions on the range of the interactions. This formulation of lattice statics is inhomogeneous and accounts for the variation of the force constants near defects. The discrete governing equations for perfect domain walls are reduced using symmetry conditions. We solve the linearized discrete governing equations directly using a novel method in the setting of the theory of difference equations. We calculate the fully nonlinear solutions using modified Newton–Raphson iterations.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/65md6-9am55Active tuning of photonic device characteristics during operation by ferroelectric domain switching
https://resolver.caltech.edu/CaltechAUTHORS:DAYjap07
Authors: {'items': [{'id': 'Dayal-K', 'name': {'family': 'Dayal', 'given': 'Kaushik'}, 'orcid': '0000-0002-0516-3066'}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'Kaushik'}, 'orcid': '0000-0003-2908-5469'}]}
Year: 2007
DOI: 10.1063/1.2779261
Ferroelectrics have many unusual properties. Two properties that are often exploited are first, their complex, nonlinear optical response and second, their strong nonlinear coupling between electromagnetic and mechanical fields through the domain patterns or microstructure. The former has led to the use of ferroelectrics in optical devices and the latter is used in ferroelectric sensors and actuators. We show the feasibility of using these properties together in nanoscale photonic devices. The electromechanical coupling allows us to change the domain patterns or microstructure. This in turn changes the optical characteristics. Together, these could provide photonic devices with tunable properties. We present calculations for two model devices. First, in a photonic crystal consisting of a triangular lattice of air holes in barium titanate, we find the change in the band structure when the domains are switched. The change is significant compared to the frequency spread of currently available high-quality light sources and may provide a strategy for optical switching. Second, we show that periodically poled 90° domain patterns, despite their complex geometry, do not cause dispersion or have band gaps. Hence, they may provide an alternative to the antiparallel domains that are usually used in quasiphase matching and allow for tunable higher-harmonic generation.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/99az3-7fz90Experimental investigation of crack initiation in thin sheets of nitinol
https://resolver.caltech.edu/CaltechAUTHORS:20131008-084446067
Authors: {'items': [{'id': 'Daly-S', 'name': {'family': 'Daly', 'given': 'S.'}}, {'id': 'Miller-A', 'name': {'family': 'Miller', 'given': 'A.'}}, {'id': 'Ravichandran-G', 'name': {'family': 'Ravichandran', 'given': 'G.'}, 'orcid': '0000-0002-2912-0001'}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'K.'}, 'orcid': '0000-0003-2908-5469'}]}
Year: 2007
DOI: 10.1016/j.actamat.2007.07.038
An experimental investigation into the fracture properties of 160-μm-thick edge-cracked specimens of austenitic nickel–titanium (nitinol) under uniaxial tension is presented. Using the in situ optical technique of digital image correlation (DIC), strain fields directly relating to phase boundary nucleation and propagation of fracture samples were observed for the first time. The shape and size of the saturation and transformation zones as a function of loading near the crack tip were examined. An average plane strain crack initiation fracture toughness (K_C) of 51.4 ± 3.6 MPa √m for fine grained polycrystalline nitinol sheets at room temperature was measured. The extent and nature of the phase transformation obtained from DIC, combined with the relatively high value of K_C, underscores the importance of crack tip shielding in the fracture of shape memory alloys.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/6e767-rc584A micromechanics-inspired constitutive model for shape-memory alloys
https://resolver.caltech.edu/CaltechAUTHORS:SADsms07b
Authors: {'items': [{'id': 'Sadjadpour-A', 'name': {'family': 'Sadjadpour', 'given': 'Amir'}}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'Kaushik'}, 'orcid': '0000-0003-2908-5469'}]}
Year: 2007
DOI: 10.1088/0964-1726/16/5/030
This paper presents a three-dimensional constitutive model for shape-memory alloys that generalizes the one-dimensional model presented earlier (Sadjadpour and Bhattacharya 2007 Smart Mater. Struct. 16 S51–62). These models build on recent micromechanical studies of the underlying microstructure of shape-memory alloys, and a key idea is that of an effective transformation strain of the martensitic microstructure. This paper explains the thermodynamic setting of the model, demonstrates it through examples involving proportional and non-proportional loading, and shows that the model can be fitted to incorporate the effect of texture in polycrystalline shape-memory alloys.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/btkt5-vhf94Computational analysis of martensitic thin films using subdivision surfaces
https://resolver.caltech.edu/CaltechAUTHORS:20131008-085924006
Authors: {'items': [{'id': 'Dondl-P-W', 'name': {'family': 'Dondl', 'given': 'Patrick W.'}}, {'id': 'Shen-Ching-Ping', 'name': {'family': 'Shen', 'given': 'Ching-Ping'}}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'Kaushik'}, 'orcid': '0000-0003-2908-5469'}]}
Year: 2007
DOI: 10.1002/nme.2005
This paper studies numerically the deformation of thin films made of materials undergoing martensitic phase transformations by using subdivision surfaces. These thin films have received interest as potential microactuators, and specifically a tent-like configuration has recently been proposed. In order to model martensitic materials we use a multi-well strain energy combined with an interfacial energy penalizing strain gradients. The study of such configurations requires adequate resolution of inhomogeneous in-plane stretch, out-of-plane deformation and transition regions across which the deformation gradient changes sharply. This paper demonstrates that subdivision surfaces provide an attractive tool in the numerical study of such configurations, and also provides insights into the tent-like deformations.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/ww6kw-rjs70Vacancy clustering and prismatic dislocation loop formation in aluminum
https://resolver.caltech.edu/CaltechAUTHORS:GAVprb07
Authors: {'items': [{'id': 'Gavirini-V', 'name': {'family': 'Gavirini', 'given': 'Vikram'}}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'Kaushik'}, 'orcid': '0000-0003-2908-5469'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'Michael'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2007
DOI: 10.1103/PhysRevB.76.180101
The formation of prismatic dislocation loops is an important factor leading to radiation damage of metals. However, the formation mechanism and the size of the smallest stable loop has remained unclear. In this Rapid Communication, we use electronic structure calculations with millions of atoms to address this problem in aluminum. Our results show that there is a cascade of larger and larger vacancy clusters with smaller and smaller energy. Further, the results show that a seven vacancy cluster on the (111) plane can collapse into a stable prismatic loop. This supports the long-standing hypothesis that vacancy clustering leads to a prismatic loop, and that these loops can be stable at extremely small sizes. Finally our results show that it is important to conduct calculations using realistic concentrations (computational cell size) to obtain physically meaningful results.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/dkmmq-hez16The Relaxation of Two-well Energies with Possibly Unequal Moduli
https://resolver.caltech.edu/CaltechAUTHORS:20131008-143908773
Authors: {'items': [{'id': 'Chenchiah-I-V', 'name': {'family': 'Chenchiah', 'given': 'Isaac V.'}}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'Kaushik'}, 'orcid': '0000-0003-2908-5469'}]}
Year: 2008
DOI: 10.1007/s00205-007-0075-3
The elastic energy of a multiphase solid is a function of its microstructure. Determining the infimum of the energy of such a solid and characterizing the associated optimal microstructures is an important problem that arises in the modeling of the shape memory effect, microstructure evolution, and optimal design. Mathematically, the problem is to determine the relaxation under fixed phase fraction of a multiwell energy. This paper addresses two such problems in the geometrically linear setting. First, in two dimensions, we compute the relaxation under fixed phase fraction for a two-well elastic energy with arbitrary elastic moduli and transformation strains, and provide a characterization of the optimal microstructures and the associated strain. Second, in three dimensions, we compute the relaxation under fixed phase fraction for a two-well elastic energy when either (1) both elastic moduli are isotropic, or (2) the elastic moduli are well ordered and the smaller elastic modulus is isotropic. In both cases we impose no restrictions on the transformation strains. We provide a characterization of the optimal microstructures and the associated strain. We also compute a lower bound that is optimal except possibly in one regime when either (1) both elastic moduli are cubic, or (2) the elastic moduli are well ordered and the smaller elastic modulus is cubic; for moduli with arbitrary symmetry we obtain a lower bound that is sometimes optimal. In all these cases we impose no restrictions on the transformation strains and whenever the bound is optimal we provide a characterization of the optimal microstructures and the associated strain. In both two and three dimensions the quasiconvex envelope of the energy can be obtained by minimizing over the phase fraction. We also characterize optimal microstructures under applied stress.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/8gzkh-rxx56Deformation Behavior of a Shape Memory Alloy, Nitinol
https://resolver.caltech.edu/CaltechAUTHORS:20160127-072106515
Authors: {'items': [{'id': 'Daly-S', 'name': {'family': 'Daly', 'given': 'Samantha'}}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'Kaushik'}, 'orcid': '0000-0003-2908-5469'}, {'id': 'Ravichandran-G', 'name': {'family': 'Ravichandran', 'given': 'Guruswami'}, 'orcid': '0000-0002-2912-0001'}]}
Year: 2008
DOI: 10.1115/ESDA2008-59187
Nickel-Titanium, commonly referred to as Nitinol, is a shape-memory alloy with numerous
applications due to its superelastic nature and its ability to revert to a previously defined shape
when deformed and then heated past a set transformation temperature. While the
crystallography and the overall phenomenology are reasonably well understood, much remains
unknown about the deformation and failure mechanisms of these materials. These latter issues
are becoming critically important as Nitinol is being increasingly used in medical devices and
space applications. The talk will describe the investigation of the deformation and failure of
Nitinol using an in-situ optical technique called Digital Image Correlation (DIC). With this
technique, full-field quantitative maps of strain localization are obtained for the first time in
thin sheets of Nitinol under tension. These experiments provide new information connecting
previous observations on the micro- and macro- scale. They show that martensitic
transformation initiates before the formation of localized bands, and that the strain inside the
bands does not saturate when the bands nucleate. The effect of rolling texture, the validity of
the widely used resolved stress transformation criterion, and the role of geometric defects are
examined.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/yhgba-w7z71A continuum theory of deformable, semiconducting ferroelectrics
https://resolver.caltech.edu/CaltechAUTHORS:20131009-085950220
Authors: {'items': [{'id': 'Xiao-Yu', 'name': {'family': 'Xiao', 'given': 'Yu'}}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'Kaushik'}, 'orcid': '0000-0003-2908-5469'}]}
Year: 2008
DOI: 10.1007/s00205-007-0096-y
Ferroelectric solids, especially ferroelectric perovskites, are widely used as sensors, actuators, filters, memory devices, and optical components. While these have traditionally been treated as insulators, they are in reality wide-band-gap semiconductors. This semiconducting behavior affects the microstructures or domain patterns of the ferroelectric material and the interaction of ferroelectrics with electrodes, and is affected significantly by defects and dopants. In this paper, we develop a continuum theory of deformable, semiconducting ferroelectrics. A key idea is to introduce space charges and dopant density as field (state) variables in addition to polarization and deformation. We demonstrate the theory by studying oxygen vacancies in barium titanate. We find the formation of depletion layers, regions of depleted electrons, and a large electric field at the ferroelectric–electrode boundary. We also find the formation of a charge double layer and a large electric field across 90° domain walls but not across 180° domain walls. We show that these internal electric fields can give rise to a redistribution or forced diffusion of oxygen vacancies, which provides a mechanism for aging of ferroelectric materials.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/j5nvb-qg698Electrooptic Modulation in Thin Film Barium Titanate Plasmonic Interferometers
https://resolver.caltech.edu/CaltechAUTHORS:DICnl08
Authors: {'items': [{'id': 'Dicken-M-J', 'name': {'family': 'Dicken', 'given': 'Matthew J.'}}, {'id': 'Sweatlock-L-A', 'name': {'family': 'Sweatlock', 'given': 'Luke A.'}}, {'id': 'Pacifici-D', 'name': {'family': 'Pacifici', 'given': 'Domenico'}}, {'id': 'Lezec-H-J', 'name': {'family': 'Lezec', 'given': 'Henri J.'}}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'Kaushik'}, 'orcid': '0000-0003-2908-5469'}, {'id': 'Atwater-H-A', 'name': {'family': 'Atwater', 'given': 'Harry A.'}, 'orcid': '0000-0001-9435-0201'}]}
Year: 2008
DOI: 10.1021/nl802981q
We demonstrate control of the surface plasmon polariton wavevector in an active metal−dielectric plasmonic interferometer by utilizing electrooptic barium titanate as the dielectric layer. Arrays of subwavelength interferometers were fabricated from pairs of parallel slits milled in silver on barium titanate thin films. Plasmon-mediated transmission of incident light through the subwavelength slits is modulated by an external voltage applied across the barium titanate thin film. Transmitted light modulation is ascribed to two effects, electrically induced domain switching and electrooptic modulation of the barium titanate index.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/85kn5-3xp29A coarse-grained model of the myofibril: overall dynamics and the evolution of sarcomere non-uniformities
https://resolver.caltech.edu/CaltechSOLIDS:2008.002
Authors: {'items': [{'id': 'Givli-S', 'name': {'family': 'Givli', 'given': 'Sefi'}}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'Kaushik'}, 'orcid': '0000-0003-2908-5469'}]}
Year: 2008
A theoretical framework for predicting the macroscopic behavior of a muscle myofibril based on the collective behavior of sarcomeres is presented. The analysis is accomplished by rigorously transforming the nonlinear dynamics of an assemblage of sarcomeres into a partial differential equation for the probability distribution function of sarcomere lengths in the presence of stochastic temporal fluctuations and biological variability. This enables the study of biologically relevant specimens with reasonable computational effort. The model is validated by a comparison to quantitative experimental results. Further, it reproduces experimental observations that can not be explained by standard single sarcomere models, and provides new insights into muscle function and muscle damage during cyclic loading. We show that the accumulation of overstretched sarcomeres, which is related to muscle damage, depends on a delicate interplay between the dynamics of a large number of sarcomeres and the load characteristics, such as its magnitude and frequency. Further, we show that biological variability rather than stochastic fluctuations are the main source for sarcomere non-uniformities.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/46y76-5bg40A sharp interface model for the propagation of martensitic phase boundaries
https://resolver.caltech.edu/CaltechSOLIDS:2008.003
Authors: {'items': [{'id': 'Dondl-P-W', 'name': {'family': 'Dondl', 'given': 'Patrick W.'}}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'Kaushik'}, 'orcid': '0000-0003-2908-5469'}]}
Year: 2008
A model for the quasistatic evolution of martensitic phase boundaries is presented. The model is essentially the gradient flow of an energy that can contains elastic energy due to the underlying change in crystal structure in the course of the phase transformation and surface energy penalizing the area of the phase boundary. This leads to a free boundary problem with a nonlocal velocity that arises from the coupling to the elasticity equation. We show existence of solutions under a technical convergence condition using an implicit time-discretization.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/ehbhb-36c73Stress-induced phase transformations in shape-memory polycrystals
https://resolver.caltech.edu/CaltechSOLIDS:2008.005
Authors: {'items': [{'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'Kaushik'}, 'orcid': '0000-0003-2908-5469'}, {'id': 'Schlömerkemper-A', 'name': {'family': 'Schlömerkemper', 'given': 'Anja'}}]}
Year: 2008
Shape-memory alloys undergo a solid-to-solid phase transformation involving a change of crystal structure. We examine model problems in the scalar setting motivated by the situation when this transformation is induced by the application of stress in a polycrystalline material made of numerous grains of the same crystalline solid with varying orientations. We show that the onset of transformation in a granular polycrystal with homogeneous elasticity is in fact predicted accurately by the so-called Sachs bound based on the ansatz of uniform stress. We also present a simple example where the onset of phase transformation is given by the Sachs bound, and the extent of phase transformation is given by the constant strain Taylor bound. Finally we discuss the stress-strain relations of the general problem using Milton-Serkov bounds.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/s7889-26981Characterization of soft stripe-domain deformations in SmC and SmC* liquid-crystal elastomers
https://resolver.caltech.edu/CaltechSOLIDS:2008.004
Authors: {'items': [{'id': 'Biggins-J-S', 'name': {'family': 'Biggins', 'given': 'J. S.'}}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'K.'}, 'orcid': '0000-0003-2908-5469'}]}
Year: 2008
The neo-classical model of SmC (and SmC*) elastomers developed by Warner and Adams predicts a class of "soft" (zero energy) deformations. We find and describe the full set of stripe-domains – laminate structures in which the laminates alternate between two different deformations – that can form between pairs of these soft deformations. All the stripe-domains fall into two classes, one in which the smectic layers are not bent at the interfaces, but for which, in the SmC* case, the interfaces are charged, and one in which the smectic layers are bent but the interfaces are never charged. Striped deformations significantly enhance the softness of the macroscopic elastic response.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/dwtww-vnd56A coarse-grained model of the myofibril: Overall dynamics and the evolution of sarcomere non-uniformities
https://resolver.caltech.edu/CaltechAUTHORS:20090424-093629858
Authors: {'items': [{'id': 'Givli-S', 'name': {'family': 'Givli', 'given': 'Sefi'}}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'Kaushik'}, 'orcid': '0000-0003-2908-5469'}]}
Year: 2009
DOI: 10.1016/j.jmps.2008.10.013
A theoretical framework for predicting the macroscopic behavior of a muscle myofibril based on the collective behavior of sarcomeres is presented. The analysis is accomplished by rigorously transforming the nonlinear dynamics of an assemblage of sarcomeres into a partial differential equation for the probability distribution function of sarcomere lengths in the presence of stochastic temporal fluctuations and biological variability. This enables the study of biologically relevant specimens with reasonable computational effort. The model is validated by a comparison to quantitative experimental results. Further, it reproduces experimental observations that cannot be explained by standard single sarcomere models, and provides new insights into muscle function and muscle damage during cyclic loading. We show that the accumulation of overstretched sarcomeres, which is related to muscle damage, depends on a delicate interplay between the dynamics of a large number of sarcomeres and the load characteristics, such as its magnitude and frequency. Further, we show that biological variability rather than stochastic fluctuations are the main source for sarcomere non-uniformities.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/6vz8w-bed86Phase shifting full-field interferometric methods for determination of in-plane tensorial stress
https://resolver.caltech.edu/CaltechAUTHORS:20090811-084717973
Authors: {'items': [{'id': 'Kramer-S-L-B', 'name': {'family': 'Kramer', 'given': 'S. L. B.'}}, {'id': 'Mello-M', 'name': {'family': 'Mello', 'given': 'M.'}, 'orcid': '0000-0003-2129-9235'}, {'id': 'Ravichandran-G', 'name': {'family': 'Ravichandran', 'given': 'G.'}, 'orcid': '0000-0002-2912-0001'}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'K.'}, 'orcid': '0000-0003-2908-5469'}]}
Year: 2009
DOI: 10.1007/s11340-009-9230-0
A new method that combines phase shifting photoelasticity and transmission Coherent Gradient Sensing (CGS) is developed to determine the tensorial stress field in thin plates of photoelastic materials. A six step phase shifting photoelasticity method determines principal stress directions and the difference of principal stresses. The transmission CGS method utilizes a standard four step phase shifting method to measure the x and y first derivatives of the sum of principal stresses. These stress derivatives are numerically integrated using a weighted preconditioned conjugate gradient (PCG) algorithm, which is also used for the phase unwrapping of the photoelastic and CGS phases. With full-field measurement of the sum and difference of principal stresses, the principal stresses may be separated, followed by the Cartesian and polar coordinate stresses using the principal stress directions. The method is demonstrated for a compressed polycarbonate plate with a side V-shaped notch. The experimental stress fields compare well with theoretical stress fields derived from Williams solution for a thin plate with an angular corner.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/ddv7d-tbe03Large deformation of nitinol under shear dominant loading
https://resolver.caltech.edu/CaltechAUTHORS:20090519-114619132
Authors: {'items': [{'id': 'Daly-S', 'name': {'family': 'Daly', 'given': 'S.'}}, {'id': 'Rittel-D', 'name': {'family': 'Rittel', 'given': 'D.'}}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'K.'}, 'orcid': '0000-0003-2908-5469'}, {'id': 'Ravichandran-G', 'name': {'family': 'Ravichandran', 'given': 'G.'}, 'orcid': '0000-0002-2912-0001'}]}
Year: 2009
DOI: 10.1007/s11340-008-9178-5
Full-field quantitative strain maps of phase transformation and plasticity in Nitinol under large shear-dominated deformation are presented. To achieve a shear-dominated deformation mode with relatively uniform stresses and strains, a shear compression specimen (SCS) geometry was utilized. Shear deformation appears to impede the development of the strain localization during phase transformation that is seen in uniaxial testing. The shear-dominant deformation of Nitinol in the plastic regime exhibits low hardening and results in the development of significant strain inhomogeneity.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/5y6ky-9ck14Competing failure mechanisms in thin films: Application to layer transfer
https://resolver.caltech.edu/CaltechAUTHORS:20090821-125551614
Authors: {'items': [{'id': 'Ponson-L', 'name': {'family': 'Ponson', 'given': 'L.'}}, {'id': 'Diest-K', 'name': {'family': 'Diest', 'given': 'K.'}}, {'id': 'Atwater-H-A', 'name': {'family': 'Atwater', 'given': 'H. A.'}, 'orcid': '0000-0001-9435-0201'}, {'id': 'Ravichandran-G', 'name': {'family': 'Ravichandran', 'given': 'G.'}, 'orcid': '0000-0002-2912-0001'}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'K.'}, 'orcid': '0000-0003-2908-5469'}]}
Year: 2009
DOI: 10.1063/1.3078801
We investigate the origin of transverse cracks often observed in thin films obtained by the layer transfer technique. During this process, two crystals bonded to each other containing a weak plane produced by ion implantation are heated to let a thin layer of one of the material on the other. The level of stress imposed on the film during the heating phase due to the mismatch of thermal expansion coefficients of the substrate and the film is shown to be the dominent factor in determining the quality of the transferred layer. In particular, it is shown that if the film is submitted to a tensile stress, the microcracks produced by ion implantation are not stable and deviate from the plane of implantation making the layer transfer process impossible. However, if the compressive stress exceeds a threshold value, after layer transfer, the film can buckle and delaminate, leading to transverse cracks induced by bending. As a result, we show that the imposed stress σ_m —- or equivalently the heating temperature -— must be within the range −σ_c<σ_m<0 to produce an intact thin film where σ_c depends on the interfacial fracture energy and the size of defects at the interface between film and substrate.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/kneya-7pe98Transmission wavefront shearing interferometry for photoelastic materials
https://resolver.caltech.edu/CaltechAUTHORS:20090630-101225777
Authors: {'items': [{'id': 'Kramer-S-L-B', 'name': {'family': 'Kramer', 'given': 'Sharlotte L. B.'}}, {'id': 'Ravichandran-G', 'name': {'family': 'Ravichandran', 'given': 'Guruswami'}, 'orcid': '0000-0002-2912-0001'}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'Kaushik'}, 'orcid': '0000-0003-2908-5469'}]}
Year: 2009
DOI: 10.1364/AO.48.002450
A general analysis and experimental validation of transmission wavefront shearing interferometry for photoelastic materials are presented. These interferometers applied to optically isotropic materials produce a single interference pattern related to one phase term, but when applied to photoelastic materials, they produce the sum of two different interference patterns with phase terms that are the sum and difference, respectively, of two stress-related phase terms. The two stress-related phase terms may be separated using phase shifting and polarization optics. These concepts are experimentally demonstrated using coherent gradient sensing in full field for a compressed polycarbonate plate with a V-shaped notch with good agreement with theoretical data. The analysis may be applied to any wavefront shearing interferometer by modifying parameters describing the wavefront shearing distance.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/5tb4k-jqh33Characterization of soft stripe-domain deformations in Sm-C and Sm-C* liquid-crystal elastomers
https://resolver.caltech.edu/CaltechAUTHORS:20090731-111609650
Authors: {'items': [{'id': 'Biggins-J-S', 'name': {'family': 'Biggins', 'given': 'J. S.'}}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'K.'}, 'orcid': '0000-0003-2908-5469'}]}
Year: 2009
DOI: 10.1103/PhysRevE.79.061705
The neoclassical model of Sm-C (and Sm-C*) elastomers developed by Warner and Adams predicts a class of "soft" (zero energy) deformations. We find and describe the full set of stripe domains—laminate structures in which the laminates alternate between two different deformations—that can form between pairs of these soft deformations. All the stripe domains fall into two classes, one in which the smectic layers are not bent at the interfaces, but for which—in the Sm-C* case—the interfaces are charged, and one in which the smectic layers are bent but the interfaces are never charged. Striped deformations significantly enhance the softness of the macroscopic elastic response.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/5n2sd-1vf14Supersoft elasticity in polydomain nematic elastomers
https://resolver.caltech.edu/CaltechAUTHORS:20090811-112637753
Authors: {'items': [{'id': 'Biggins-J-S', 'name': {'family': 'Biggins', 'given': 'J. S.'}}, {'id': 'Warner-M', 'name': {'family': 'Warner', 'given': 'M.'}}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'K.'}, 'orcid': '0000-0003-2908-5469'}]}
Year: 2009
DOI: 10.1103/PhysRevLett.103.037802
We consider the equilibrium stress-strain behavior of polydomain liquid crystal elastomers (PLCEs). We show that there is a fundamental difference between PLCEs cross-linked in the high temperature isotropic and low temperature aligned states. PLCEs cross-linked in the isotropic state then cooled to an aligned state will exhibit extremely soft elasticity (confirmed by recent experiments) and ordered director patterns characteristic of textured deformations. PLCEs cross-linked in the aligned state will be mechanically much harder and characterized by disclination textures.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/e5y6y-f0w19Wave propagation in a sandwich structure
https://resolver.caltech.edu/CaltechAUTHORS:20090817-144818084
Authors: {'items': [{'id': 'Liu-Liping', 'name': {'family': 'Liu', 'given': 'Liping'}}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'Kaushik'}, 'orcid': '0000-0003-2908-5469'}]}
Year: 2009
DOI: 10.1016/j.ijsolstr.2009.04.023
The propagation of elastic waves in a sandwich structure with two thin stiff face-plates and a thick compliant core is considered in this paper. A complete description of the dispersion relation with no restrictions on frequency and wavelength is provided. This is accomplished by transforming the wave equation to a Hamiltonian system and then using a transfer matrix approach for solving the Hamiltonian system. To provide insight, particular regimes of the frequency–wavelength plane are then considered. First, an explicit formula is derived for all natural frequencies at the long wavelength limit. It is shown that all waves with finite limiting frequency have zero group velocity, while those with vanishing limiting frequency correspond to longitudinal, shear and flexural waves. The displacement of the flexural waves are reminiscent of Mindlin plates, and an asymptotic procedure to find the shear correction factor is presented. Second, the lowest branch of the dispersion relation is studied in detail and mode shapes are used to motivate explicit but accurate description of this lowest branch. This approximate model is anticipated to be useful in simulations of large structures with sandwich structures.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/jwa0a-07e37Non-periodic finite-element formulation of Kohn–Sham density functional theory
https://resolver.caltech.edu/CaltechAUTHORS:20100302-131546235
Authors: {'items': [{'id': 'Suryanarayana-P', 'name': {'family': 'Suryanarayana', 'given': 'Phanish'}, 'orcid': '0000-0001-5172-0049'}, {'id': 'Vikram-G', 'name': {'family': 'Vikram', 'given': 'Gavini'}}, {'id': 'Blesgen-T', 'name': {'family': 'Blesgen', 'given': 'Thomas'}}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'Kaushik'}, 'orcid': '0000-0003-2908-5469'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'Michael'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2010
DOI: 10.1016/j.jmps.2009.10.002
We present a real-space, non-periodic, finite-element formulation for Kohn–Sham density functional theory (KS-DFT). We transform the original variational problem into a local saddle-point problem, and show its well-posedness by proving the existence of minimizers. Further, we prove the convergence of finite-element approximations including numerical quadratures. Based on domain decomposition, we develop a parallel finite-element implementation of this formulation capable of performing both all-electron and pseudopotential calculations. We assess the accuracy of the formulation through selected test cases and demonstrate good agreement with the literature. We also evaluate the numerical performance of the implementation with regard to its scalability and convergence rates. We view this work as a step towards developing a method that can accurately study defects like vacancies, dislocations and crack tips using density functional theory (DFT) at reasonable computational cost by retaining electronic resolution where it is necessary and seamlessly coarse-graining far away.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/jya74-xk759Phase transformation and hysteresis behavior in Cs_(1-x)Rb_xH_2PO_4
https://resolver.caltech.edu/CaltechAUTHORS:20100610-141653473
Authors: {'items': [{'id': 'Louie-M-W', 'name': {'family': 'Louie', 'given': 'Mary W.'}}, {'id': 'Kislitsyn-M', 'name': {'family': 'Kislitsyn', 'given': 'Mikhail'}}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'Kaushik'}, 'orcid': '0000-0003-2908-5469'}, {'id': 'Haile-S-M', 'name': {'family': 'Haile', 'given': 'Sossina M.'}, 'orcid': '0000-0002-5293-6252'}]}
Year: 2010
DOI: 10.1016/j.ssi.2008.11.014
A new theory on the origin of hysteresis in first order phase transformations was evaluated for its applicability to the phase transformation behavior in the Cs_(1 − x)Rb_xH_2PO_4 solid solution system. Specifically, the correlation between λ_2, the middle eigenvalue of the transformation matrix describing the cubic-to-monoclinic superprotonic transition, and the transformation hysteresis was examined. The value of λ_2 was estimated from a combination of room temperature diffraction data obtained for compositions in the solid solution system and high temperature diffraction data obtained for the CsH_2PO_4 end-member. The transformation hysteresis was determined for Cs_(1 − x)Rb_xH_2PO_4 compositions (x = 0, 0.25, 0.50 and 0.75) by single-frequency electrical impedance measurements. It was found that the transition temperature increases monotonically with increasing Rb content, from 227.6 ± 0.4 °C for the end-member CsH_2PO_4 to 256.1 ± 0.3 °C for Cs_(25)Rb_(75)H_2PO_4, as does the hysteresis in the phase transition, from 13.4 °C to 17.4 °C. Analysis of the transformation matrix reveals that, for this system, λ_2 depends only on the b lattice parameter of the paraelectric phase and the α_0 lattice parameter of the cubic phase. The computed values of λ_2, based on extrapolations accounting for chemical contraction with increasing Rb substitution and thermal expansion on heating, were far from 1, ranging from 0.9318 to 0.9354. The observation of λ_2 increasing with Rb content is attributed to the relatively large thermal expansion in the b-axis of the low temperature monoclinic phase in combination with an increase in transition temperature with increasing x. That the hysteresis does not decrease as λ_2 approaches 1, counter to the theoretical expectations, may reflect uncertainties in the method of estimating λ_2 for Rb substituted compositions, or the discovery of a system in which hysteresis is not dominated by considerations of crystallographic compatibility.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/yqsr4-j2584Stress-Induced Phase Transformations in Shape-Memory Polycrystals
https://resolver.caltech.edu/CaltechAUTHORS:20100518-135240082
Authors: {'items': [{'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'Kaushik'}, 'orcid': '0000-0003-2908-5469'}, {'id': 'Schlömerkemper-A', 'name': {'family': 'Schlömerkemper', 'given': 'Anja'}}]}
Year: 2010
DOI: 10.1007/s00205-009-0263-4
Shape-memory alloys undergo a solid-to-solid phase transformation involving a change of crystal structure. We examine model problems in the scalar setting motivated by the situation when this transformation is induced by the application of stress in a polycrystalline material made of numerous grains of the same crystalline solid with varying orientations. We show that the onset of transformation in a granular polycrystal with homogeneous elasticity is in fact predicted accurately by the so-called Sachs bound based on the ansatz of uniform stress. We also present a simple example where the onset of phase transformation is given by the Sachs bound, and the extent of phase transformation is given by the constant strain Taylor bound. Finally we discuss the stress–strain relations of the general problem using Milton–Serkov bounds.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/x06k4-54547Disclination-mediated thermo-optical response in nematic glass sheets
https://resolver.caltech.edu/CaltechAUTHORS:20100630-135257452
Authors: {'items': [{'id': 'Modes-C-D', 'name': {'family': 'Modes', 'given': 'Carl D.'}}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'Kaushik'}, 'orcid': '0000-0003-2908-5469'}, {'id': 'Warner-M', 'name': {'family': 'Warner', 'given': 'Mark'}}]}
Year: 2010
DOI: 10.1103/PhysRevE.81.060701
Nematic solids respond strongly to changes in ambient heat or light, significantly differently parallel and perpendicular to the director. This phenomenon is well characterized for uniform director fields but not for defect textures. We analyze the elastic ground states of a nematic glass in the membrane approximation as a function of temperature for some disclination defects with an eye toward reversibly inducing three-dimensional shapes from flat sheets of material, at the nanoscale all the way to macroscopic objects, including nondevelopable surfaces. The latter offers a paradigm to actuation via switchable stretch in thin systems.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/rwt7g-b7c14A Sharp Interface Model for the Propagation of Martensitic Phase Boundaries
https://resolver.caltech.edu/CaltechAUTHORS:20100715-084916174
Authors: {'items': [{'id': 'Dondl-P-W', 'name': {'family': 'Dondl', 'given': 'Patrick W.'}}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'Kaushik'}, 'orcid': '0000-0003-2908-5469'}]}
Year: 2010
DOI: 10.1007/s00205-009-0286-x
A model for the quasistatic evolution of martensitic phase boundaries is presented. The model is essentially the gradient flow of an energy that can contain elastic energy due to the underlying change in crystal structure in the course of the phase transformation and surface energy penalizing the area of the phase boundary. This leads to a free boundary problem with a nonlocal velocity that arises from a coupling to the elasticity equation. We show existence of solutions under a technical convergence condition using an implicit time-discretization.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/dqxdw-a0d80Optimization of magnetoelectricity in piezoelectric–magnetostrictive bilayers
https://resolver.caltech.edu/CaltechAUTHORS:20101214-131536224
Authors: {'items': [{'id': 'Kuo-Hsin-Yi', 'name': {'family': 'Kuo', 'given': 'Hsin-Yi'}}, {'id': 'Slinger-A', 'name': {'family': 'Slinger', 'given': 'Alex'}}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'Kaushik'}, 'orcid': '0000-0003-2908-5469'}]}
Year: 2010
DOI: 10.1088/0964-1726/19/12/125010
Magnetoelectric coupling is of interest for a variety of applications, but is weak in monolithic materials. Strain-coupled bilayers or multilayers of piezoelectric and magnetostrictive material are an attractive way of obtaining enhanced effective magnetoelectricity. This paper studies the optimization of magnetoelectricity with respect to the crystallographic orientations and the relative thickness of the two materials. We show that the effective transverse (α_(E, 31)) and longitudinal (α_(E, 33)) coupling constants can be enhanced many-fold at the optimal orientation compared to those at normal orientation. For example, we show that the constants are 17 and 7 times larger for the optimal orientation of a lithium niobate/Terfenol-D bilayer of equal thickness compared to the normal orientation. The coupling also increases as the piezoelectric phase gets thinner.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/5zw52-95c62Gaussian curvature from flat elastica sheets
https://resolver.caltech.edu/CaltechAUTHORS:20110317-105846413
Authors: {'items': [{'id': 'Modes-C-D', 'name': {'family': 'Modes', 'given': 'C. D.'}}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'K.'}, 'orcid': '0000-0003-2908-5469'}, {'id': 'Warner-M', 'name': {'family': 'Warner', 'given': 'M.'}}]}
Year: 2011
DOI: 10.1098/rspa.2010.0352
We discuss methods of reversibly inducing non-developable surfaces from flat sheets of material at the micro-scale all the way to macroscopic
objects. We analyse the elastic ground states of a nematic glass in the
membrane approximation as a function of temperature for disclination
defects of topological charge +1. An aim is to show that by writing an
appropriate director field into such a solid, one could create a
surface with Gaussian curvature, dynamically switchable from flat
sheets while avoiding stretch energy. In addition to the prospect of
programmable structures, such surfaces offer actuation via stretch in
thin systems since when illumination is subsequently removed,
unavoidable stretches return.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/avfx0-tck50A mesh-free convex approximation scheme for Kohn–Sham density functional theory
https://resolver.caltech.edu/CaltechAUTHORS:20110623-074123014
Authors: {'items': [{'id': 'Suryanarayana-P', 'name': {'family': 'Suryanarayana', 'given': 'Phanish'}, 'orcid': '0000-0001-5172-0049'}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'Kaushik'}, 'orcid': '0000-0003-2908-5469'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'Michael'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2011
DOI: 10.1016/j.jcp.2011.03.018
Density functional theory developed by Hohenberg, Kohn and Sham is a widely accepted, reliable ab initio method. We present a non-periodic, real space, mesh-free convex approximation scheme for Kohn–Sham density functional theory. We rewrite the original variational problem as a saddle point problem and discretize it using basis functions which form the Pareto optimum between competing objectives of maximizing entropy and minimizing the total width of the approximation scheme. We show the utility of the approximation scheme in performing both all-electron and pseudopotential calculations, the results of which are in good agreement with literature.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/4s1kv-0ma31Dielectric elastomer composites
https://resolver.caltech.edu/CaltechAUTHORS:20120106-080505466
Authors: {'items': [{'id': 'Tian-L', 'name': {'family': 'Tian', 'given': 'L.'}}, {'id': 'Tevet-Deree-L', 'name': {'family': 'Tevet-Deree', 'given': 'L.'}}, {'id': 'deBotton-G', 'name': {'family': 'deBotton', 'given': 'G.'}, 'orcid': '0000-0003-3608-1896'}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'K.'}, 'orcid': '0000-0003-2908-5469'}]}
Year: 2012
DOI: 10.1016/j.jmps.2011.08.005
The coupled electromechanical response of electroactive dielectric composites is examined in the setting of small deformation and moderate electric field. In this setting, the mechanical stress depends quadratically on the electric field through a combination of material electrostriction and Maxwell stress. It is rigorously shown that the macroscopic mechanical stress of the composite also depends quadratically on the macroscopic electric field. It is further demonstrated that the effective electromechanical coupling can be computed from the examination of the uncoupled electrostatic and elastic problems. The resulting expressions suggest that the effective electromechanical coupling may be very large for microstructures that lead to significant fluctuations of the electric field. This idea is explored through examples involving sequential laminates. It is demonstrated that the electromechanical coupling – the macroscopic strain induced in the composite through the application of a unit electric field – can be amplified by many orders of magnitude by either a combination of constituent materials with high contrast or by making a highly complex and polydisperse microstructure. These findings suggest a path forward for overcoming the main limitation hindering the development of electroactive polymers.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/1ht6y-3g422Evolution of polarization and space charges in semiconducting ferroelectrics
https://resolver.caltech.edu/CaltechAUTHORS:20120410-083810590
Authors: {'items': [{'id': 'Suryanarayana-P', 'name': {'family': 'Suryanarayana', 'given': 'Phanish'}, 'orcid': '0000-0001-5172-0049'}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'Kaushik'}, 'orcid': '0000-0003-2908-5469'}]}
Year: 2012
DOI: 10.1063/1.3678598
Ferroelectric perovskites and polymers that are used in a variety of electronic, ultrasonic, and optical applications are often wide-band-gap semiconductors. We present a time-dependent and thermodynamically consistent theory that describes the evolution of polarization and space charges in such materials. We then use it to show that the semiconducting nature of ferroelectrics can have a profound effect on polarization domain switching, hysteresis, and leakage currents. Further, we show how hysteresis and leakage are affected by doping, film thickness, electrode work function, ambient temperature, and loading frequency.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/njgzw-ynz74Snap-through actuation of thick-wall electroactive balloons
https://resolver.caltech.edu/CaltechAUTHORS:20120515-154428747
Authors: {'items': [{'id': 'Rudykh-S', 'name': {'family': 'Rudykh', 'given': 'Stephan'}}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'Kaushik'}, 'orcid': '0000-0003-2908-5469'}, {'id': 'deBotton-G', 'name': {'family': 'deBotton', 'given': 'Gal'}, 'orcid': '0000-0003-3608-1896'}]}
Year: 2012
DOI: 10.1016/j.ijnonlinmec.2011.05.006
Solution to the problem of a spherical balloon made out of an electroactive polymer which is subjected to coupled mechanical and electrical excitations is determined. It is found that for certain material behaviors instabilities that correspond to abrupt changes in the balloon size can be triggered. This can be exploited to electrically control different actuation cycles as well as to use the balloon as a micro-pump.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/3bpb7-45426Existence of Surface Waves and Band Gaps in Periodic Heterogeneous Half-spaces
https://resolver.caltech.edu/CaltechAUTHORS:20120104-100657316
Authors: {'items': [{'id': 'Hu-L-X', 'name': {'family': 'Hu', 'given': 'L. X.'}}, {'id': 'Liu-L-P', 'name': {'family': 'Liu', 'given': 'L. P.'}}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'K.'}, 'orcid': '0000-0003-2908-5469'}]}
Year: 2012
DOI: 10.1007/s10659-011-9339-0
We find a sufficient condition for the existence of surface (Rayleigh) waves based on the Rayleigh-Ritz variational method. When specialized to a homogeneous half-space, the sufficient condition recovers the known criterion for the existence of subsonic surface waves. A simple existence criterion in terms of material properties is obtained for periodic half-spaces of general anisotropic materials. Further, we numerically compute the dispersion relation of the surface waves for a half-space of periodic laminates of two materials and demonstrate the existence of surface wave band gaps.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/4t1b8-w4639Stability of MultiComponent Biological Membranes
https://resolver.caltech.edu/CaltechAUTHORS:20120518-095511348
Authors: {'items': [{'id': 'Givli-S', 'name': {'family': 'Givli', 'given': 'Sefi'}}, {'id': 'Giang-Ha', 'name': {'family': 'Giang', 'given': 'Ha'}}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'Kaushik'}, 'orcid': '0000-0003-2908-5469'}]}
Year: 2012
DOI: 10.1137/110831301
Equilibrium equations and stability conditions are derived for a general class of multicomponent biological membranes. The analysis is based on a generalized Helfrich energy that
accounts for geometry through the stretch and curvature, the composition, and the interaction between geometry and composition. The use of nonclassical differential operators and related integral theorems in conjunction with appropriate composition and mass conserving variations simplify the derivations. We show that instabilities of multicomponent membranes are significantly different from
those in single component membranes, as well as those in systems undergoing spinodal decomposition in flat spaces. This is due to the intricate coupling between composition and shape as well as the nonuniform tension in the membrane. Specifically, critical modes have high frequencies unlike single component vesicles and stability depends on system size unlike in systems undergoing spinodal
decomposition in flat space. An important implication is that small perturbations may nucleate localized but very large deformations. We show that the predictions of the analysis are in qualitative agreement with experimental observations.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/1bjr9-0d090Elasticity of polydomain liquid crystal elastomers
https://resolver.caltech.edu/CaltechAUTHORS:20120409-152020916
Authors: {'items': [{'id': 'Biggins-J-S', 'name': {'family': 'Biggins', 'given': 'J. S.'}}, {'id': 'Warner-M', 'name': {'family': 'Warner', 'given': 'M.'}}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'K.'}, 'orcid': '0000-0003-2908-5469'}]}
Year: 2012
DOI: 10.1016/j.jmps.2012.01.008
Liquid crystal elastomers are rubbery networks of entropically dominated polymer chains that exhibit mobile liquid crystalline order. These materials have been of recent interest for the soft behavior (large deformations at relatively small stresses) observed in monodomain specimens where the director is the same at every point in the relaxed elastomer. This paper concerns the soft behavior of polydomain specimens where the director points in different directions at different points in the relaxed elastomer. We show that there is a significant difference between polydomains cross-linked in homogeneous high symmetry states then cooled to low symmetry polydomain states and those cross-linked directly in the low symmetry polydomain state. Specifically, elastomers cross-linked in the isotropic state then cooled to a nematic polydomain will, in the ideal limit, be perfectly soft, and with the introduction of non-ideality, will deform at very low stress until they are macroscopically aligned. In fact, we expect these samples to exhibit elasticity significantly softer than monodomain samples, as has recently been observed by Urayama et al. Further, the director patterns will be fine-scale structures that are macroscopically isotropic and not schlieren textures. In contrast, polydomains cross-linked in the nematic polydomain state will be mechanically harder and contain characteristic schlieren director patterns. The models we use for polydomain elastomers are spatially heterogeneous extensions of the neo-classical soft and semi-soft free energies used successfully to describe monodomain samples. We elucidate the effective behavior by bounding the energies using Taylor-like (compatible test strain fields) and Sachs-like (equilibrated stress field) bounds, both valid to large deformations. Good agreement is found with experiments. We also analyze smectic polydomain elastomers and propose that polydomain SmC* elastomers cross-linked in the SmA monodomain state are promising candidates for low field electrical actuation.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/adgtm-hg506Effect of doping on polarization profiles and switching in semiconducting
ferroelectric thin films
https://resolver.caltech.edu/CaltechAUTHORS:20120605-102823159
Authors: {'items': [{'id': 'Shenoy-V-B', 'name': {'family': 'Shenoy', 'given': 'Vivek B.'}}, {'id': 'Xiao-Yu', 'name': {'family': 'Xiao', 'given': 'Yu'}}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'Kaushik'}, 'orcid': '0000-0003-2908-5469'}]}
Year: 2012
DOI: 10.1063/1.3702849
This paper proposes a theory to describe the polarization and switching behavior of ferroelectrics
that are also wide-gap semiconductors. The salient feature of our theory is that it does not make
any a priori assumption about either the space charge distribution or the polarization profile. The
theory is used to study a metal-ferroelectric-metal capacitor configuration, where the ferroelectric
is n-type doped. The main result of our work is a phase diagram as a function of doping level and
thickness that shows different phases, namely, films with polarization profiles that resemble that of
undoped classical ferroelectrics, paraelectric, and a new head-to-tail domain structure. We have
identified a critical doping level, which depends on the energy barrier in the Landau energy and the
built-in potential, which is decided by the electronic structures of both the film and the electrodes.
When the doping level is below this critical value, the behavior of the films is almost classical. We
see a depleted region, which extends through the film when the film thickness is very small, but is
confined to two boundary layers near the electrodes for large film thickness. When the doping level
is higher than the critical value, the behavior is classical for only very thin films. Thicker films at
this doping level are forced into a tail-to-tail configuration with three depletion layers, lose their
ferroelectricity, and may thus be described as nonlinear dielectric or paraelectric. For films which
are doped below the critical level, we show that the field required for switching starts out at the
classical coercive field for very thin films, but gradually decreases.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/7zztj-zm902Toughening and Asymmetry in Peeling of Heterogeneous Adhesives
https://resolver.caltech.edu/CaltechAUTHORS:20120605-104732297
Authors: {'items': [{'id': 'Xia-S', 'name': {'family': 'Xia', 'given': 'S.'}}, {'id': 'Ponson-L', 'name': {'family': 'Ponson', 'given': 'L.'}}, {'id': 'Ravichandran-G', 'name': {'family': 'Ravichandran', 'given': 'G.'}, 'orcid': '0000-0002-2912-0001'}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'K.'}, 'orcid': '0000-0003-2908-5469'}]}
Year: 2012
DOI: 10.1103/PhysRevLett.108.196101
The effective adhesive properties of heterogeneous thin films are characterized through a combined
experimental and theoretical investigation. By bridging scales, we show how variations of elastic or
adhesive properties at the microscale can significantly affect the effective peeling behavior of the adhesive
at the macroscale. Our study reveals three elementary mechanisms in heterogeneous systems involving
front propagation: (i) patterning the elastic bending stiffness of the film produces fluctuations of the
driving force resulting in dramatically enhanced resistance to peeling; (ii) optimized arrangements of
pinning sites with large adhesion energy are shown to control the effective system resistance, allowing the
design of highly anisotropic and asymmetric adhesives; (iii) heterogeneities of both types result in front
motion instabilities producing sudden energy releases that increase the overall adhesion energy. These
findings open potentially new avenues for the design of thin films with improved adhesion properties, and
motivate new investigations of other phenomena involving front propagation.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/c6th0-rs737Coarse-graining Kohn–Sham Density Functional Theory
https://resolver.caltech.edu/CaltechAUTHORS:20121204-074348348
Authors: {'items': [{'id': 'Suryanarayana-P', 'name': {'family': 'Suryanarayana', 'given': 'Phanish'}, 'orcid': '0000-0001-5172-0049'}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'Kaushik'}, 'orcid': '0000-0003-2908-5469'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'Michael'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2013
DOI: 10.1016/j.jmps.2012.09.002
We present a real-space formulation for coarse-graining Kohn–Sham Density Functional Theory that significantly speeds up the analysis of material defects without appreciable loss of accuracy. The approximation scheme consists of two steps. First, we develop a linear-scaling method that enables the direct evaluation of the electron density without the need to evaluate individual orbitals. We achieve this by performing Gauss quadrature over the spectrum of the linearized Hamiltonian operator appearing in each iteration of the self-consistent field method. Building on the linear-scaling method, we introduce a spatial approximation scheme resulting in a coarse-grained Density Functional Theory. The spatial approximation is adapted so as to furnish fine resolution where necessary and to coarsen elsewhere. This coarse-graining step enables the analysis of defects at a fraction of the original computational cost, without any significant loss of accuracy. Furthermore, we show that the coarse-grained solutions are convergent with respect to the spatial approximation. We illustrate the scope, versatility, efficiency and accuracy of the scheme by means of selected examples.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/745vs-5kc97Coarse-graining Kohn-Sham Density Functional Theory
https://resolver.caltech.edu/CaltechAUTHORS:20160316-132823605
Authors: {'items': [{'id': 'Suryanarayana-P', 'name': {'family': 'Suryanarayana', 'given': 'Phanish'}, 'orcid': '0000-0001-5172-0049'}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'Kaushik'}, 'orcid': '0000-0003-2908-5469'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'Michael'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2013
DOI: 10.1016/j.jmps.2012.09.002
We present a real-space formulation for coarse-graining Kohn–Sham Density Functional Theory that significantly speeds up the analysis of material defects without appreciable loss of accuracy. The approximation scheme consists of two steps. First, we develop a linear-scaling method that enables the direct evaluation of the electron density without the need to evaluate individual orbitals. We achieve this by performing Gauss quadrature over the spectrum of the linearized Hamiltonian operator appearing in each iteration of the self-consistent field method. Building on the linear-scaling method, we introduce a spatial approximation scheme resulting in a coarse-grained Density Functional Theory. The spatial approximation is adapted so as to furnish fine resolution where necessary and to coarsen elsewhere. This coarse-graining step enables the analysis of defects at a fraction of the original computational cost, without any significant loss of accuracy. Furthermore, we show that the coarse-grained solutions are convergent with respect to the spatial approximation. We illustrate the scope, versatility, efficiency and accuracy of the scheme by means of selected examples.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/wxqcb-3s146Adhesion of heterogeneous thin films—I: Elastic heterogeneity
https://resolver.caltech.edu/CaltechAUTHORS:20130228-134415560
Authors: {'items': [{'id': 'Xia-S-M', 'name': {'family': 'Xia', 'given': 'S. M.'}}, {'id': 'Ponson-L', 'name': {'family': 'Ponson', 'given': 'L.'}}, {'id': 'Ravichandran-G', 'name': {'family': 'Ravichandran', 'given': 'G.'}, 'orcid': '0000-0002-2912-0001'}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'K.'}, 'orcid': '0000-0003-2908-5469'}]}
Year: 2013
DOI: 10.1016/j.jmps.2012.10.014
We study the adhesion of thin films on rigid substrates in the presence of spatial heterogeneities. While adhesion is relatively well-understood in the context of homogeneous systems, much remains open concerning the adhesion of heterogeneous systems. In this paper, we focus on thin adhesive tape with heterogeneities in the elastic stiffness, and show that these heterogeneities have a profound effect on adhesion raising the effective force required to peel the film by an order of magnitude with no modification of the actual adhesive interface. We show through theory and experiment that this apparent increase is caused by fluctuations in the elastic bending energy. We also show that heterogeneities can be used to create asymmetry in that the force required to peel the tape in one direction can be different from that in the other. In short, this work shows that fluctuations in a small component of the overall energy of the system can give rise to a significant macroscopic consequence. We comment on the broader implications of this observation.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/fy4cd-c2556Parallel edge cracks due to a phase transformation
https://resolver.caltech.edu/CaltechAUTHORS:20130528-085615965
Authors: {'items': [{'id': 'Penmecha-B', 'name': {'family': 'Penmecha', 'given': 'Bharat'}}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'Kaushik'}, 'orcid': '0000-0003-2908-5469'}]}
Year: 2013
DOI: 10.1016/j.ijsolstr.2013.01.027
We study the nucleation and propagation of parallel cracks in the wake of a solid–solid phase boundary. Our results are also applicable to situations where one has a sharp change of concentration or temperature. We identify conditions on the transformation strain when we expect parallel edge cracks. We show that cracks have little affect on the overall evolution of the phase boundary. We also show that cracks nucleate when the phase boundary has propagated a certain distance from the free edge. The cracks have uniform spacing and their tips reach slightly beyond the phase boundary. Subsequently all cracks propagate with the propagating phase boundary in such a manner that the spacing remains uniform and the tips reach just beyond the phase boundary. Importantly, we show that there is no period-doubling or other instabilities common to thermal cracking when the gradient is small.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/b9tpz-r5x41Interplay of martensitic phase transformation and plastic slip in polycrystals
https://resolver.caltech.edu/CaltechAUTHORS:20130802-100002122
Authors: {'items': [{'id': 'Richards-A-W', 'name': {'family': 'Richards', 'given': 'A. W.'}}, {'id': 'Lebensohn-R-A', 'name': {'family': 'Lebensohn', 'given': 'R. A.'}}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'K.'}, 'orcid': '0000-0003-2908-5469'}]}
Year: 2013
DOI: 10.1016/j.actamat.2013.03.053
We study the interplay between martensitic phase transformation and plastic slip in polycrystalline media. The work is motivated by the phenomenon of superelasticity – the ability of the material to recover strains beyond their apparent elastic limit – observed in shape-memory alloys. Often the recovery is not perfect with residual strain after a deformation and recovery cycle, and the stress–strain curve changes with cycling. We develop a mesoscale model at the single crystal level, and use it to study polycrystals. The model is able to reproduce various observations and provide important insight into the interplay. In particular, we show that transformation and plasticity can occur synergistically, with plasticity providing a mechanism for bridging across poorly oriented and thus non-transforming grains.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/wsamq-x8328Fibrous composites of piezoelectric and piezomagnetic phases
https://resolver.caltech.edu/CaltechAUTHORS:20130523-100758825
Authors: {'items': [{'id': 'Kuo-Hsin-Yi', 'name': {'family': 'Kuo', 'given': 'Hsin-Yi'}}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'Kaushik'}, 'orcid': '0000-0003-2908-5469'}]}
Year: 2013
DOI: 10.1016/j.mechmat.2012.12.004
We propose a theoretical framework for evaluation of magnetoelectroelastic potentials in a fibrous composite with piezoelectric and piezomagnetic phases, motivated by the technological desire for materials with large magnetoelectric coupling. We show that the problem with transversely isotropic phases can be decomposed into two independent problems, plane strain with transverse electromagnetic fields and anti-plane shear with in-plane electromagnetic fields. We then consider the second problem in detail, and generalize the classic work of Lord Rayleigh (1892) to obtain the electrostatic potential in an ordered conductive composite and its extension to a disordered system by Kuo and Chen (2008) to the current coupled magnetoelectroelastic problem. We use this method to study BaTiO_3–CoFe_2O_4 composites and provide insights into obtaining large effective magnetoelectric coefficient.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/yb0xn-rbm69Sixtieth anniversary issue in honor of Professor Rodney Hill
https://resolver.caltech.edu/CaltechAUTHORS:20140130-125634637
Authors: {'items': [{'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'Kaushik'}, 'orcid': '0000-0003-2908-5469'}, {'id': 'Gao-Huajian', 'name': {'family': 'Gao', 'given': 'Huajian'}, 'orcid': '0000-0002-8656-846X'}]}
Year: 2014
DOI: 10.1016/j.jmps.2013.09.016
The Journal of Mechanics and Physics of Solids was started in 1952 by Rodney Hill who passed away in 2011. To mark the sixtieth anniversary of the Journal and to pay tribute to the vision of our founder, we dedicate this issue to his memory.
Over the last six decades, the Journal has played a pivotal role in the Mechanics of Solids. The topics of interest have evolved with time, but the basic ethos of publishing research of the highest quality relating to the subject has remained unchanged. To emphasize this, we decided that the Hill Memorial Volume should look to the future. We invited a representative group of eminent but early career researchers to submit their best work to the volume. We are delighted with the manuscripts we have received, and we strongly believe that these articles represent the vitality of the community served by this Journal. The volume also contains an article by the Michael Ortiz related to the Hill Lecture he delivered at the ICTAM in Adelaide as well as the Hill Lecture delivered by Huajian Gao at the ICTAM in Beijing.
This issue also marks a major change in our Board of Editorial Advisors. We have added eight eminent scholars who bring diverse backgrounds to our Board of Editorial Advisors. We have also created a Board of Senior Editorial Advisors, and are fortunate that five distinguished researchers who have been pivotal in guiding the Journal in the past decades have agreed to serve on it.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/j8yez-cbs76Computational analysis of liquid crystalline elastomer membranes: Changing Gaussian curvature without stretch energy
https://resolver.caltech.edu/CaltechAUTHORS:20140102-152736248
Authors: {'items': [{'id': 'Cirak-F', 'name': {'family': 'Cirak', 'given': 'F.'}}, {'id': 'Long-Q', 'name': {'family': 'Long', 'given': 'Q.'}}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'K.'}, 'orcid': '0000-0003-2908-5469'}, {'id': 'Warner-M', 'name': {'family': 'Warner', 'given': 'M.'}}]}
Year: 2014
DOI: 10.1016/j.ijsolstr.2013.09.019
Liquid crystalline elastomers (LCEs) can undergo extremely large reversible shape changes when exposed to external stimuli, such as mechanical deformations, heating or illumination. The deformation of LCEs result from a combination of directional reorientation of the nematic director and entropic elasticity. In this paper, we study the energetics of initially flat, thin LCE membranes by stress driven reorientation of the nematic director. The energy functional used in the variational formulation includes contributions depending on the deformation gradient and the second gradient of the deformation. The deformation gradient models the in-plane stretching of the membrane. The second gradient regularises the non-convex membrane energy functional so that infinitely fine in-plane microstructures and infinitely fine out-of-plane membrane wrinkling are penalised. For a specific example, our computational results show that a non-developable surface can be generated from an initially flat sheet at cost of only energy terms resulting from the second gradients. That is, Gaussian curvature can be generated in LCE membranes without the cost of stretch energy in contrast to conventional materials.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/qyxhz-e1751Linear Scaling DFT for defects in metals
https://resolver.caltech.edu/CaltechAUTHORS:20141124-095544294
Authors: {'items': [{'id': 'Ponga-Mauricio', 'name': {'family': 'Ponga', 'given': 'Mauricio'}, 'orcid': '0000-0001-5058-1454'}, {'id': 'Ariza-Pilar', 'name': {'family': 'Ariza', 'given': 'Pilar'}, 'orcid': '0000-0003-0266-0216'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'Michael'}, 'orcid': '0000-0001-5877-4824'}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'Kaushik'}, 'orcid': '0000-0003-2908-5469'}]}
Year: 2014
DOI: 10.1002/9781118889879.ch35
This work presents a study of defects in solid using Density Functional Theory (DFT) as the only input to predict its information energies. The method used, called the Linnear Scaling Spectral Gauss Quadrature (LSSGQ), has linear scaling with the number of atoms for insulators as well as for metals. This behaviour allows us to stimulate relatively large systems in a fraction of the time demanded by other traditional DFT methods. We demostrate the effectiveness of the method, the linear scaling of large problems and also the size dependence in the formation energy of defects through the simulation of (001) surface relaxation and single vacancy in Body Centered Cubic (BCC) Sodium crystals.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/kv9tb-zp895Applications of Wavelets in the Representation and Prediction of Transformation in Shape-Memory Polycrystals
https://resolver.caltech.edu/CaltechAUTHORS:20150623-085602848
Authors: {'items': [{'id': 'Shmuel- b', 'name': {'family': 'Shmuel', 'given': 'Gal'}}, {'id': 'Thorgeirsson-Adam-Thor', 'name': {'family': 'Thorgeirsson', 'given': 'Adam Thor'}}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'Kaushik'}, 'orcid': '0000-0003-2908-5469'}]}
Year: 2014
DOI: 10.1002/9781118889879.ch64
In recent years, new developments in materials characterization techniques have led to a vast amount of data on the microstructure of polycrystals. Simultaneously,
improvements in computational capabilities have enabled accurate full-field simulations for the micro-mechanical fields developing in polycrystalline aggregates. These show that in phenomena including phase transformation, localized bands of deformation percolate in a complex way across various grains. Our objective is to develop a methodology for analyzing, storing and representing microstructure
data and, in turn, to identify the relevant information dictating the macroscopic behavior in superelastic polycrystals. To this end, wavelets are used in a case
study of a polycrystalline aggregate in anti-plane shear. It is demonstrated how the transformation fields developing within the material can be efficiently represented by thresholding their wavelet expansion, maintaining more than 90% of the L_2 norm of the original field, while using approximately 10% of the number of terms in the original data. The macroscopic stress-strain relation resulting from
solving the governing equations using a thresholded transformation strain is shown to be in a good agreement with the exact relation. Finally, the set of the functions
retained in the expansion after thresholding was found to be similar in adjacent loading steps. Motivated by these observations, we propose a new wavelet-based algorithm for calculating the developing fields in phase transforming polycrystals.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/jb1tn-mtd29Multiscale instabilities in soft heterogeneous dielectric elastomers
https://resolver.caltech.edu/CaltechAUTHORS:20140422-105630959
Authors: {'items': [{'id': 'Rudykh-S', 'name': {'family': 'Rudykh', 'given': 'S.'}}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'K.'}, 'orcid': '0000-0003-2908-5469'}, {'id': 'deBotton-G', 'name': {'family': 'deBotton', 'given': 'G.'}, 'orcid': '0000-0003-3608-1896'}]}
Year: 2014
DOI: 10.1098/rspa.2013.0618
The development of instabilities in soft heterogeneous dielectric elastomers is investigated. Motivated by experiments and possible applications, we use in our analysis the physically relevant referential electric field instead of electric displacement. In terms of this variable, a closed form solution is derived for the class of layered neo-Hookean dielectrics. A criterion for the onset of electromechanical multiscale instabilities for the layered composites with anisotropic phases is formulated. A general condition for the onset of the macroscopic instability in soft multiphase dielectrics is introduced. In the example of the layered dielectrics, the essential influence of the microstructure on the onset of instabilities is revealed. We found that: (i) macroscopic instabilities dominate at moderate volume fractions of the stiffer phase, (ii) interface instabilities appear at small volume fractions of the stiffer phase and (iii) instabilities of a finite scale, comparable to the microstructure size, occur at large volume fractions of the stiffer phase. The latest new type of instabilities does not appear in the purely mechanical case and dominates in the region of large volume fractions of the stiff phase.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/xeee9-v3f33Wavelet analysis of microscale strains
https://resolver.caltech.edu/CaltechAUTHORS:20140911-091253456
Authors: {'items': [{'id': 'Shmuel-G', 'name': {'family': 'Shmuel', 'given': 'Gal'}}, {'id': 'Thorgeirsson-A-T', 'name': {'family': 'Thorgeirsson', 'given': 'Adam Thor'}}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'Kaushik'}, 'orcid': '0000-0003-2908-5469'}]}
Year: 2014
DOI: 10.1016/j.actamat.2014.05.018
Recent improvements in experimental and computational techniques have led to a vast amount of data on the microstructure and deformation of polycrystals. These show that, in a number of phenomena, including phase transformation, localized bands of deformation percolate in a complex way across various grains. Often, this information is given as point-wise values arrayed in pixels, voxels and grids. The massive extent of data in this form renders identifying key features difficult and the cost of digital storage expensive. This work explores the efficiency of wavelets in storing, representing and analyzing such data on shape-memory polycrystals as a specific example. It is demonstrated how a compact wavelet representation captures the essential physics contained in experimental and simulated strains in superelastic media.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/51bfk-dvy78Transformation strains and temperatures of a nickel–titanium–hafnium high temperature shape memory alloy
https://resolver.caltech.edu/CaltechAUTHORS:20140911-142231035
Authors: {'items': [{'id': 'Stebner-A-P', 'name': {'family': 'Stebner', 'given': 'Aaron P.'}}, {'id': 'Bigelow-G-S', 'name': {'family': 'Bigelow', 'given': 'Glen S.'}}, {'id': 'Yang-Jin', 'name': {'family': 'Yang', 'given': 'Jin'}}, {'id': 'Shukla-D-P', 'name': {'family': 'Shukla', 'given': 'Dhwanil P.'}}, {'id': 'Saghaian-S-M', 'name': {'family': 'Saghaian', 'given': 'Sayed M.'}}, {'id': 'Rogers-R', 'name': {'family': 'Rogers', 'given': 'Richard'}}, {'id': 'Garg-A', 'name': {'family': 'Garg', 'given': 'Anita'}}, {'id': 'Karaca-H-E', 'name': {'family': 'Karaca', 'given': 'Haluk E.'}}, {'id': 'Chumlyakov-Y', 'name': {'family': 'Chumlyakov', 'given': 'Yuriy'}}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'Kaushik'}, 'orcid': '0000-0003-2908-5469'}, {'id': 'Noebe-R-D', 'name': {'family': 'Noebe', 'given': 'Ronald D.'}}]}
Year: 2014
DOI: 10.1016/j.actamat.2014.04.071
A combined experimental and theoretical investigation of the transformation temperature and transformation strain behaviors of a promising new Ni_(50.3)Ti_(29.7)Hf_(20) high-temperature shape memory alloy was conducted. Actuation behavior of single crystals with loading orientations near [001]_(B2), [110]_(B2), and [111]_(B2), as well as polycrystalline material in aged and unaged conditions was studied, together with the superelastic, polycrystalline torsion response. These results were compared to analytic calculations of the ideal transformation strains for tension, compression, and torsion loading of single crystals as a function of single crystal orientation, and polycrystalline material of common processing textures. H-phase precipitates on the order of 10–30 nm were shown to increase transformation temperatures and also to narrow thermal hysteresis, compared to unaged material. The mechanical effects of increased residual stresses and numbers of transformation nucleation sites caused by the precipitates provide a plausible explanation for the observed transformation temperature trends. Grain boundaries were shown to have similar effects on transformation temperatures. The work output and recoverable strain exhibited by the alloy were shown to approach maximums at stresses of 500–800 MPa, suggesting these to be optimal working loads with respect to single cycle performance. The potential for transformation strain in single crystals of this material was calculated to be superior to binary NiTi in tension, compression, and torsion loading modes. However, the large volume fraction of precipitate phase, in part, prevents the material from realizing its full single crystal transformation strain potential in return for outstanding functional stability by inhibiting plastic strain accumulation during transformation. Finally, calculations showed that of the studied polycrystalline textures, [001]_(B2) fiber texture results in superior torsion performance, while [011]_(B2) fiber texture results in superior tensile behavior, and both [011]_(B2) and random textures will result in the best possible compression performance.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/ekye8-ng212Shock wave propagation through a model one dimensional heterogeneous medium
https://resolver.caltech.edu/CaltechAUTHORS:20141023-102817916
Authors: {'items': [{'id': 'Agrawal-V', 'name': {'family': 'Agrawal', 'given': 'Vinamra'}}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'Kaushik'}, 'orcid': '0000-0003-2908-5469'}]}
Year: 2014
DOI: 10.1016/j.ijsolstr.2014.06.021
We study the problem of impact-induced shock wave propagation through a model one-dimensional heterogeneous medium. This medium is made of a model material with spatially varying parameters such that it is heterogeneous to shock waves but homogeneous to elastic waves. Using the jump conditions and maximal dissipation criteria, we obtain the exact solution to the shock propagation problem. We use it to study how the nature of the heterogeneity changes material response, the structure of the shock front and the dissipation.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/tv97r-myd41Effective toughness of heterogeneous media
https://resolver.caltech.edu/CaltechAUTHORS:20141120-101117142
Authors: {'items': [{'id': 'Hossain-M-Z', 'name': {'family': 'Hossain', 'given': 'M. Z.'}}, {'id': 'Hsueh-C-J', 'name': {'family': 'Hsueh', 'given': 'C.-J.'}}, {'id': 'Bourdin-B', 'name': {'family': 'Bourdin', 'given': 'B.'}}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'K.'}, 'orcid': '0000-0003-2908-5469'}]}
Year: 2014
DOI: 10.1016/j.jmps.2014.06.002
We propose a versatile approach to computing the effective toughness of heterogeneous media. This approach focusses on the material property independent of the details of the boundary condition. The key idea is what we call a surfing boundary condition, where a steadily propagating crack opening displacement is applied as a boundary condition to a large domain while the crack set is allowed to evolve as it chooses. The approach is verified and used to study examples in brittle fracture. We demonstrate that effective toughness is different from effective or weighted surface area of the crack set. Furthermore, we demonstrate that elastic heterogeneity can have a profound effect on fracture toughness: it can be a significant toughening mechanism and it can lead to toughness asymmetry wherein the toughness depends not only on the direction but also on the sense of propagation. The role of length-scale is also discussed.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/47xca-3ge08A phase-field approach for the modeling of nematic liquid crystal elastomers
https://resolver.caltech.edu/CaltechAUTHORS:20170330-074710264
Authors: {'items': [{'id': 'Keip-M-A', 'name': {'family': 'Keip', 'given': 'Marc-André'}}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'Kaushik'}, 'orcid': '0000-0003-2908-5469'}]}
Year: 2014
DOI: 10.1002/pamm.201410276
Liquid crystal elastomers combine the elastic properties of rubber with the orientational properties of liquid crystals. Amongst the various types of liquid crystal elastomers, nematic elastomers are one special class. Nematic elastomers undergo a phase transition from a high-temperature isotropic state to a low-temperature nematic state, which is generally accompanied by large deformations. In the present contribution, a phase-field model for the continuum-mechanical description of nematic elastomers will be introduced. The model is implemented into the finite element method and employed for the simulation of domain evolution under specified initial boundary conditions.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/csz64-tp719A Phase Field Approach for Martensitic Transformations and Crystal Plasticity
https://resolver.caltech.edu/CaltechAUTHORS:20170330-082031305
Authors: {'items': [{'id': 'Schmitt-R', 'name': {'family': 'Schmitt', 'given': 'Regina'}}, {'id': 'Mayer-P', 'name': {'family': 'Mayer', 'given': 'Patrick'}}, {'id': 'Kirsch-B', 'name': {'family': 'Kirsch', 'given': 'Benjamin'}}, {'id': 'Aurich-J', 'name': {'family': 'Aurich', 'given': 'Jan'}}, {'id': 'Kuhn-C', 'name': {'family': 'Kuhn', 'given': 'Charlotte'}}, {'id': 'Müller-R', 'name': {'family': 'Müller', 'given': 'Ralf'}}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'Kaushik'}, 'orcid': '0000-0003-2908-5469'}]}
Year: 2014
DOI: 10.1002/pamm.201410179
This work is motivated by cryogenic turning which allows end shape machining and simultaneously attaining a hardened surface due to deformation induced martensitic transformations. To study the process on the microscale, a multivariant phase field model for martensitic transformations in conjunction with a crystal plastic material model is introduced. The evolution of microstructure is assumed to follow a time-dependent Ginzburg-Landau equation. To solve the field equations the finite element method is used. Time integration is performed with Euler backward schemes, on the global level for the evolution equation of the phase field, and on the element level for the crystal plastic material law.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/bs0rd-69s31A model coupling plasticity and phase transformation with application to dynamic shear deformation of iron
https://resolver.caltech.edu/CaltechAUTHORS:20150205-140856431
Authors: {'items': [{'id': 'Sadjadpour-A', 'name': {'family': 'Sadjadpour', 'given': 'Amir'}}, {'id': 'Rittel-D', 'name': {'family': 'Rittel', 'given': 'Daniel'}}, {'id': 'Ravichandran-G', 'name': {'family': 'Ravichandran', 'given': 'Guruswami'}, 'orcid': '0000-0002-2912-0001'}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'Kaushik'}, 'orcid': '0000-0003-2908-5469'}]}
Year: 2015
DOI: 10.1016/j.mechmat.2014.04.010
A simple model that brings together well-established thermo-mechanical models of plasticity with those of martensitic phase transformation into a single thermodynamic framework is proposed. The presentation is in one space dimension, but the framework is general so that the model may be extended to higher dimensions. The model is used to study recent experiments on the α⇔∊ martensitic phase transformation of pure iron under dynamic, shear-dominant loading conditions. It is shown that the model fitted to established thermodynamic data and selected experiments is able to reproduce the experimental observations in a wide range of loading rates ranging from quasistatic to 10^4 s^−1 as well as a wide range of phenomena ranging including overall rate hardening and thermal softening. In doing so, the model also provides new insight into the α⇔∊α⇔∊ phase transformation in iron.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/jevgn-nwc08Collective behavior of viscoelastic asperities as a model for static and kinetic friction
https://resolver.caltech.edu/CaltechAUTHORS:20140603-102932593
Authors: {'items': [{'id': 'Hulikal-S', 'name': {'family': 'Hulikal', 'given': 'Srivatsan'}}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'Kaushik'}, 'orcid': '0000-0003-2908-5469'}, {'id': 'Lapusta-N', 'name': {'family': 'Lapusta', 'given': 'Nadia'}, 'orcid': '0000-0001-6558-0323'}]}
Year: 2015
DOI: 10.1016/j.jmps.2014.10.008
We propose a statistical model for static and sliding friction between rough surfaces. Approximating the contact between rough surfaces by the contact of an ensemble of one-dimensional viscoelastic elements with a rough rigid surface, we study the collective behavior of the elements. We find that collective response of the contacts can lead to macroscopic behavior very different from the microscopic behavior. Specifically, various observed features of friction emerge as collective phenomena, without postulating them directly at the microscale. We discuss how parameters in our model can be related to material and surface properties of the contacting surfaces. We compare our results to commonly used rate and state phenomenological models, and propose a new interpretation of the state variable.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/vep55-wns78The Influence of the R-Phase on the Superelastic Behavior of NiTi
https://resolver.caltech.edu/CaltechAUTHORS:20170616-104220103
Authors: {'items': [{'id': 'Duerig-T-W', 'name': {'family': 'Duerig', 'given': 'T. W.'}}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'K.'}, 'orcid': '0000-0003-2908-5469'}]}
Year: 2015
DOI: 10.1007/s40830-015-0013-4
Approximately equiatomic Ni–Ti alloys, or Nitinol, can transform upon cooling or when stressed from a parent ordered cubic (B2) Austenite phase into two martensitic structures: a monoclinic structure commonly referred to as simply martensite and a rhombohedrally distorted martensite referred to as the R-phase. While the former is often more stable, the R-phase presents a substantially lower barrier to formation, creating an interesting competition for the succession of Austenite. This competition has markedly different outcomes depending upon whether Austenite instability is caused by cooling or by the application of stress. While medical applications are generally used isothermally, most characterization is done using thermal scans such as differential scanning calorimetry. This leads to frequent and significant misunderstandings regarding plateau stresses in particular. The purpose of this paper is to discuss the competition between these two martensites as the parent Austenite phase loses stability, and to clarify how tests can be properly conducted and interpreted to avoid confusion. To that end, the examples shown are not selected to be ideal or theoretical, but rather to illustrate complexities typical of those found in medical devices, such as cold worked conditions that make peaks difficult to interpret and "plateaus" ill-defined. Finally, a stress-induced M ⇒ R ⇒ M sequence will be discussed.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/zrv0z-72225Adhesion of heterogeneous thin films II: Adhesive heterogeneity
https://resolver.caltech.edu/CaltechAUTHORS:20151030-095316823
Authors: {'items': [{'id': 'Xia-S-M', 'name': {'family': 'Xia', 'given': 'S. M.'}}, {'id': 'Ponson-L', 'name': {'family': 'Ponson', 'given': 'L.'}}, {'id': 'Ravichandran-G', 'name': {'family': 'Ravichandran', 'given': 'G.'}, 'orcid': '0000-0002-2912-0001'}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'K.'}, 'orcid': '0000-0003-2908-5469'}]}
Year: 2015
DOI: 10.1016/j.jmps.2015.06.010
This paper continues the study of the effective adhesion of thin films on rigid substrates in the presence of spatial heterogeneities started in Xia et al. (2013). In this paper, we focus on thin adhesive tape with spatial heterogeneity in the adhesive strength. This heterogeneity leads to a wavy peel front and consequently a complex corrugated shape in the tape. We develop a theory for the evolution of the peel front that accounts for this complex interaction, and an experimental method that is able to examine this in detail. We show through theory and experimentation that spatial patterning of the adhesive strength can lead to a very rich range of behaviors in the effective adhesive strength. In particular we show that adhesive heterogeneity can be used to create asymmetry in that the force required to peel the tape in one direction can be different from that in the other.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/3jdfh-jqp62Effective Behavior of Nematic Elastomer Membranes
https://resolver.caltech.edu/CaltechAUTHORS:20150825-104728003
Authors: {'items': [{'id': 'Cesana-P', 'name': {'family': 'Cesana', 'given': 'Pierluigi'}}, {'id': 'Plucinsky-P', 'name': {'family': 'Plucinsky', 'given': 'Paul'}, 'orcid': '0000-0003-2060-8657'}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'Kaushik'}, 'orcid': '0000-0003-2908-5469'}]}
Year: 2015
DOI: 10.1007/s00205-015-0871-0
We derive the effective energy density of thin membranes of liquid crystal elastomers as the Γ -limit of a widely used bulk model. These membranes can display fine-scale features both due to wrinkling that one expects in thin elastic membranes and due to oscillations in the nematic director that one expects in liquid crystal elastomers. We provide an explicit characterization of the effective energy density of membranes and the effective state of stress as a function of the planar deformation gradient. We also provide a characterization of the fine-scale features. We show the existence of four regimes: one where wrinkling and microstructure reduces the effective membrane energy and stress to zero, a second where wrinkling leads to uniaxial tension, a third where nematic oscillations lead to equi-biaxial tension and a fourth with no fine scale features and biaxial tension. Importantly, we find a region where one has shear strain but no shear stress and all the fine-scale features are in-plane with no wrinkling.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/6ym5k-7d947Measuring the Effective Fracture Toughness of Heterogeneous Materials
https://resolver.caltech.edu/CaltechAUTHORS:20160211-094810104
Authors: {'items': [{'id': 'Hsueh-Chun-Jen', 'name': {'family': 'Hsueh', 'given': 'Chun-Jen'}}, {'id': 'Ravichandran-G', 'name': {'family': 'Ravichandran', 'given': 'Guruswami'}, 'orcid': '0000-0002-2912-0001'}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'Kaushik'}, 'orcid': '0000-0003-2908-5469'}]}
Year: 2016
DOI: 10.1007/978-3-319-21611-9_19
Heterogeneous materials where the scale of the heterogeneities is small compared to the scale of applications are common in nature. These materials are also engineered synthetically with the aim of improving performance. The overall properties of heterogeneous materials can be different from those of its constituents; however, it is challenging to characterize effective fracture toughness of these materials. We present a new method of experimentally determining the effective fracture toughness. The key idea is to impose a steady process at the macroscale while allowing the fracture process to freely explore at the level of microstructure. We apply a time-dependent displacement boundary condition called the surfing boundary condition that corresponds to a steadily propagating macroscopic crack opening displacement. We then measure the full-field displacement using digital image correlation (DIC) method, and use it to obtain the macroscopic energy release rate. In particular, we develop a global approach to extract information from DIC. The effective toughness is obtained at the peak of the energy release rate. Finally, the full field images also provide us insight into the role of the microstructure in determining effective toughness.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/p1yq5-1fh78Effective behavior of an interface propagating through a periodic elastic medium
https://resolver.caltech.edu/CaltechAUTHORS:20160701-103557323
Authors: {'items': [{'id': 'Dondl-P-W', 'name': {'family': 'Dondl', 'given': 'Patrick W.'}}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'Kaushik'}, 'orcid': '0000-0003-2908-5469'}]}
Year: 2016
DOI: 10.4171/IFB/358
We consider a moving interface that is coupled to an elliptic equation in a heterogeneous medium. The problem is motivated by the study of displacive solid-solid phase transformations. We show that a nearly flat interface is given by the graph of the function g which evolves according to the equation g_t(x)=−(−Δ)^(1/2)g(x)+φ(x,g(x))+F. This equation also arises in the study of dislocations and fracture. We show in the periodic setting that such interfaces exhibit a stick-slip behavior associated with pinning and depinning. Further, we present some numerical evidence that the effective velocity of the phase boundary scales as the square-root of the excess macroscopic force above the depinning transition.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/536hy-9xa51Length scales and pinning of interfaces
https://resolver.caltech.edu/CaltechAUTHORS:20160328-104058900
Authors: {'items': [{'id': 'Tan-L', 'name': {'family': 'Tan', 'given': 'Likun'}}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'Kaushik'}, 'orcid': '0000-0003-2908-5469'}]}
Year: 2016
DOI: 10.1098/rsta.2015.0167
The pinning of interfaces and free discontinuities by defects and heterogeneities plays an important role in a variety of phenomena, including grain growth, martensitic phase transitions, ferroelectricity, dislocations and fracture. We explore the role of length scale on the pinning of interfaces and show that the width of the interface relative to the length scale of the heterogeneity can have a profound effect on the pinning behaviour, and ultimately on hysteresis. When the heterogeneity is large, the pinning is strong and can lead to stick–slip behaviour as predicted by various models in the literature. However, when the heterogeneity is small, we find that the interface may not be pinned in a significant manner. This shows that a potential route to making materials with low hysteresis is to introduce heterogeneities at a length scale that is small compared with the width of the phase boundary. Finally, the intermediate setting where the length scale of the heterogeneity is comparable to that of the interface width is characterized by complex interactions, thereby giving rise to a non-monotone relationship between the relative heterogeneity size and the critical depinning stress.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/pewbj-enw86Origin of undesirable cracks during layer transfer
https://resolver.caltech.edu/CaltechAUTHORS:20160322-074244346
Authors: {'items': [{'id': 'Ponson-L', 'name': {'family': 'Ponson', 'given': 'L.'}}, {'id': 'Diest-K', 'name': {'family': 'Diest', 'given': 'K.'}}, {'id': 'Atwater-H-A', 'name': {'family': 'Atwater', 'given': 'H. A.'}, 'orcid': '0000-0001-9435-0201'}, {'id': 'Ravichandran-G', 'name': {'family': 'Ravichandran', 'given': 'G.'}, 'orcid': '0000-0002-2912-0001'}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'K.'}, 'orcid': '0000-0003-2908-5469'}]}
Year: 2016
DOI: 10.48550/arXiv.0810.5053
We investigate the origin of undesirable transverse cracks often observed in thin films obtained by the layer transfer technique. During this process, two crystals bonded to each other containing a weak plan produced by ion implantation are heated to let a thin layer of one of the material on the other. The level of stress imposed on the film during the heating phase due to the mismatch of thermal expansion coefficients of the substrate and the film is shown to be the relevant parameter of the problem. In particular, it is shown that if the film is submitted to a tensile stress, the microcracks produced by ion implantation are not stable and deviate from their straight trajectory making the layer transfer process impossible. However, if the compressive stress exceeds a threshold value, after layer transfer, the film can buckle and delaminate, leading to transverse cracks induced by bending. As a result, we show that the imposed stress σ_m - or equivalently the heating temperature - must be within the range -σ_c < σ_m < 0 to produce an intact thin film where σ_c depends on the interfacial fracture energy and the size of defects at the interface between film and substrate.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/3b0d5-g6s72Morphing surfaces for the control of boundary layer transition
https://resolver.caltech.edu/CaltechAUTHORS:20200224-133536093
Authors: {'items': [{'id': 'McKeon-B-J', 'name': {'family': 'McKeon', 'given': 'Beverley'}, 'orcid': '0000-0003-4220-1583'}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'Kaushik'}, 'orcid': '0000-0003-2908-5469'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'Michael'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2016
A structure configured to modify its surface morphology between a smooth state and a rough state in response to an applied stress. In demonstrated examples, a soft (PDMS) substrate is produced, and is pre-strained. A relatively stiff overlayer of a metal, such as chromium and gold, is applied to the substrate. When the pre-strained substrate is allowed to relax, the free surface of the stiff overlayer is forced to become distorted, yielding a free surface having a roughness of less than 1 millimeter. Repeated application and removal of the applied stress has been shown to yield reproducible changes in the morphology of the free surface. An application of such morphing free surface is to control a boundary layer transition of an aerodynamic fluid flowing over the surface.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/91ahb-x7g76Programming complex shapes in thin nematic elastomer and glass sheets
https://resolver.caltech.edu/CaltechAUTHORS:20160729-124907729
Authors: {'items': [{'id': 'Plucinsky-P', 'name': {'family': 'Plucinsky', 'given': 'Paul'}, 'orcid': '0000-0003-2060-8657'}, {'id': 'Lemm-M', 'name': {'family': 'Lemm', 'given': 'Marius'}}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'Kaushik'}, 'orcid': '0000-0003-2908-5469'}]}
Year: 2016
DOI: 10.1103/PhysRevE.94.010701
Nematic elastomers and glasses are solids that display spontaneous distortion under external stimuli. Recent advances in the synthesis of sheets with controlled heterogeneities have enabled their actuation into nontrivial shapes with unprecedented energy density. Thus, these have emerged as powerful candidates for soft actuators. To further this potential, we introduce the key metric constraint which governs shape-changing actuation in these sheets. We then highlight the richness of shapes amenable to this constraint through two broad classes of examples which we term nonisometric origami and lifted surfaces. Finally, we comment on the derivation of the metric constraint, which arises from energy minimization in the interplay of stretching, bending, and heterogeneity in these sheets.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/1c50f-4zy46Plates with Incompatible Prestrain
https://resolver.caltech.edu/CaltechAUTHORS:20160509-105130410
Authors: {'items': [{'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'Kaushik'}, 'orcid': '0000-0003-2908-5469'}, {'id': 'Lewicka-M', 'name': {'family': 'Lewicka', 'given': 'Marta'}}, {'id': 'Schäffner-M', 'name': {'family': 'Schäffner', 'given': 'Mathias'}}]}
Year: 2016
DOI: 10.1007/s00205-015-0958-7
We study effective elastic behavior of the incompatibly prestrained thin plates, where the prestrain is independent of thickness and uniform through the plate's thickness h. We model such plates as three-dimensional elastic bodies with a prescribed pointwise stress-free state characterized by a Riemannian metric G, and seek the limiting behavior as h→0. We first establish that when the energy per volume scales as the second power of h, the resulting Γ-limit is a Kirchhoff-type bending theory. We then show the somewhat surprising result that there exist non-immersible metrics G for whom the infimum energy (per volume) scales smaller than h^2. This implies that the minimizing sequence of deformations carries nontrivial residual three-dimensional energy but it has zero bending energy as seen from the limit Kirchhoff theory perspective. Another implication is that other asymptotic scenarios are valid in appropriate smaller scaling regimes of energy. We characterize the metrics G with the above property, showing that the zero bending energy in the Kirchhoff limit occurs if and only if the Riemann curvatures R_(1213), R_(1223) and R_(1212) of G vanish identically. We illustrate our findings with examples; of particular interest is an example where G_(2×2), the two-dimensional restriction of G, is flat but the plate still exhibits the energy scaling of the Föppl–von Kármán type. Finally, we apply these results to a model of nematic glass, including a characterization of the condition when the metric is immersible, for G=Id_3+γn⊗n given in terms of the inhomogeneous unit director field distribution n∈R^3.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/035e4-d6993Dynamic behavior of nano-voids in magnesium under hydrostatic tensile stress
https://resolver.caltech.edu/CaltechAUTHORS:20160729-162325302
Authors: {'items': [{'id': 'Ponga-M', 'name': {'family': 'Ponga', 'given': 'Mauricio'}, 'orcid': '0000-0001-5058-1454'}, {'id': 'Ramabathiran-A-A', 'name': {'family': 'Ramabathiran', 'given': 'Amuthan A.'}}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'Kaushik'}, 'orcid': '0000-0003-2908-5469'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'Michael'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2016
DOI: 10.1088/0965-0393/24/6/065003
We investigate the mechanisms responsible for nano-void growth in single crystal magnesium under dynamic hydrostatic tensile stress. A key conclusion derived from our study is that there is no secondary strain hardening near the nano-void. This behavior, which is in remarkable contrast to face-centered cubic and body-centered cubic materials, greatly limits the peak stress and explains the relatively lower spall strength of magnesium. The lack of secondary strain hardening is due to the fact that pyramidal dislocations do not interact with basal or prismatic dislocations. Our analysis also shows that for loads applied at moderate strain rates (ϵ ⩽ 10^6 s^(−1)) the peak stress, dislocation velocity and temperature distribution converge asymptotically. However at very high strain rates (ϵ ⩾ 10^8 s^(−1)), there is a sharp transition in these quantities.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/8wm9s-5n146A Variational Framework for Spectral Approximations of Kohn–Sham Density Functional Theory
https://resolver.caltech.edu/CaltechAUTHORS:20160523-075651915
Authors: {'items': [{'id': 'Wang-Xin-Cindy', 'name': {'family': 'Wang', 'given': 'Xin-Cindy'}, 'orcid': '0000-0003-3854-4831'}, {'id': 'Blesgen-T', 'name': {'family': 'Blesgen', 'given': 'Thomas'}}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'Kaushik'}, 'orcid': '0000-0003-2908-5469'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'Michael'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2016
DOI: 10.1007/s00205-016-0978-y
We reformulate the Kohn–Sham density functional theory (KSDFT) as a nested variational problem in the one-particle density operator, the electrostatic potential and a field dual to the electron density. The corresponding functional is linear in the density operator and thus amenable to spectral representation. Based on this reformulation, we introduce a new approximation scheme, termed spectral binning, which does not require smoothing of the occupancy function and thus applies at arbitrarily low temperatures. We prove convergence of the approximate solutions with respect to spectral binning and with respect to an additional spatial discretization of the domain.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/1qh75-bs514Investigating the Effective Fracture Toughness of Heterogeneous Materials
https://resolver.caltech.edu/CaltechAUTHORS:20161108-142119224
Authors: {'items': [{'id': 'Hsueh-Chun-Jen', 'name': {'family': 'Hsueh', 'given': 'Chun-Jen'}}, {'id': 'Ravichandran-G', 'name': {'family': 'Ravichandran', 'given': 'Guruswami'}, 'orcid': '0000-0002-2912-0001'}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'Kaushik'}, 'orcid': '0000-0003-2908-5469'}]}
Year: 2016
DOI: 10.1007/978-3-319-42195-7_3
Heterogeneous materials are ubiquitous in nature, and are increasingly being engineered to obtain desirable mechanical properties. Naturally, the bulk properties of a heterogeneous material can be different from those of its constituents. Thus, one needs to determine its overall or effective properties. For some of these properties, like effective elastic modulus, the characterization is well-known, while for other such as effective fracture toughness, it is a matter of ongoing research. In this paper, we present a method to measure the effective fracture toughness. For the method, we apply a time-dependent displacement condition called the surfing boundary condition. This boundary condition leads the crack to propagate steadily macroscopically but in an unconstrained manner microscopically. We then use the grid method, a non-contact full-field displacement measurement technique, to obtain the displacement gradient. With this field, we compute the macroscopic energy release rate via the area J-integral. Finally, we interpret the effective toughness as the peak of the energy release rate. Using this method, we investigate the influence of heterogeneity on effective fracture toughness. We find that the effective toughness can be enhanced due to the heterogeneity. Consequently, engineered heterogeneity may provide a means to improve fracture toughness in solids.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/n9jzn-v0q21Homogenization and Path Independence of the J-Integral in Heterogeneous Materials
https://resolver.caltech.edu/CaltechAUTHORS:20161017-154928755
Authors: {'items': [{'id': 'Hsueh-Chun-Jen', 'name': {'family': 'Hsueh', 'given': 'Chun-Jen'}}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'Kaushik'}, 'orcid': '0000-0003-2908-5469'}]}
Year: 2016
DOI: 10.1115/1.4034294
The J-integral that determines the driving force on a crack tip is a central concept of fracture mechanics. It is particularly useful since it is path independent in homogeneous materials. However, most materials are heterogeneous at a microscopic scale, and the J-integral is not necessarily path independent in heterogeneous media. In this paper, we prove the existence of an effective J-integral in heterogeneous media, show that it can be computed from the knowledge of the macroscopic or homogenized displacement fields and that it is path independent in macroscopically homogeneous media as long as the contours are large compared to the length scale of the heterogeneities. This result justifies the common engineering use of the J-integral.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/1pk2q-bfr53A sublinear-scaling approach to density-functional-theory analysis of crystal defects
https://resolver.caltech.edu/CaltechAUTHORS:20161006-104337036
Authors: {'items': [{'id': 'Ponga-M', 'name': {'family': 'Ponga', 'given': 'M.'}, 'orcid': '0000-0001-5058-1454'}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'K.'}, 'orcid': '0000-0003-2908-5469'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2016
DOI: 10.1016/j.jmps.2016.05.029
We develop a sublinear-scaling method, referred to as MacroDFT, for the study of crystal defects using ab-initio Density Functional Theory (DFT). The sublinear scaling is achieved using a combination of the Linear Scaling Spectral Gauss Quadrature method (LSSGQ) and a Coarse-Graining approach (CG) based on the quasi-continuum method. LSSGQ reformulates DFT and evaluates the electron density without computing individual orbitals. This direct evaluation is possible by recourse to Gaussian quadrature over the spectrum of the linearized Hamiltonian operator. Furthermore, the nodes and weights of the quadrature can be computed independently for each point in the domain. This property is exploited in CG, where fields of interest are computed at selected nodes and interpolated elsewhere. In this paper, we present the MacroDFT method, its parallel implementation and an assessment of convergence and performance by means of test cases concerned with point defects in magnesium.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/gnfy7-ppc38A threshold-force model for adhesion and mode I fracture
https://resolver.caltech.edu/CaltechAUTHORS:20161012-160619944
Authors: {'items': [{'id': 'Hulikal-S', 'name': {'family': 'Hulikal', 'given': 'Srivatsan'}}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'Kaushik'}, 'orcid': '0000-0003-2908-5469'}, {'id': 'Lapusta-N', 'name': {'family': 'Lapusta', 'given': 'Nadia'}, 'orcid': '0000-0001-6558-0323'}]}
Year: 2016
DOI: 10.48550/arXiv.1606.03166
We study the relation between a threshold-force based model at the microscopic scale and mode I fracture at the macroscopic scale in a system of discrete interacting springs. Specifically, we idealize the contact between two surfaces as that between a rigid surface and a collection of springs with long-range interaction and a constant tensile threshold force. We show that a particular scaling similar to that of crack-tip stress in Linear Elastic Fracture Mechanics leads to a macroscopic limit behavior. The model also reproduces the scaling behaviors of the JKR model of adhesive contact. We determine how the threshold force depends on the fracture energy and elastic properties of the material. The model can be used to study rough-surface adhesion.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/k0b54-psh43A micromechanics-inspired constitutive model for shape-memory alloys that accounts for initiation and saturation of phase transformation
https://resolver.caltech.edu/CaltechAUTHORS:20160328-095717320
Authors: {'items': [{'id': 'Kelly-A', 'name': {'family': 'Kelly', 'given': 'Alex'}}, {'id': 'Stebner-A-P', 'name': {'family': 'Stebner', 'given': 'Aaron P.'}}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'Kaushik'}, 'orcid': '0000-0003-2908-5469'}]}
Year: 2016
DOI: 10.1016/j.jmps.2016.02.007
A constitutive model to describe macroscopic elastic and transformation behaviors of polycrystalline shape-memory alloys is formulated using an internal variable thermodynamic framework. In a departure from prior phenomenological models, the proposed model treats initiation, growth kinetics, and saturation of transformation distinctly, consistent with physics revealed by recent multi-scale experiments and theoretical studies. Specifically, the proposed approach captures the macroscopic manifestations of three micromechanial facts, even though microstructures are not explicitly modeled: (1) Individual grains with favorable orientations and stresses for transformation are the first to nucleate martensite, and the local nucleation strain is relatively large. (2) Then, transformation interfaces propagate according to growth kinetics to traverse networks of grains, while previously formed martensite may reorient. (3) Ultimately, transformation saturates prior to 100% completion as some unfavorably-oriented grains do not transform; thus the total transformation strain of a polycrystal is modest relative to the initial, local nucleation strain. The proposed formulation also accounts for tension–compression asymmetry, processing anisotropy, and the distinction between stress-induced and temperature-induced transformations. Consequently, the model describes thermoelastic responses of shape-memory alloys subject to complex, multi-axial thermo-mechanical loadings. These abilities are demonstrated through detailed comparisons of simulations with experiments.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/cbt2r-03g97Exceptional resilience of small-scale Au_(30)Cu_(25)Zn_(45) under cyclic stress-induced phase transformation
https://resolver.caltech.edu/CaltechAUTHORS:20161107-113303591
Authors: {'items': [{'id': 'Ni-Xiaoyue', 'name': {'family': 'Ni', 'given': 'Xiaoyue'}}, {'id': 'Greer-J-R', 'name': {'family': 'Greer', 'given': 'Julia R.'}, 'orcid': '0000-0002-9675-1508'}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'Kaushik'}, 'orcid': '0000-0003-2908-5469'}, {'id': 'James-R-D', 'name': {'family': 'James', 'given': 'Richard D.'}, 'orcid': '0000-0001-6019-6613'}, {'id': 'Chen-Xian', 'name': {'family': 'Chen', 'given': 'Xian'}}]}
Year: 2016
DOI: 10.1021/acs.nanolett.6b03555
Shape memory alloys that produce and recover from large deformation driven by martensitic transformation are widely exploited in biomedical devices and micro-actuators. Generally their actuation work degrades significantly within first a few cycles, and is reduced at smaller dimensions. Further, alloys exhibiting unprecedented reversibility have relatively small superelastic strain, 0.7%. These raise the questions of whether high reversibility is necessarily accompanied by small work and strain, and whether high work and strain is necessarily diminished at small scale. Here we conclusively demonstrate that these are not true by showing that Au_(30)Cu_(25)Zn_(45) pillars exhibit 12 MJ m^(−3) work and 3.5% superelastic strain even after 100,000 phase transformation cycles. Our findings confirm that the lattice compatibility dominates themechanical behavior of phase-changing materials at nano to micron scales, and points a way for smart micro-actuators design having the mutual benefits of high actuation work and long lifetime.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/2rtf6-pb168Spectrum-splitting approach for Fermi-operator expansion in all-electron Kohn-Sham DFT calculations
https://resolver.caltech.edu/CaltechAUTHORS:20161012-162032480
Authors: {'items': [{'id': 'Motamarri-P', 'name': {'family': 'Motamarri', 'given': 'Phani'}}, {'id': 'Gavini-V', 'name': {'family': 'Gavini', 'given': 'Vikram'}}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'Kaushik'}, 'orcid': '0000-0003-2908-5469'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'Michael'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2017
DOI: 10.1103/PhysRevB.95.035111
We present a spectrum-splitting approach to conduct all-electron Kohn-Sham density functional theory (DFT) calculations by employing Fermi-operator expansion of the Kohn-Sham Hamiltonian. The proposed approach splits the subspace containing the occupied eigenspace into a core subspace, spanned by the core eigenfunctions, and its complement, the valence subspace, and thereby enables an efficient computation of the Fermi-operator expansion by reducing the expansion to the valence-subspace projected Kohn-Sham Hamiltonian. The key ideas used in our approach are as follows: (i) employ Chebyshev filtering to compute a subspace containing the occupied states followed by a localization procedure to generate nonorthogonal localized functions spanning the Chebyshev-filtered subspace; (ii) compute the Kohn-Sham Hamiltonian projected onto the valence subspace; (iii) employ Fermi-operator expansion in terms of the valence-subspace projected Hamiltonian to compute the density matrix, electron density, and band energy. We demonstrate the accuracy and performance of the method on benchmark materials systems involving silicon nanoclusters up to 1330 electrons, a single gold atom, and a six-atom gold nanocluster. The benchmark studies on silicon nanoclusters revealed a staggering fivefold reduction in the Fermi-operator expansion polynomial degree by using the spectrum-splitting approach for accuracies in the ground-state energies of ∼10^(−4) Ha/atom with respect to reference calculations. Further, numerical investigations on gold suggest that spectrum splitting is indispensable to achieve meaningful accuracies, while employing Fermi-operator expansion.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/tqz39-kaw25Microstructure-enabled control of wrinkling in nematic elastomer sheets
https://resolver.caltech.edu/CaltechAUTHORS:20170313-074644448
Authors: {'items': [{'id': 'Plucinsky-P', 'name': {'family': 'Plucinsky', 'given': 'Paul'}, 'orcid': '0000-0003-2060-8657'}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'Kaushik'}, 'orcid': '0000-0003-2908-5469'}]}
Year: 2017
DOI: 10.1016/j.jmps.2017.02.009
Nematic elastomers are rubbery solids which have liquid crystals incorporated into their polymer chains. These materials display many unusual mechanical properties, one such being the ability to form fine-scale microstructure. In this work, we explore the response of taut and appreciably stressed sheets made of nematic elastomer. Such sheets feature two potential instabilities – the formation of fine-scale material microstructure and the formation of fine-scale wrinkles. We develop a theoretical framework to study these sheets that accounts for both instabilities, and we implement this framework numerically. Specifically, we show that these instabilities occur for distinct mesoscale stretches, and observe that microstructure is finer than wrinkles for physically relevant parameters. Therefore, we relax (i.e., implicitly but rigorously account for) the microstructure while we regularize (i.e., compute the details explicitly) the wrinkles. Using both analytical and numerical studies, we show that nematic elastomer sheets can suppress wrinkling by modifying the expected state of stress through the formation of microstructure.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/9853y-18y82The relation between a microscopic threshold-force model and macroscopic models of adhesion
https://resolver.caltech.edu/CaltechAUTHORS:20170615-065728719
Authors: {'items': [{'id': 'Hulikal-S', 'name': {'family': 'Hulikal', 'given': 'Srivatsan'}}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'Kaushik'}, 'orcid': '0000-0003-2908-5469'}, {'id': 'Lapusta-N', 'name': {'family': 'Lapusta', 'given': 'Nadia'}, 'orcid': '0000-0001-6558-0323'}]}
Year: 2017
DOI: 10.1007/s10409-016-0630-y
This paper continues our recent work on the relationship between discrete contact interactions at the microscopic scale and continuum contact interactions at the macroscopic scale (Hulikal et al., J. Mech. Phys. Solids 76, 144–161, 2015). The focus of this work is on adhesion. We show that a collection of a large number of discrete elements governed by a threshold-force based model at the microscopic scale collectively gives rise to continuum fracture mechanics at the macroscopic scale. A key step is the introduction of an efficient numerical method that enables the computation of a large number of discrete contacts. Finally, while this work focuses on scaling laws, the methodology introduced in this paper can also be used to study rough-surface adhesion.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/kbgv8-msj95Electroclinic effect in chiral smectic - A liquid crystal elastomers
https://resolver.caltech.edu/CaltechAUTHORS:20170918-090755079
Authors: {'items': [{'id': 'Cohen-Noy', 'name': {'family': 'Cohen', 'given': 'Noy'}, 'orcid': '0000-0003-2224-640X'}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'Kaushik'}, 'orcid': '0000-0003-2908-5469'}]}
Year: 2017
DOI: 10.1103/PhysRevE.96.032701
Chiral smectic-A liquid crystal elastomers are rubbery materials composed of a lamellar arrangement of liquid crystalline mesogens. It has been shown experimentally that these materials shear when subjected to an electric field due to the electrically induced tilt of the director. Experiments have also shown that shearing a chiral smectic-A elastomer gives rise to a polarization. Roughly, the shear force tilts the directors which, in turn, induce electric dipoles. This paper builds on previous works and models the electromechanical response of smectic-A elastomers using free energy contributions that are associated with the lamellar structure, the relative tilt between the director and the layer normal, and the coupling between the director and the electric field. To illustrate the merit of the proposed model, two cases are considered—a deformation induced polarization and an electrically induced deformation. The predictions according to these two models qualitatively agree with experimental findings. Finally, a cylinder composed of helical smectic layers is also considered. It is shown that the electromechanical response varies as a function of the helix angle.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/aztae-nh429The Measurement and Interpretation of Transformation Temperatures in Nitinol
https://resolver.caltech.edu/CaltechAUTHORS:20171108-100437078
Authors: {'items': [{'id': 'Duerig-T-W', 'name': {'family': 'Duerig', 'given': 'T. W.'}}, {'id': 'Pelton-A-R', 'name': {'family': 'Pelton', 'given': 'A. R.'}}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'K.'}, 'orcid': '0000-0003-2908-5469'}]}
Year: 2017
DOI: 10.1007/s40830-017-0133-0
A previous paper (Duerig and Bhattacharya in Shap Mem Superelasticity 1:153–161, 2015) introduced several engineering considerations surrounding the R-phase in Nitinol and highlighted a common, if not pervasive, misconception regarding the use of the term Af by the medical device industry. This paper brings additional data to bear on the issue and proposes more accurate terminology. Moreover, a variety of tools are used to establish the forward and reverse stress–temperature phase diagrams for a superelastic wire typical of that used in medical devices. Once established, the two most common methods of measuring transformation temperatures, Differential Scanning Calorimetry and Bend Free Recovery, are tested against the observed behavior. Light is also shed upon the origin of the Clausius–Clapeyron ratio (dσ/dT), the triple point, and why such large variations are reported in superelastic alloys.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/4sbr0-3tx43Actuation of thin nematic elastomer sheets with controlled heterogeneity
https://resolver.caltech.edu/CaltechAUTHORS:20170130-115632977
Authors: {'items': [{'id': 'Plucinsky-P', 'name': {'family': 'Plucinsky', 'given': 'Paul'}, 'orcid': '0000-0003-2060-8657'}, {'id': 'Lemm-M', 'name': {'family': 'Lemm', 'given': 'Marius'}}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'Kaushik'}, 'orcid': '0000-0003-2908-5469'}]}
Year: 2018
DOI: 10.1007/s00205-017-1167-3
Nematic elastomers and glasses deform spontaneously when subjected to temperature changes. This property can be exploited in the design of heterogeneously patterned thin sheets that deform into a non-trivial shape when heated or cooled. In this paper, we start from a variational formulation for the entropic elastic energy of liquid crystal elastomers and we derive an effective two-dimensional metric constraint, which links the deformation and the heterogeneous director field. Our main results show that satisfying the metric constraint is both necessary and sufficient for the deformation to be an approximate minimizer of the energy. We include several examples which show that the class of deformations satisfying the metric constraint is quite rich.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/18mz1-dg842Proliferation of twinning in hexagonal close-packed metals: Application to magnesium
https://resolver.caltech.edu/CaltechAUTHORS:20171221-151321326
Authors: {'items': [{'id': 'Sun-Dingyi', 'name': {'family': 'Sun', 'given': 'D.'}}, {'id': 'Ponga-M', 'name': {'family': 'Ponga', 'given': 'M.'}, 'orcid': '0000-0001-5058-1454'}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'K.'}, 'orcid': '0000-0003-2908-5469'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2018
DOI: 10.1016/j.jmps.2017.12.009
Plastic deformation of metallic alloys usually takes place through slip, but occasionally involves twinning. In particular, twinning is important in hexagonal close packed (HCP) materials where the easy slip systems are insufficient to accommodate arbitrary deformations. While deformation by slip mechanisms is reasonably well understood, comparatively less is known about deformation by twinning. Indeed, the identification of relevant twinning modes remains an art. In this paper, we develop a framework combining a fundamental kinematic definition of twins with large-scale atomistic calculations to predict twinning modes of crystalline materials. We apply this framework to magnesium where there are two accepted twin modes, tension and compression, but a number of anomalous observations. Remarkably, our framework shows that there is a very large number of twinning modes that are important in magnesium. Thus, in contrast to the traditional view that plastic deformation is kinematically partitioned between a few modes, our results suggest that deformation in HCP materials is the result of an energetic and kinetic competition between numerous possibilities. Consequently, our findings suggest that the commonly used models of deformation need to be extended in order to take into account a broader and richer variety of twin modes, which, in turn, opens up new avenues for improving the mechanical properties.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/8bvbe-ead24Patterning nonisometric origami in nematic elastomer sheets
https://resolver.caltech.edu/CaltechAUTHORS:20180301-153833459
Authors: {'items': [{'id': 'Plucinsky-P', 'name': {'family': 'Plucinsky', 'given': 'Paul'}, 'orcid': '0000-0003-2060-8657'}, {'id': 'Kowalski-B-A', 'name': {'family': 'Kowalski', 'given': 'Benjamin A.'}}, {'id': 'White-T-J', 'name': {'family': 'White', 'given': 'Timothy J.'}, 'orcid': '0000-0001-8006-7173'}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'Kaushik'}, 'orcid': '0000-0003-2908-5469'}]}
Year: 2018
DOI: 10.1039/c8sm00103k
Nematic elastomers dramatically change their shape in response to diverse stimuli including light and heat. In this paper, we provide a systematic framework for the design of complex three dimensional shapes through the actuation of heterogeneously patterned nematic elastomer sheets. These sheets are composed of nonisometric origami building blocks which, when appropriately linked together, can actuate into a diverse array of three dimensional faceted shapes. We demonstrate both theoretically and experimentally that the nonisometric origami building blocks actuate in the predicted manner, and that the integration of multiple building blocks leads to complex, yet predictable and robust, shapes. We then show that this experimentally realized functionality enables a rich design landscape for actuation using nematic elastomers. We highlight this landscape through examples, which utilize large arrays of these building blocks to realize a desired three dimensional origami shape. In combination, these results amount to an engineering design principle, which provides a template for the programming of arbitrarily complex three dimensional shapes on demand.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/t0m8s-apc66Impact induced depolarization of ferroelectric materials
https://resolver.caltech.edu/CaltechAUTHORS:20180327-082448880
Authors: {'items': [{'id': 'Agrawal-V', 'name': {'family': 'Agrawal', 'given': 'Vinamra'}}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'Kaushik'}, 'orcid': '0000-0003-2908-5469'}]}
Year: 2018
DOI: 10.1016/j.jmps.2018.03.011
We study the large deformation dynamic behavior and the associated nonlinear electro-thermo-mechanical coupling exhibited by ferroelectric materials in adiabatic environments. This is motivated by a ferroelectric generator which involves pulsed power generation by loading the ferroelectric material with a shock, either by impact or a blast. Upon impact, a shock wave travels through the material inducing a ferroelectric to nonpolar phase transition giving rise to a large voltage difference in an open circuit situation or a large current in a closed circuit situation. In the first part of this paper, we provide a general continuum mechanical treatment of the situation assuming a sharp phase boundary that is possibly charged. We derive the governing laws, as well as the driving force acting on the phase boundary. In the second part, we use the derived equations and a particular constitutive relation that describes the ferroelectric to nonpolar phase transition to study a uniaxial plate impact problem. We develop a numerical method where the phase boundary is tracked but other discontinuities are captured using a finite volume method. We compare our results with experimental observations to find good agreement. Specifically, our model reproduces the observed exponential rise of charge as well as the resistance dependent Hugoniot. We conclude with a parameter study that provides detailed insight into various aspects of the problem.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/chaf3-5zd79Static and sliding contact of rough surfaces: effect of asperity-scale properties and long-range elastic interactions
https://resolver.caltech.edu/CaltechAUTHORS:20180402-100646598
Authors: {'items': [{'id': 'Hulikal-S', 'name': {'family': 'Hulikal', 'given': 'Srivatsan'}}, {'id': 'Lapusta-N', 'name': {'family': 'Lapusta', 'given': 'Nadia'}, 'orcid': '0000-0001-6558-0323'}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'Kaushik'}, 'orcid': '0000-0003-2908-5469'}]}
Year: 2018
DOI: 10.1016/j.jmps.2018.03.022
Friction in static and sliding contact of rough surfaces is important in numerous physical phenomena. We seek to understand macroscopically observed static and sliding contact behavior as the collective response of a large number of microscopic asperities. To that end, we build on Hulikal et al. (2015) and develop an efficient numerical framework that can be used to investigate how the macroscopic response of multiple frictional contacts depends on long-range elastic interactions, different constitutive assumptions about the deforming contacts and their local shear resistance, and surface roughness. We approximate the contact between two rough surfaces as that between a regular array of discrete deformable elements attached to a elastic block and a rigid rough surface. The deformable elements are viscoelastic or elasto/viscoplastic with a range of relaxation times, and the elastic interaction between contacts is long-range. We find that the model reproduces the main macroscopic features of evolution of contact and friction for a range of constitutive models of the elements, suggesting that macroscopic frictional response is robust with respect to the microscopic behavior. Viscoelasticity/viscoplasticity contributes to the increase of friction with contact time and leads to a subtle history dependence. Interestingly, long-range elastic interactions only change the results quantitatively compared to the meanfield response. The developed numerical framework can be used to study how specific observed macroscopic behavior depends on the microscale assumptions. For example, we find that sustained increase in the static friction coefficient during long hold times suggests viscoelastic response of the underlying material with multiple relaxation time scales. We also find that the experimentally observed proportionality of the direct effect in velocity jump experiments to the logarithm of the velocity jump points to a complex material-dependent shear resistance at the microscale.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/wxnkm-ktg86Optimizing microstructure for toughness: the model problem of peeling
https://resolver.caltech.edu/CaltechAUTHORS:20180402-101222389
Authors: {'items': [{'id': 'Hsueh-Chun-Jen', 'name': {'family': 'Hsueh', 'given': 'Chun-Jen'}}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'Kaushik'}, 'orcid': '0000-0003-2908-5469'}]}
Year: 2018
DOI: 10.1007/s00158-018-1952-0
We consider the problem of peeling an adhesive thin film from a substrate that has a non-uniform distribution of adhesive. When the length scale of the non-uniformity is small compared to the overall dimensions of the film being peeled, it is possible to describe the overall peeling behavior with an effective adhesive strength. In this paper, we seek to find the distributions of adhesive strength at the microscale that optimize various aspects of the effective adhesive strength at the macroscale. We do so using both analytic bounds and topology optimization. We formulate the problem of peeling as a free boundary problem, and the effective strength as a maximum principle over the trajectory. For topology optimization, we replace the maximum with an integral norm, and use an adjoint method for the sensitivity. The problem of peeling may be viewed as a model problem in fracture mechanics where the crack (peel) front is confined to a plane, and thus our analysis as a first step toward studying the more general problem of optimizing microstructure for toughness.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/db80a-z7346Cohesive Zone Smoothing of Bending Stiffness Heterogeneities in Tape Peeling Experiments
https://resolver.caltech.edu/CaltechAUTHORS:20200828-121917087
Authors: {'items': [{'id': 'Avellar-Louisa', 'name': {'family': 'Avellar', 'given': 'Louisa'}}, {'id': 'Reese-Tucker', 'name': {'family': 'Reese', 'given': 'Tucker'}}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'Kaushik'}, 'orcid': '0000-0003-2908-5469'}, {'id': 'Ravichandran-G', 'name': {'family': 'Ravichandran', 'given': 'Guruswami'}, 'orcid': '0000-0002-2912-0001'}]}
Year: 2018
DOI: 10.1007/978-3-319-95879-8_12
This work studies the interaction between the cohesive zone and elastic stiffness heterogeneity in the peeling of an adhesive tape from a rigid substrate. It is understood that elastic stiffness heterogeneities can greatly enhance the adhesion of a tape without changing the properties of the interface. However, in experiments performed on adhesive tapes with both an elastic stiffness heterogeneity and a substantial cohesive zone, muted adhesion enhancement was observed. It is proposed that the cohesive zone acts to smooth out the effect of the discontinuity at the edge of the elastic stiffness heterogeneities, suppressing their effect on adhesion. This work presents peel tests performed with heterogeneously layered 3 M 810 tape that demonstrate the muted enhancement. Additionally, numerical simulations further investigating the interaction between elastic heterogeneity and cohesive zone are presented.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/8ajnp-7c720Fast Adaptive Global Digital Image Correlation
https://resolver.caltech.edu/CaltechAUTHORS:20201215-100834960
Authors: {'items': [{'id': 'Yang-Jin', 'name': {'family': 'Yang', 'given': 'Jin'}}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'Kaushik'}, 'orcid': '0000-0003-2908-5469'}]}
Year: 2018
DOI: 10.1007/978-3-319-97481-1_7
Digital image correlation (DIC) is a powerful experimental technique to compute full-field displacements and strains. The basic idea of the method is to compare images of an object decorated with a speckle pattern before and after deformation, and thereby to compute displacements and strains. Since DIC is a non-contact method that gives the whole field deformation, it is widely used to measure complex deformation patterns. Finite element (FE)-based Global DIC with regularization is one of the commonly used algorithms and it can be combined with finite element numerical simulations at the same time (Besnard et al., J Strain Anal Eng Design 47(4):214–228, 2012). However, Global DIC algorithm is usually computationally expensive and converges slowly. Further, it is difficult to directly apply an adaptive finite element mesh to Global DIC because the stiffness matrix and the external force vector have to be rebuilt every time the mesh is changed.
In this paper, we report a new Global DIC algorithm that uses adaptive mesh. It builds on our recent work on the augmented Lagrangian digital image correlation (ALDIC) (Yang and Bhattacharya, Exp Mech, submitted). We consider the global compatibility condition as a constraint and formulate it using an augmented Lagrangian (AL) method. We solve the resulting problem using the alternating direction method of multipliers (ADMM) (Boyd et al., Mach Learn 3(1):1–122, 2010) where we separate the problem into two subproblems. The first subproblem is computed fast, locally and in parallel, and the second subproblem is computed globally without image grayscale value terms where nine point Gaussian quadrature works very well. Compared with current Global DIC algorithm, this new adaptive Global DIC algorithm decreases computation time significantly with no loss (and some gain) in accuracy.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/bbwxj-tj840Stress fluctuation, crack renucleation and toughening in layered materials
https://resolver.caltech.edu/CaltechAUTHORS:20180425-144713630
Authors: {'items': [{'id': 'Hsueh-Chun-Jen', 'name': {'family': 'Hsueh', 'given': 'C.-J.'}}, {'id': 'Avellar-L', 'name': {'family': 'Avellar', 'given': 'L.'}}, {'id': 'Bourdin-B', 'name': {'family': 'Bourdin', 'given': 'B.'}}, {'id': 'Ravichandran-G', 'name': {'family': 'Ravichandran', 'given': 'G.'}, 'orcid': '0000-0002-2912-0001'}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'K.'}, 'orcid': '0000-0003-2908-5469'}]}
Year: 2018
DOI: 10.1016/j.jmps.2018.04.011
It has been established that contrast in the elastic properties can lead to enhancement of fracture toughness in heterogeneous materials. Focussing on layered materials as a model system, we show that this enhancement is a result of two distinct phenomena – first, fluctuations in stress leading to regions where the stress intensity at the crack is considerably smaller than that of the macroscopically applied value; and second, the lack of stress intensity when a crack is at a compliant to stiff interface thereby requiring renucleation. Using theoretical, computational and experimental methods, we study two geometries – a layered material and a layered material with a narrow channel – to separate the two phenomena. The stress fluctuation is present in both, but renucleation is present only in the layered medium. We provide quantitative estimates for the enhanced toughness.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/8e4sj-22g25Effect of Cohesive Zone Size on Peeling of Heterogeneous Adhesive Tape
https://resolver.caltech.edu/CaltechAUTHORS:20190201-111654305
Authors: {'items': [{'id': 'Avellar-L-T', 'name': {'family': 'Avellar', 'given': 'L.'}}, {'id': 'Reese-T', 'name': {'family': 'Reese', 'given': 'T.'}}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'K.'}, 'orcid': '0000-0003-2908-5469'}, {'id': 'Ravichandran-G', 'name': {'family': 'Ravichandran', 'given': 'G.'}, 'orcid': '0000-0002-2912-0001'}]}
Year: 2018
DOI: 10.1115/1.4041224
The interaction between the cohesive zone and the elastic stiffness heterogeneity in the peeling of an adhesive tape from a rigid substrate is examined experimentally and with finite element simulations. It is established in the literature that elastic stiffness heterogeneities can greatly enhance the force required to peel a tape without changing the properties of the interface. However, much of these concern brittle materials where the cohesive zone is limited in size. This paper reports the results of peeling experiments performed on pressure-sensitive adhesive tapes with both an elastic stiffness heterogeneity and a substantial cohesive zone. These experiments show muted enhancement in the peeling force and suggest that the cohesive zone acts to smooth out the effect of the discontinuity at the edge of the elastic stiffness heterogeneities, suppressing their effect on peel force enhancement. This mechanism is examined through numerical simulation which confirms that the peel force enhancement depends on the strength of the adhesive and the size of the cohesive zone.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/rt5n5-af319A Macroscopic Strain-Space Model of Anisotropic, Cyclic Plasticity with Hardening
https://resolver.caltech.edu/CaltechAUTHORS:20180131-112423318
Authors: {'items': [{'id': 'Paranjape-H-M', 'name': {'family': 'Paranjape', 'given': 'Harshad M.'}}, {'id': 'Stebner-A-P', 'name': {'family': 'Stebner', 'given': 'Aaron P.'}}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'Kaushik'}, 'orcid': '0000-0003-2908-5469'}]}
Year: 2018
DOI: 10.1016/j.ijmecsci.2018.01.012
We present a strain-based formulation of macroscopic plastic deformation that accounts for anisotropy in both the initial yielding and subsequent hardening. Both isotropic and kinematic hardening are considered. Thus the model captures the evolution in the deformation response on cyclic loading including the Bauschinger effect, and the accumulation of plastic strain (ratcheting response). The model is formulated in the strain space and implemented using an implicit time integration scheme. The capabilities of the model are demonstrated through material parameter studies and by calibrating the model to experimental data for uniaxial tensile loading of Inconel alloy and anisotropic yielding of rolled aluminum alloy sheets. We also show that this strain-based approach is equivalent to the more traditional stress-based approach. The strain-based formulation of this model makes it attractive for coupling with other strain-based phenomena like phase-transformations in shape-memory alloys and failure.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/z9wcs-zre81Stochastic modeling of discontinuous dynamic recrystallization at finite strains in hcp metals
https://resolver.caltech.edu/CaltechAUTHORS:20180926-083949101
Authors: {'items': [{'id': 'Tutcuoglu-A-D', 'name': {'family': 'Tutcuoglu', 'given': 'A. D.'}}, {'id': 'Vidyasagar-A', 'name': {'family': 'Vidyasagar', 'given': 'A.'}}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'K.'}, 'orcid': '0000-0003-2908-5469'}, {'id': 'Kochmann-D-M', 'name': {'family': 'Kochmann', 'given': 'D. M.'}, 'orcid': '0000-0002-9112-6615'}]}
Year: 2019
DOI: 10.1016/j.jmps.2018.09.032
We present a model that aims to describe the effective, macroscale material response as well as the underlying mesoscale processes during discontinuous dynamic recrystallization under severe plastic deformation. Broadly, the model brings together two well-established but distinct approaches – first, a continuum crystal plasticity and twinning approach to describe complex deformation in the various grains, and second, a discrete Monte-Carlo-Potts approach to describe grain boundary migration and nucleation. The model is implemented within a finite-strain Fast Fourier Transform-based framework that allows for efficient simulations of recrystallization at high spatial resolution, while the grid-based Fourier treatment lends itself naturally to the Monte-Carlo approach. The model is applied to pure magnesium as a representative hexagonal closed packed metal, but is sufficiently general to admit extension to other material systems. Results demonstrate the evolution of the grain architecture in representative volume elements and the associated stress–strain history during the severe simple shear deformation typical of equal channel angular extrusion. We confirm that the recrystallization kinetics converge with increasing grid resolution and that the resulting model captures the experimentally observed transition from single- to multi-peak stress–strain behavior as a function of temperature and rate.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/4jenk-vdb24A numerical study of the electromechanical response of liquid metal embedded elastomers
https://resolver.caltech.edu/CaltechAUTHORS:20181029-094837837
Authors: {'items': [{'id': 'Cohen-Noy', 'name': {'family': 'Cohen', 'given': 'Noy'}, 'orcid': '0000-0003-2224-640X'}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'Kaushik'}, 'orcid': '0000-0003-2908-5469'}]}
Year: 2019
DOI: 10.1016/j.ijnonlinmec.2018.10.011
Liquid metal embedded elastomers (LMEE) are soft, stretchable materials that become conductive upon application of a compressive force. The conductance stems from the compression-induced percolation of the liquid metal inclusions. Interestingly, a recent work showed that once the elastomer becomes conductive, its resistance is independent of stretch. This work aims to understand these phenomena. We start by simulating the response of an elastomer composite with two soft inclusions subjected to a compressive force. It is shown that the presence of the inclusions can give rise to a tensile stress in the elastomer, leading to rupture and percolation. Next, we study the dependence of the resistance and the conductivity on an applied uniaxial stretch in LMEEs with several microstructures. The simulations are in good qualitative agreement with experimental findings. It is also demonstrated that the electromechanical properties highly depend on the microstructural arrangement of the inclusions and can therefore be tuned by microstructural design.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/y5ara-t4x55Optimizing Bone Scaffold Porosity Distributions
https://resolver.caltech.edu/CaltechAUTHORS:20190123-111634389
Authors: {'items': [{'id': 'Poh-P-S-P', 'name': {'family': 'Poh', 'given': 'Patrina S. P.'}}, {'id': 'Valainis-D', 'name': {'family': 'Valainis', 'given': 'Dvina'}}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'Kaushik'}, 'orcid': '0000-0003-2908-5469'}, {'id': 'van-Griensven-M', 'name': {'family': 'van Griensven', 'given': 'Martijn'}, 'orcid': '0000-0001-5104-9881'}, {'id': 'Dondl-P-W', 'name': {'family': 'Dondl', 'given': 'Patrick'}}]}
Year: 2019
DOI: 10.48550/arXiv.1809.08179
We consider a simple one-dimensional time-dependent model for bone regeneration in the presence of a bio-resorbable polymer scaffold. Within the framework of the model, we optimize the effective mechanical stiffness of the polymer scaffold together with the regenerated bone matrix. The result of the optimization procedure is a scaffold porosity distribution which maximizes the stiffness of the scaffold-bone system over the regeneration time, such that the propensity for mechanical failure is reduced.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/rtqr7-q7986Optimal design of a model energy conversion device
https://resolver.caltech.edu/CaltechAUTHORS:20180302-065336857
Authors: {'items': [{'id': 'Collins-Lincoln', 'name': {'family': 'Collins', 'given': 'Lincoln'}}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'Kaushik'}, 'orcid': '0000-0003-2908-5469'}]}
Year: 2019
DOI: 10.1007/s00158-018-2072-6
Fuel cells, batteries, and thermochemical and other energy conversion devices involve the transport of a number of (electro-) chemical species through distinct materials so that they can meet and react at specified multi-material interfaces. Therefore, morphology or arrangement of these different materials can be critical in the performance of an energy conversion device. In this paper, we study a model problem motivated by a solar-driven thermochemical conversion device that splits water into hydrogen and oxygen. We formulate the problem as a system of coupled multi-material reaction-diffusion equations where each species diffuses selectively through a given material and where the reaction occurs at multi-material interfaces. We introduce a phase-field formulation of the optimal design problem and numerically study selected examples.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/ndcac-30e98Augmented Lagrangian Digital Image Correlation
https://resolver.caltech.edu/CaltechAUTHORS:20181206-144519373
Authors: {'items': [{'id': 'Yang-J', 'name': {'family': 'Yang', 'given': 'J.'}}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'K.'}, 'orcid': '0000-0003-2908-5469'}]}
Year: 2019
DOI: 10.1007/s11340-018-00457-0
Digital image correlation (DIC) is a powerful experimental technique for measuring full-field displacement and strain. The basic idea of the method is to compare images of an object decorated with a speckle pattern before and after deformation, and thereby to compute the displacement and strain fields. Local subset DIC and finite element-based global DIC are two widely used image matching methods. However there are some drawbacks to these methods. In local subset DIC, the computed displacement field may not be compatible, and the deformation gradient may be noisy, especially when the subset size is small. Global DIC incorporates displacement compatibility, but can be computationally expensive. In this paper, we propose a new method, the augmented-Lagrangian digital image correlation (ALDIC), that combines the advantages of both the local (fast) and global (compatible) methods. We demonstrate that ALDIC has higher accuracy and behaves more robustly compared to both local subset DIC and global DIC.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/xdz6e-dr072Photovoltaic effect in multi-domain ferroelectric perovskite oxides
https://resolver.caltech.edu/CaltechAUTHORS:20190124-122550312
Authors: {'items': [{'id': 'Teh-Ying-Shi', 'name': {'family': 'Teh', 'given': 'Ying Shi'}, 'orcid': '0000-0003-1743-4158'}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'Kaushik'}, 'orcid': '0000-0003-2908-5469'}]}
Year: 2019
DOI: 10.1063/1.5083632
We propose a device model that elucidates the role of domain walls in the photovoltaic effect in multi-domain ferroelectric perovskites. The model accounts for the intricate interplay between ferroelectric polarization, space charges, photo-generation, and electronic transport. When applied to bismuth ferrite, results show a significant electric potential step across both 71° and 109° domain walls, which in turn contributes to the photovoltaic (PV) effect. We also find a strong correlation between polarization and oxygen octahedra tilts, which indicates the nontrivial role of the latter in the PV effect. The domain wall-based PV effect is further shown to be additive in nature, allowing for the possibility of generating the above-bandgap voltage.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/jz8e1-0kn48Combining Image Compression with Digital Image Correlation
https://resolver.caltech.edu/CaltechAUTHORS:20190123-095233323
Authors: {'items': [{'id': 'Yang-J', 'name': {'family': 'Yang', 'given': 'J.'}}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'K.'}, 'orcid': '0000-0003-2908-5469'}]}
Year: 2019
DOI: 10.1007/s11340-018-00459-y
Digital image correlation (DIC) is a powerful experimental technique to determine displacement and strain fields. DIC methods usually require a large number of high resolution images, and this imposes significant needs on data storage and transmission. In this work, we combine digital image correlation with image compression techniques and show that it is possible to obtain accurate displacement and strain fields with only 5% of the original image size. We study two compression techniques – discrete cosine transform (DCT) and wavelet transform, and three DIC algorithms – Local Subset DIC, Global DIC and the recently proposed augmented Lagrangian DIC (ALDIC). We find that Local Subset DIC leads to the largest errors and ALDIC to the smallest when compressed images are used. We also find that wavelet-based image compression introduces less error compared to DCT image compression.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/rv346-82297Optimization of Bone Scaffold Porosity Distributions
https://resolver.caltech.edu/CaltechAUTHORS:20190711-095431496
Authors: {'items': [{'id': 'Poh-P-S-P', 'name': {'family': 'Poh', 'given': 'Patrina S. P.'}}, {'id': 'Valainis-D', 'name': {'family': 'Valainis', 'given': 'Dvina'}}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'Kaushik'}, 'orcid': '0000-0003-2908-5469'}, {'id': 'van-Griensven-M', 'name': {'family': 'van Griensven', 'given': 'Martijn'}, 'orcid': '0000-0001-5104-9881'}, {'id': 'Dondl-P', 'name': {'family': 'Dondl', 'given': 'Patrick'}, 'orcid': '0000-0003-3035-7230'}]}
Year: 2019
DOI: 10.1038/s41598-019-44872-2
PMCID: PMC6591284
Additive manufacturing (AM) is a rapidly emerging technology that has the potential to produce personalized scaffolds for tissue engineering applications with unprecedented control of structural and functional design. Particularly for bone defect regeneration, the complex coupling of biological mechanisms to the scaffolds' properties has led to a predominantly trial-and-error approach. To mitigate this, shape or topology optimization can be a useful tool to design a scaffold architecture that matches the desired design targets, albeit at high computational cost. Here, we consider an efficient macroscopic optimization routine based on a simple one-dimensional time-dependent model for bone regeneration in the presence of a bioresorbable polymer scaffold. The result of the optimization procedure is a scaffold porosity distribution which maximizes the stiffness of the scaffold and regenerated bone system over the entire regeneration time, so that the propensity for mechanical failure is minimized.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/54mzw-arm61Phase-field study of crack nucleation and propagation in elastic-perfectly plastic bodies
https://resolver.caltech.edu/CaltechAUTHORS:20190124-072222651
Authors: {'items': [{'id': 'Brach-S', 'name': {'family': 'Brach', 'given': 'Stella'}, 'orcid': '0000-0003-4766-8131'}, {'id': 'Tanné-E', 'name': {'family': 'Tanné', 'given': 'Erwan'}}, {'id': 'Bourdin-B', 'name': {'family': 'Bourdin', 'given': 'Blaise'}}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'Kaushik'}, 'orcid': '0000-0003-2908-5469'}]}
Year: 2019
DOI: 10.1016/j.cma.2019.04.027
Crack initiation and propagation in elastic–perfectly plastic bodies is studied in a phase-field or variational gradient damage formulation. A rate-independent formulation that naturally couples elasticity, perfect plasticity and fracture is presented, and used to study crack initiation in notched specimens and crack propagation using a surfing boundary condition. Both plane strain and plane stress are addressed. It is shown that in plane strain, a plastic zone blunts the notch or crack tip which in turn inhibits crack nucleation and propagation. Sufficient load causes the crack to nucleate or unpin, but the crack does so with a finite jump. Therefore the propagation is intermittent or jerky leaving behind a rough surface. In plane stress, failure proceeds with an intense shear zone ahead of the notch or crack tip and the fracture process is not complete.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/0zfjx-qtj39Obreimoff revisited: controlled heterogeneous fracture through the splitting of mica
https://resolver.caltech.edu/CaltechAUTHORS:20190614-153313032
Authors: {'items': [{'id': 'Johnson-M-T', 'name': {'family': 'Johnson', 'given': 'M. T.'}, 'orcid': '0000-0002-3710-1070'}, {'id': 'Brodnik-N-R', 'name': {'family': 'Brodnik', 'given': 'N. R.'}}, {'id': 'Ekeh-T', 'name': {'family': 'Ekeh', 'given': 'T.'}}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'K.'}, 'orcid': '0000-0003-2908-5469'}, {'id': 'Faber-K-T', 'name': {'family': 'Faber', 'given': 'K. T.'}, 'orcid': '0000-0001-6585-2536'}]}
Year: 2019
DOI: 10.1016/j.mechmat.2019.103088
Obreimoff reported his first instrumented measurements of the cleavage of muscovite mica in 1930 and that work helped to propel a greater understanding of fracture. This study builds upon that effort by investigating the role of compliance heterogeneities in brittle materials through mica splitting in a manner similar to Obreimoff. The natural layered structure of mica makes it ideal as a model system for studying fracture as crack propagation can be constrained along a single controlled cleavage plane. Cleavage through the insertion of a rounded wedge provides a straightforward mechanical setup that produces stable crack propagation, so long as the effects of friction and wedge geometry are properly considered. First, homogeneous mica sheets of uniform thickness are cleaved in ambient atmosphere to establish a baseline splitting force and critical strain energy release rate, similar Obreimoff's original work. After establishing this baseline, mica sheets with prescribed thickness heterogeneities are investigated. It is found that the splitting force required to propagate a crack along a specimen with a sharp increase in layer thickness is significantly larger than the analogous homogeneous splitting forces, even though the crack is not deflected. This indicates that a sharp increase in stiffness can produce an increase in toughness in layered structures without the need for any actual toughness contrast between constituent components or any crack deflection. This toughening effect produced by compliance contrast may have implications in the context of layered ceramic composite design, where systems are often composed of a stiff outer shell and a more compliant and damage-tolerant functional layer.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/4mq2s-4ek78Anisotropy of the effective toughness of layered media
https://resolver.caltech.edu/CaltechAUTHORS:20190709-085719234
Authors: {'items': [{'id': 'Brach-S', 'name': {'family': 'Brach', 'given': 'S.'}, 'orcid': '0000-0003-4766-8131'}, {'id': 'Hossain-M-Z', 'name': {'family': 'Hossain', 'given': 'M. Z.'}}, {'id': 'Bourdin-B', 'name': {'family': 'Bourdin', 'given': 'B.'}}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'K.'}, 'orcid': '0000-0003-2908-5469'}]}
Year: 2019
DOI: 10.1016/j.jmps.2019.06.021
This continues the study of the effective toughness of layered materials started in Hossain et al. (2014) and Hsueh et al. (2018), with a focus on anisotropy. We use the phase-field model and the surfing boundary condition to propagate a crack macroscopically at various angles to the layers. We study two idealized situations, the first where the elastic modulus is uniform while the toughness alternates and a second where the toughness is uniform and the elastic modulus alternates. We find that in the first case of toughness heterogeneity the effective toughness displays 'anomalous isotropy' in that it is independent of the propagation direction and equal to that of the tougher material except when the crack propagation is parallel to the layers. In the second case of elastic heterogeneity, we find the behavior more anisotropic and consistent with the toughening effects of stress fluctuation and need for crack renucleation at the compliant-to-stiff interface. In both cases, the effective toughness is not convex in the sense of interfacial energy or Wulff shape reflecting the fact that crack propagation follows a critical path. Further, in both cases the crack path is not straight and consistent with a maximal dissipation principle. Finally, the effective toughness depends on the contrast and pinning, rather than on the extent of crack fluctuation.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/2cws7-tac72Photo-Motile Structures
https://resolver.caltech.edu/CaltechAUTHORS:20191111-090332268
Authors: {'items': [{'id': 'Korner-K', 'name': {'family': 'Korner', 'given': 'Kevin'}}, {'id': 'Audoly-B', 'name': {'family': 'Audoly', 'given': 'Basile'}, 'orcid': '0000-0002-0534-1467'}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'Kaushik'}, 'orcid': '0000-0003-2908-5469'}]}
Year: 2019
DOI: 10.48550/arXiv.1909.02643
Actuation remains a signifcant challenge in soft robotics. Actuation by light has important advantages: objects can be actuated from a distance, distinct frequencies can be used to actuate and control distinct modes with minimal interference and signifcant power can be transmitted over long distances through corrosion-free, lightweight fiber optic cables. Photo-chemical processes that directly convert photons to configurational changes are particularly attractive for actuation. Various researchers have demonstrated light-induced actuation with liquid crystal elastomers combined with azobenzene photochromes. We present a simple modeling framework and a series of examples that studies actuation by light. Of particular interest is the generation of cyclic or periodic motion under steady illumination. We show that this emerges as a result of a coupling between light absorption and deformation. As the structure absorbs light and deforms, the conditions of illumination change, and this in turn changes the nature of further deformation. This coupling can be exploited in either closed structures or with structural instabilities to generate cyclic motion.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/ybrf8-w3b07Metamaterials with engineered failure load and stiffness
https://resolver.caltech.edu/CaltechAUTHORS:20191111-154114590
Authors: {'items': [{'id': 'Injeti-S-S', 'name': {'family': 'Injeti', 'given': 'Sai Sharan'}}, {'id': 'Daraio-C', 'name': {'family': 'Daraio', 'given': 'Chiara'}, 'orcid': '0000-0001-5296-4440'}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'Kaushik'}, 'orcid': '0000-0003-2908-5469'}]}
Year: 2019
DOI: 10.1073/pnas.1911535116
PMCID: PMC6883817
Architected materials or metamaterials have proved to be a very effective way of making materials with unusual mechanical properties. For example, by designing the mesoscale geometry of architected materials, it is possible to obtain extremely high stiffness-to-weight ratio or unusual Poisson's ratio. However, much of this work has focused on designing properties like stiffness and density, and much remains unknown about the critical load to failure. This is the focus of the current work. We show that the addition of local internal prestress in selected regions of architected materials enables the design of materials where the critical load to failure can be optimized independently from the density and/or quasistatic stiffness. We propose a method to optimize the specific load to failure and specific stiffness using sensitivity analysis and derive the maximum bounds on the attainable properties. We demonstrate the method in a 2D triangular lattice and a 3D octahedral truss, showing excellent agreement between experimental and theoretical results. The method can be used to design materials with predetermined fracture load, failure location, and fracture paths.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/9gz8j-0n622Guiding and Trapping Cracks With Compliant Inclusions for Enhancing Toughness of Brittle Composite Materials
https://resolver.caltech.edu/CaltechAUTHORS:20200430-104816477
Authors: {'items': [{'id': 'Brodnik-N-R', 'name': {'family': 'Brodnik', 'given': 'Neal R.'}}, {'id': 'Hsueh-Chun-Jen', 'name': {'family': 'Hsueh', 'given': 'Chun-Jen'}}, {'id': 'Faber-K-T', 'name': {'family': 'Faber', 'given': 'Katherine T.'}, 'orcid': '0000-0001-6585-2536'}, {'id': 'Bourdin-B', 'name': {'family': 'Bourdin', 'given': 'Blaise'}}, {'id': 'Ravichandran-G', 'name': {'family': 'Ravichandran', 'given': 'Guruswami'}, 'orcid': '0000-0002-2912-0001'}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'Kaushik'}, 'orcid': '0000-0003-2908-5469'}]}
Year: 2020
DOI: 10.1115/1.4045682
The problem of toughening heterogeneous materials with a stiff matrix and compliant inclusions is investigated through numerical simulations and experiments. Specifically, the problem of optimizing a combination of effective toughness and effective elastic modulus in the context of a square array of compliant inclusions in a stiff matrix is explored. Crack propagation in the heterogeneous material is simulated using a variational phase-field approach. It is found that the crack can meander between or get attracted to and trapped in the inclusions. Composite specimens with a stiff matrix and compliant circular inclusions were 3D printed, and their fracture toughness was measured using a specially designed loading fixture. The experimental results show agreement with the numerical predictions by demonstrating the attraction and trapping of cracks in the inclusions. This study demonstrates the potential for significant enhancement of toughness through elastic compliance contrast between the matrix and the inclusion without notably compromising the effective elastic modulus of the composite material.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/efmzk-d2m21Neural Operator: Graph Kernel Network for Partial Differential Equations
https://resolver.caltech.edu/CaltechAUTHORS:20200402-133318521
Authors: {'items': [{'id': 'Li-Zongyi', 'name': {'family': 'Li', 'given': 'Zongyi'}, 'orcid': '0000-0003-2081-9665'}, {'id': 'Kovachki-Nikola-B', 'name': {'family': 'Kovachki', 'given': 'Nikola'}, 'orcid': '0000-0002-3650-2972'}, {'id': 'Azizzadenesheli-Kamyar', 'name': {'family': 'Azizzadenesheli', 'given': 'Kamyar'}, 'orcid': '0000-0001-8507-1868'}, {'id': 'Liu-Burigede', 'name': {'family': 'Liu', 'given': 'Burigede'}, 'orcid': '0000-0002-6518-3368'}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'Kaushik'}, 'orcid': '0000-0003-2908-5469'}, {'id': 'Stuart-A-M', 'name': {'family': 'Stuart', 'given': 'Andrew'}}, {'id': 'Anandkumar-A', 'name': {'family': 'Anandkumar', 'given': 'Anima'}, 'orcid': '0000-0002-6974-6797'}]}
Year: 2020
DOI: 10.48550/arXiv.2003.03485
The classical development of neural networks has been primarily for mappings between a finite-dimensional Euclidean space and a set of classes, or between two finite-dimensional Euclidean spaces. The purpose of this work is to generalize neural networks so that they can learn mappings between infinite-dimensional spaces (operators). The key innovation in our work is that a single set of network parameters, within a carefully designed network architecture, may be used to describe mappings between infinite-dimensional spaces and between different finite-dimensional approximations of those spaces. We formulate approximation of the infinite-dimensional mapping by composing nonlinear activation functions and a class of integral operators. The kernel integration is computed by message passing on graph networks. This approach has substantial practical consequences which we will illustrate in the context of mappings between input data to partial differential equations (PDEs) and their solutions. In this context, such learned networks can generalize among different approximation methods for the PDE (such as finite difference or finite element methods) and among approximations corresponding to different underlying levels of resolution and discretization. Experiments confirm that the proposed graph kernel network does have the desired properties and show competitive performance compared to the state of the art solvers.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/k3t18-we744Large scale ab-initio simulations of dislocations
https://resolver.caltech.edu/CaltechAUTHORS:20200110-142048574
Authors: {'items': [{'id': 'Ponga-M', 'name': {'family': 'Ponga', 'given': 'Mauricio'}, 'orcid': '0000-0001-5058-1454'}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'Kaushik'}, 'orcid': '0000-0003-2908-5469'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'Michael'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2020
DOI: 10.1016/j.jcp.2020.109249
We present a novel methodology to compute relaxed dislocations core configurations, and their energies in crystalline metallic materials using large-scale ab-intio simulations. The approach is based on MacroDFT, a coarse-grained density functional theory method that accurately computes the electronic structure with sub-linear scaling resulting in a tremendous reduction in cost. Due to its implementation in real-space, MacroDFT has the ability to harness petascale resources to study materials and alloys through accurate ab-initio calculations. Thus, the proposed methodology can be used to investigate dislocation cores and other defects where long range elastic effects play an important role, such as in dislocation cores, grain boundaries and near precipitates in crystalline materials. We demonstrate the method by computing the relaxed dislocation cores in prismatic dislocation loops and dislocation segments in magnesium (Mg). We also study the interaction energy with a line of Aluminum (Al) solutes. Our simulations elucidate the essential coupling between the quantum mechanical aspects of the dislocation core and the long range elastic fields that they generate. In particular, our quantum mechanical simulations are able to describe the logarithmic divergence of the energy in the far field as is known from classical elastic theory. In order to reach such scaling, the number of atoms in the simulation cell has to be exceedingly large, and cannot be achieved with the state-of-the-art density functional theory implementations.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/c8912-wt574A nonlinear beam model of photomotile structures
https://resolver.caltech.edu/CaltechAUTHORS:20200417-123145473
Authors: {'items': [{'id': 'Korner-K', 'name': {'family': 'Korner', 'given': 'Kevin'}, 'orcid': '0000-0002-2967-9657'}, {'id': 'Kuenstler-A-S', 'name': {'family': 'Kuenstler', 'given': 'Alexa S.'}, 'orcid': '0000-0003-0432-2173'}, {'id': 'Hayward-R-C', 'name': {'family': 'Hayward', 'given': 'Ryan C.'}, 'orcid': '0000-0001-6483-2234'}, {'id': 'Audoly-B', 'name': {'family': 'Audoly', 'given': 'Basile'}, 'orcid': '0000-0002-0534-1467'}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'Kaushik'}, 'orcid': '0000-0003-2908-5469'}]}
Year: 2020
DOI: 10.1073/pnas.1915374117
PMCID: PMC7211941
Actuation remains a significant challenge in soft robotics. Actuation by light has important advantages: Objects can be actuated from a distance, distinct frequencies can be used to actuate and control distinct modes with minimal interference, and significant power can be transmitted over long distances through corrosion-free, lightweight fiber optic cables. Photochemical processes that directly convert photons to configurational changes are particularly attractive for actuation. Various works have reported light-induced actuation with liquid crystal elastomers combined with azobenzene photochromes. We present a simple modeling framework and a series of examples that study actuation by light. Of particular interest is the generation of cyclic or periodic motion under steady illumination. We show that this emerges as a result of a coupling between light absorption and deformation. As the structure absorbs light and deforms, the conditions of illumination change, and this, in turn, changes the nature of further deformation. This coupling can be exploited in either closed structures or with structural instabilities to generate cyclic motion.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/vbnp1-n9s96Model Reduction and Neural Networks for Parametric PDEs
https://resolver.caltech.edu/CaltechAUTHORS:20200527-074228185
Authors: {'items': [{'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'Kaushik'}, 'orcid': '0000-0003-2908-5469'}, {'id': 'Hosseini-Bamdad', 'name': {'family': 'Hosseini', 'given': 'Bamdad'}}, {'id': 'Kovachki-N-B', 'name': {'family': 'Kovachki', 'given': 'Nikola B.'}, 'orcid': '0000-0002-3650-2972'}, {'id': 'Stuart-A-M', 'name': {'family': 'Stuart', 'given': 'Andrew M.'}}]}
Year: 2020
DOI: 10.48550/arXiv.2005.03180
We develop a general framework for data-driven approximation of input-output maps between infinite-dimensional spaces. The proposed approach is motivated by the recent successes of neural networks and deep learning, in combination with ideas from model reduction. This combination results in a neural network approximation which, in principle, is defined on infinite-dimensional spaces and, in practice, is robust to the dimension of finite-dimensional approximations of these spaces required for computation. For a class of input-output maps, and suitably chosen probability measures on the inputs, we prove convergence of the proposed approximation methodology. Numerically we demonstrate the effectiveness of the method on a class of parametric elliptic PDE problems, showing convergence and robustness of the approximation scheme with respect to the size of the discretization, and compare our method with existing algorithms from the literature.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/0e45m-qwh51Bounds on precipitate hardening of line and surface defects in solids
https://resolver.caltech.edu/CaltechAUTHORS:20200702-080619417
Authors: {'items': [{'id': 'Courte-L', 'name': {'family': 'Courte', 'given': 'Luca'}}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'Kaushik'}, 'orcid': '0000-0003-2908-5469'}, {'id': 'Dondl-P', 'name': {'family': 'Dondl', 'given': 'Patrick'}, 'orcid': '0000-0003-3035-7230'}]}
Year: 2020
DOI: 10.1007/s00033-020-01327-3
The yield behavior of crystalline solids is determined by the motion of defects like dislocations, twin boundaries and coherent phase boundaries. These solids are hardened by introducing precipitates—small particles of a second phase. It is generally observed that the motion of line defects like dislocations are strongly inhibited or pinned by precipitates while the motion of surface defects like twin and phase boundaries are minimally affected. In this article, we provide insight into why line defects are more susceptible to the effect of precipitates than surface defects. Based on mathematical models that describe both types of motion, we show that for small concentrations of a nearly periodic arrangement of precipitates, the critical force that is required for a surface defect to overcome a precipitate is smaller than that required for a line defect. In particular, the critical forces for surface and line defects scale with the radius of precipitates to the second and first power, respectively.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/etymj-1st18Influence of thermomechanical loads on the energetics of precipitation in magnesium aluminum alloys
https://resolver.caltech.edu/CaltechAUTHORS:20200224-124229768
Authors: {'items': [{'id': 'Ghosh-Swarnava', 'name': {'family': 'Ghosh', 'given': 'Swarnava'}, 'orcid': '0000-0003-3800-5264'}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'Kaushik'}, 'orcid': '0000-0003-2908-5469'}]}
Year: 2020
DOI: 10.1016/j.actamat.2020.03.007
We use first principles calculations to study the influence of thermomechanical loads on the energetics of precipitation in magnesium-aluminum alloys. Using Density Functional Theory simulations, we present expressions of the energy of magnesium-aluminum binary solid solutions as a function of concentration, strain and temperature. Additionally, from these calculations, we observe an increase in equilibrium volume (and hence the equilibrium lattice constants) with the increase in concentration of magnesium. We also observe an increase in the cohesive energy of solutions with increase in concentration, and also present their dependence on strain. Calculations also show that the formation enthalpy of β phase solutions to be strongly influenced by hydrostatic stress, however the formation enthalpy of α phase solutions remain unaffected by hydrostatic stress. We present an expression of the free energy of any magnesium aluminum solid solution, that takes into account the contributions of strain and temperature. We note that these expressions can serve as input to process models of magnesium-aluminum alloys. We use these expressions to report the influence of strains and temperature on the solubility limits and equilibrium chemical potential in Mg-Al alloys. Finally, we report the influence of thermomechanical loads on the growth of precipitates, where we observe compressive strains along the c axis promotes growth of precipiates with a (0001)_α habit plane, whereas strains along the a and b directions do not influence the growth of precipitates.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/rstta-a7h83Photomechanical coupling in photoactive nematic elastomers
https://resolver.caltech.edu/CaltechAUTHORS:20200323-074401386
Authors: {'items': [{'id': 'Bai-Ruobing', 'name': {'family': 'Bai', 'given': 'Ruobing'}, 'orcid': '0000-0002-5847-0502'}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'Kaushik'}, 'orcid': '0000-0003-2908-5469'}]}
Year: 2020
DOI: 10.1016/j.jmps.2020.104115
Photoactive nematic elastomers are soft rubbery solids that undergo deformation when illuminated. They are made by incorporating photoactive molecules like azobenzene into nematic liquid crystal elastomers. Since its initial demonstration in 2001, it has received increasing interest with many recent studies of periodic and buckling behavior. However, theoretical models developed have focused on describing specific deformation modes (e.g., beam bending and uniaxial contraction) in the absence of mechanical loads, with only limited attention to the interplay between mechanical stress and light-induced deformation. This paper explores photomechanical coupling in a photoactive nematic elastomer under both light illumination and mechanical stress. We begin with a continuum framework built on the free energy developed by Corbett and Warner (Phys. Rev. Lett. 2006). Mechanical stress leads to nematic alignment parallel to a uniaxial tensile stress. In the absence of mechanical stress, in the photo-stationary state where the system reaches equilibrium, the nematic director tends to align perpendicular to the polarization of a linearly polarized light. However, sufficient illumination can destroy nematic order through a first-order nematic-isotropic phase transition which is accompanied by a snap through deformation. Combined illumination and mechanical stress can lead to an exchange of stability accompanied by stripe domains. Finally, the stress-intensity phase diagram shows a critical point that may be of interest for energy conversion.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/qttj8-nac66Fourier Neural Operator for Parametric Partial Differential Equations
https://resolver.caltech.edu/CaltechAUTHORS:20201106-120140981
Authors: {'items': [{'id': 'Li-Zongyi', 'name': {'family': 'Li', 'given': 'Zongyi'}, 'orcid': '0000-0003-2081-9665'}, {'id': 'Kovachki-N-B', 'name': {'family': 'Kovachki', 'given': 'Nikola'}, 'orcid': '0000-0002-3650-2972'}, {'id': 'Azizzadenesheli-K', 'name': {'family': 'Azizzadenesheli', 'given': 'Kamyar'}, 'orcid': '0000-0001-8507-1868'}, {'id': 'Liu-Burigede', 'name': {'family': 'Liu', 'given': 'Burigede'}, 'orcid': '0000-0002-6518-3368'}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'Kaushik'}, 'orcid': '0000-0003-2908-5469'}, {'id': 'Stuart-A-M', 'name': {'family': 'Stuart', 'given': 'Andrew'}}, {'id': 'Anandkumar-A', 'name': {'family': 'Anandkumar', 'given': 'Anima'}}]}
Year: 2020
DOI: 10.48550/arXiv.2010.08895
The classical development of neural networks has primarily focused on learning mappings between finite-dimensional Euclidean spaces. Recently, this has been generalized to neural operators that learn mappings between function spaces. For partial differential equations (PDEs), neural operators directly learn the mapping from any functional parametric dependence to the solution. Thus, they learn an entire family of PDEs, in contrast to classical methods which solve one instance of the equation. In this work, we formulate a new neural operator by parameterizing the integral kernel directly in Fourier space, allowing for an expressive and efficient architecture. We perform experiments on Burgers' equation, Darcy flow, and the Navier-Stokes equation (including the turbulent regime). Our Fourier neural operator shows state-of-the-art performance compared to existing neural network methodologies and it is up to three orders of magnitude faster compared to traditional PDE solvers.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/hpbg9-9ea84Accelerated computational micromechanics
https://resolver.caltech.edu/CaltechAUTHORS:20201110-073310991
Authors: {'items': [{'id': 'Zhou-Hao', 'name': {'family': 'Zhou', 'given': 'Hao'}}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'Kaushik'}, 'orcid': '0000-0003-2908-5469'}]}
Year: 2020
DOI: 10.48550/arXiv.2010.06697
We present an approach to solving problems in micromechanics that is amenable to massively parallel calculations through the use of graphical processing units and other accelerators. The problems lead to nonlinear differential equations that are typically second order in space and first order in time. This combination of nonlinearity and nonlocality makes such problems difficult to solve in parallel. However, this combination is a result of collapsing nonlocal, but linear and universal physical laws (kinematic compatibility, balance laws), and nonlinear but local constitutive relations. We propose an operator-splitting scheme inspired by this structure. The governing equations are formulated as (incremental) variational problems, the differential constraints like compatibility are introduced using an augmented Lagrangian, and the resulting incremental variational principle is solved by the alternating direction method of multipliers. The resulting algorithm has a natural connection to physical principles, and also enables massively parallel implementation on structured grids. We present this method and use it to study two examples. The first concerns the long wavelength instability of finite elasticity, and allows us to verify the approach against previous numerical simulations. We also use this example to study convergence and parallel performance. The second example concerns microstructure evolution in liquid crystal elastomers and provides new insights into some counter-intuitive properties of these materials. We use this example to validate the model and the approach against experimental observations.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/y5khy-p2w24Multipole Graph Neural Operator for Parametric Partial Differential Equations
https://resolver.caltech.edu/CaltechAUTHORS:20201106-120222366
Authors: {'items': [{'id': 'Li-Zongyi', 'name': {'family': 'Li', 'given': 'Zongyi'}, 'orcid': '0000-0003-2081-9665'}, {'id': 'Kovachki-Nikola-B', 'name': {'family': 'Kovachki', 'given': 'Nikola'}, 'orcid': '0000-0002-3650-2972'}, {'id': 'Azizzadenesheli-Kamyar', 'name': {'family': 'Azizzadenesheli', 'given': 'Kamyar'}, 'orcid': '0000-0001-8507-1868'}, {'id': 'Liu-Burigede', 'name': {'family': 'Liu', 'given': 'Burigede'}, 'orcid': '0000-0002-6518-3368'}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'Kaushik'}, 'orcid': '0000-0003-2908-5469'}, {'id': 'Stuart-A-M', 'name': {'family': 'Stuart', 'given': 'Andrew'}, 'orcid': '0000-0001-9091-7266'}, {'id': 'Anandkumar-A', 'name': {'family': 'Anandkumar', 'given': 'Anima'}, 'orcid': '0000-0002-6974-6797'}]}
Year: 2020
DOI: 10.48550/arXiv.2006.09535
One of the main challenges in using deep learning-based methods for simulating physical systems and solving partial differential equations (PDEs) is formulating physics-based data in the desired structure for neural networks. Graph neural networks (GNNs) have gained popularity in this area since graphs offer a natural way of modeling particle interactions and provide a clear way of discretizing the continuum models. However, the graphs constructed for approximating such tasks usually ignore long-range interactions due to unfavorable scaling of the computational complexity with respect to the number of nodes. The errors due to these approximations scale with the discretization of the system, thereby not allowing for generalization under mesh-refinement. Inspired by the classical multipole methods, we purpose a novel multi-level graph neural network framework that captures interaction at all ranges with only linear complexity. Our multi-level formulation is equivalent to recursively adding inducing points to the kernel matrix, unifying GNNs with multi-resolution matrix factorization of the kernel. Experiments confirm our multi-graph network learns discretization-invariant solution operators to PDEs and can be evaluated in linear time.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/gqmwj-t9b36Fracture Diodes: Directional Asymmetry of Fracture Toughness
https://resolver.caltech.edu/CaltechAUTHORS:20210114-143037831
Authors: {'items': [{'id': 'Brodnik-Neal-R', 'name': {'family': 'Brodnik', 'given': 'N. R.'}}, {'id': 'Brach-Stella', 'name': {'family': 'Brach', 'given': 'S.'}, 'orcid': '0000-0003-4766-8131'}, {'id': 'Long-C-M', 'name': {'family': 'Long', 'given': 'C.\u2009M.'}}, {'id': 'Ravichandran-G', 'name': {'family': 'Ravichandran', 'given': 'G.'}, 'orcid': '0000-0002-2912-0001'}, {'id': 'Bourdin-Blaise', 'name': {'family': 'Bourdin', 'given': 'B.'}, 'orcid': '0000-0002-1312-9175'}, {'id': 'Faber-K-T', 'name': {'family': 'Faber', 'given': 'K.\u2009T.'}, 'orcid': '0000-0001-6585-2536'}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'K.'}, 'orcid': '0000-0003-2908-5469'}]}
Year: 2021
DOI: 10.1103/physrevlett.126.025503
Toughness describes the ability of a material to resist fracture or crack propagation. It is demonstrated here that fracture toughness of a material can be asymmetric, i.e., the resistance of a medium to a crack propagating from right to left can be significantly different from that to a crack propagating from left to right. Such asymmetry is unknown in natural materials, but we show that it can be built into artificial materials through the proper control of microstructure. This paves the way for control of crack paths and direction, where fracture—when unavoidable—can be guided through predesigned paths to minimize loss of critical components.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/jvzm3-47c46Collective behavior in the kinetics and equilibrium of solid-state photoreaction
https://resolver.caltech.edu/CaltechAUTHORS:20201111-073222508
Authors: {'items': [{'id': 'Bai-Ruobing', 'name': {'family': 'Bai', 'given': 'Ruobing'}, 'orcid': '0000-0002-5847-0502'}, {'id': 'Teh-Ying-Shi', 'name': {'family': 'Teh', 'given': 'Ying Shi'}, 'orcid': '0000-0003-1743-4158'}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'Kaushik'}, 'orcid': '0000-0003-2908-5469'}]}
Year: 2021
DOI: 10.1016/j.eml.2020.101160
There is current interest in developing photoactive materials that deform on illumination. The strategy is to develop new photoactive molecules in solution, and then to incorporate these in the solid-state either by crystallization or by inserting them into polymers. This letter shows that the kinetics and the nature of the photo-induced phase transitions are profoundly different in single molecules (solution) and in the solid state using a lattice spin model. In solution, where the molecules act independently, the photoreaction follows first-order kinetics. However, in the solid state where the photoactive molecules interact with each other and therefore behave collectively during reaction, photoreactions follow the sigmoidal kinetics of nucleation and growth as in a first-order phase transition. Further, we find that the exact nature of the photo-induced strain has a critical effect on the kinetics, equilibrium, and microstructure formation. These predictions agree qualitatively with experimental observations, and provide insights for the development of new photoactive materials.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/wv0s0-cc526Photochemical-induced phase transitions in photoactive semicrystalline polymers
https://resolver.caltech.edu/CaltechAUTHORS:20210106-131335150
Authors: {'items': [{'id': 'Bai-Ruobing', 'name': {'family': 'Bai', 'given': 'Ruobing'}, 'orcid': '0000-0002-5847-0502'}, {'id': 'Ocegueda-Eric', 'name': {'family': 'Ocegueda', 'given': 'Eric'}, 'orcid': '0000-0001-7845-6890'}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'Kaushik'}, 'orcid': '0000-0003-2908-5469'}]}
Year: 2021
DOI: 10.1103/PhysRevE.103.033003
The emergent photoactive materials obtained through photochemistry make it possible to directly convert photon energy to mechanical work. There has been much recent work in developing appropriate materials, and a promising system is semicrystalline polymers of the photoactive molecule azobenzene. We develop a phase field model with two order parameters for the crystal-melt transition and the trans-cis photoisomerization to understand such materials, and the model describes the rich phenomenology. We find that the photoreaction rate depends sensitively on temperature: At temperatures below the crystal-melt transition temperature, photoreaction is collective, requires a critical light intensity, and shows an abrupt first-order phase transition manifesting nucleation and growth; at temperatures above the transition temperature, photoreaction is independent and follows first-order kinetics. Further, the phase transition depends significantly on the exact forms of spontaneous strain during the crystal-melt and trans-cis transitions. A nonmonotonic change of photopersistent cis ratio with increasing temperature is observed accompanied by a reentrant crystallization of trans below the melting temperature. A pseudo phase diagram is subsequently presented with varying temperature and light intensity along with the resulting actuation strain. These insights can assist the further development of these materials.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/1kq42-pn895Actuation of cylindrical nematic elastomer balloons
https://resolver.caltech.edu/CaltechAUTHORS:20210119-161700259
Authors: {'items': [{'id': 'Lee-Victoria', 'name': {'family': 'Lee', 'given': 'Victoria'}, 'orcid': '0000-0002-2748-0089'}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'Kaushik'}, 'orcid': '0000-0003-2908-5469'}]}
Year: 2021
DOI: 10.1063/5.0041288
Nematic elastomers are programmable soft materials that display large, reversible, and predictable deformation under an external stimulus such as a change in temperature or light. While much of the work in the field has focused on actuation from flat sheets, recent advances in 3D printing and other methods of directed synthesis have motivated the study of actuation of curved shells. Snap-through buckling has been a topic of particular interest. In this work, we present theoretical calculations to motivate another mode of actuation that combines programmable soft materials as well as instabilities associated with large deformation. Specifically, we analyze the deformation of a cylindrical shell of a patterned nematic elastomer under pressure, show that it can undergo an enormous change of volume with changing temperature and suggest its application as a pump with extremely high ejection fraction.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/mtpgy-33d96Fast Adaptive Mesh Augmented Lagrangian Digital Image Correlation
https://resolver.caltech.edu/CaltechAUTHORS:20210518-120552786
Authors: {'items': [{'id': 'Yang-Jin', 'name': {'family': 'Yang', 'given': 'J.'}, 'orcid': '0000-0002-5967-980X'}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'K.'}, 'orcid': '0000-0003-2908-5469'}]}
Year: 2021
DOI: 10.1007/s11340-021-00695-9
Background: Digital image correlation (DIC) is a widely used experimental method to measure full-field displacements and strains. This technique compares images of speckle patterns before and after deformation to computationally infer the displacement and strain fields. Of particular interest are complex mechanical phenomena where strains are far from uniform.
Objective: In such situations, it would be desirable to use an adaptive technique with higher resolution in the regions of rapidly changing strain and lower resolution elsewhere.
Methods: This paper builds on the recently proposed augmented Lagrangian digital image correlation (ALDIC) method to incorporate mesh adaptivity. We call the resulting approach adapt-ALDIC.
Results: We show that the structure of ALDIC makes it easy to incorporate adaptive resolution. We demonstrate through both synthetic and experimental examples that adapt-ALDIC is robust and saves significant computational time with almost no loss in accuracy. Among two types of adaptive mesh strategies, we find that adaptive quadtree mesh outperforms Kuhn triangulation mesh both in accuracy and computational cost. Indeed, we demonstrate that quadtree adapt-ALDIC provides compatible deformation and noise insensitivity typical of global DIC at the cost of local DIC.
Conclusions Adapt-ALDIC with adaptive quadtree mesh can analyze heterogeneous deformations accurately and efficiently. An open-source Matlab code is freely available through GitHub and Caltech DATA.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/e09m2-tha17Understanding the morphotropic phase boundary of perovskite solid solutions as a frustrated state
https://resolver.caltech.edu/CaltechAUTHORS:20201111-074328723
Authors: {'items': [{'id': 'Teh-Ying-Shi', 'name': {'family': 'Teh', 'given': 'Ying Shi'}, 'orcid': '0000-0003-1743-4158'}, {'id': 'Li-Jiangyu', 'name': {'family': 'Li', 'given': 'Jiangyu'}, 'orcid': '0000-0003-0533-1397'}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'Kaushik'}, 'orcid': '0000-0003-2908-5469'}]}
Year: 2021
DOI: 10.1103/PhysRevB.103.144201
This paper presents a lattice model incorporating random fields and long-range interactions where a frustrated state emerges at a specific composition but is suppressed elsewhere. The model is motivated by perovskite solid solutions and explains the phase diagram in such materials including the morphotropic phase boundary (MPB) that plays a critical role in applications for its enhanced dielectric, piezoelectric, and optical properties. Further, the model also suggests the possibility of phenomena by exploiting MPBs.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/yvtff-sc311Learning Dissipative Dynamics in Chaotic Systems
https://resolver.caltech.edu/CaltechAUTHORS:20210719-210135878
Authors: {'items': [{'id': 'Li-Zongyi', 'name': {'family': 'Li', 'given': 'Zongyi'}, 'orcid': '0000-0003-2081-9665'}, {'id': 'Kovachki-Nikola-B', 'name': {'family': 'Kovachki', 'given': 'Nikola'}, 'orcid': '0000-0002-3650-2972'}, {'id': 'Azizzadenesheli-Kamyar', 'name': {'family': 'Azizzadenesheli', 'given': 'Kamyar'}, 'orcid': '0000-0001-8507-1868'}, {'id': 'Liu-Burigede', 'name': {'family': 'Liu', 'given': 'Burigede'}, 'orcid': '0000-0002-6518-3368'}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'Kaushik'}, 'orcid': '0000-0003-2908-5469'}, {'id': 'Stuart-A-M', 'name': {'family': 'Stuart', 'given': 'Andrew'}, 'orcid': '0000-0001-9091-7266'}, {'id': 'Anandkumar-A', 'name': {'family': 'Anandkumar', 'given': 'Anima'}, 'orcid': '0000-0002-6974-6797'}]}
Year: 2021
DOI: 10.48550/arXiv.2106.06898
Chaotic systems are notoriously challenging to predict because of their sensitivity to perturbations and errors due to time stepping. Despite this unpredictable behavior, for many dissipative systems the statistics of the long term trajectories are governed by an invariant measure supported on a set, known as the global attractor; for many problems this set is finite dimensional, even if the state space is infinite dimensional. For Markovian systems, the statistical properties of long-term trajectories are uniquely determined by the solution operator that maps the evolution of the system over arbitrary positive time increments. In this work, we propose a machine learning framework to learn the underlying solution operator for dissipative chaotic systems, showing that the resulting learned operator accurately captures short-time trajectories and long-time statistical behavior. Using this framework, we are able to predict various statistics of the invariant measure for the turbulent Kolmogorov Flow dynamics with Reynolds numbers up to 5000.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/wm6xz-zgz78Probing the in-plane liquid-like behavior of liquid crystal elastomers
https://resolver.caltech.edu/CaltechAUTHORS:20210621-195349634
Authors: {'items': [{'id': 'Tokumoto-Haruki', 'name': {'family': 'Tokumoto', 'given': 'Haruki'}, 'orcid': '0000-0002-3658-3848'}, {'id': 'Zhou-Hao', 'name': {'family': 'Zhou', 'given': 'Hao'}, 'orcid': '0000-0002-6011-6422'}, {'id': 'Takebe-Asaka', 'name': {'family': 'Takebe', 'given': 'Asaka'}}, {'id': 'Kamitani-Kazutaka', 'name': {'family': 'Kamitani', 'given': 'Kazutaka'}, 'orcid': '0000-0002-5000-3467'}, {'id': 'Kojio-Ken', 'name': {'family': 'Kojio', 'given': 'Ken'}, 'orcid': '0000-0002-6917-7029'}, {'id': 'Takahara-Atsushi', 'name': {'family': 'Takahara', 'given': 'Atsushi'}}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'Kaushik'}, 'orcid': '0000-0003-2908-5469'}, {'id': 'Urayama-Kenji', 'name': {'family': 'Urayama', 'given': 'Kenji'}, 'orcid': '0000-0002-2823-6344'}]}
Year: 2021
DOI: 10.1126/sciadv.abe9495
PMCID: PMC8213220
When isotropic solids are unequally stretched in two orthogonal directions, the true stress (force per actual cross-sectional area) in the larger strain direction is typically higher than that in the smaller one. We show that thiol-acrylate liquid crystal elastomers with polydomain texture exhibit an unusual tendency: The true stresses in the two directions are always identical and governed only by the area change in the loading plane, independently of the combination of imposed strains in the two directions. This feature proves a previously unidentified state of matter that can vary its shape freely with no extra mechanical energy like liquids when deformed in the plane. The theory and simulation that explain the unique behavior are also provided. The in-plane liquid-like behavior opens doors for manifold applications, including wrinkle-free membranes and adaptable materials.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/g9emr-z9f62Concurrent goal-oriented materials-by-design
https://resolver.caltech.edu/CaltechAUTHORS:20210713-212259269
Authors: {'items': [{'id': 'Sun-Xingsheng', 'name': {'family': 'Sun', 'given': 'Xingsheng'}, 'orcid': '0000-0003-1527-789X'}, {'id': 'Liu-Burigede', 'name': {'family': 'Liu', 'given': 'Burigede'}, 'orcid': '0000-0002-6518-3368'}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'Kaushik'}, 'orcid': '0000-0003-2908-5469'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'Michael'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2021
DOI: 10.48550/arXiv.2106.06074
The development of new materials and structures for extreme conditions including impact remains a continuing challenge despite steady advances. Design is currently accomplished using a sequential approach: an optimal material is first developed using the process-structure-properties paradigm, where performance is measured against a blended measure. Then, the structure is optimized while holding the material properties fixed. In this paper, we propose an alternative concurrent and goal-oriented optimization approach where both the material properties and the structure are optimized simultaneously against an overall system-wide performance measure. We develop a non-intrusive, high-performance computational framework based on DAKOTA and GMSH and use it to study the ballistic impact of a double-layer plate of strong AZ31B magnesium alloy and soft polyurea. We show that the proposed concurrent and goal-oriented optimization strategy can provide significant advantage over the traditional sequential optimization approach.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/3nqk7-yhe03Tuning acoustic impedance in load-bearing structures
https://resolver.caltech.edu/CaltechAUTHORS:20210716-222546164
Authors: {'items': [{'id': 'Injeti-Sai-Sharan', 'name': {'family': 'Injeti', 'given': 'Sai Sharan'}, 'orcid': '0000-0003-1941-9752'}, {'id': 'Celli-Paolo', 'name': {'family': 'Celli', 'given': 'Paolo'}, 'orcid': '0000-0001-7839-7472'}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'Kaushik'}, 'orcid': '0000-0003-2908-5469'}, {'id': 'Daraio-C', 'name': {'family': 'Daraio', 'given': 'Chiara'}, 'orcid': '0000-0001-5296-4440'}]}
Year: 2021
DOI: 10.48550/arXiv.2106.10573
Acoustic transparency is the capability of a medium to transmit mechanical waves to adjacent media, without scattering. This characteristic can be achieved by carefully engineering the acoustic impedance of the medium -- a combination of wave speed and density, to match that of the surroundings. Owing to the strong correlation between acoustic wave speed and static stiffness, it is challenging to design acoustically transparent materials in a fluid, while maintaining their high structural rigidity. In this work, we propose a method to design architected lattices with independent control of the elastic wave speed at a chosen frequency, the mass density, and the static stiffness, along a chosen loading direction. We provide a sensitivity analysis to optimize these properties with respect to design parameters of the structure, that include localized masses at specific positions. We demonstrate the method on five different periodic, three dimensional lattices, to calculate bounds on the longitudinal wave speed as a function of their density and stiffness. We then perform experiments on 3-D printed structures, to validate our numerical simulations. The tools developed in this work can be used to design lightweight and stiff materials with optimized acoustic impedance for a plethora of applications, including ultrasound imaging, wave filtering and waveguiding.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/ed6ms-7ze27Hierarchical multiscale quantification of material uncertainty
https://resolver.caltech.edu/CaltechAUTHORS:20210225-132735184
Authors: {'items': [{'id': 'Liu-Burigede', 'name': {'family': 'Liu', 'given': 'Burigede'}, 'orcid': '0000-0002-6518-3368'}, {'id': 'Sun-Xingsheng', 'name': {'family': 'Sun', 'given': 'Xingsheng'}}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'Kaushik'}, 'orcid': '0000-0003-2908-5469'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'Michael'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2021
DOI: 10.1016/j.jmps.2021.104492
The macroscopic behavior of many materials is complex and the end result of mechanisms that operate across a broad range of disparate scales. An imperfect knowledge of material behavior across scales is a source of epistemic uncertainty of the overall material behavior. However, assessing this uncertainty is difficult due to the complex nature of material response and the prohibitive computational cost of integral calculations. In this paper, we exploit the multiscale and hierarchical nature of material response to develop an approach to quantify the overall uncertainty of material response without the need for integral calculations. Specifically, we bound the uncertainty at each scale and then combine the partial uncertainties in a way that provides a bound on the overall or integral uncertainty. The bound provides a conservative estimate on the uncertainty. Importantly, this approach does not require integral calculations that are prohibitively expensive. We demonstrate the framework on the problem of ballistic impact of a polycrystalline magnesium plate. Magnesium and its alloys are of current interest as promising light-weight structural and protective materials. Finally, we remark that the approach can also be used to study the sensitivity of the overall response to particular mechanisms at lower scales in a materials-by-design approach.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/cx5h6-8ef30Accelerated computational micromechanics and its application to polydomain liquid crystal elastomers
https://resolver.caltech.edu/CaltechAUTHORS:20210514-140222487
Authors: {'items': [{'id': 'Zhou-Hao', 'name': {'family': 'Zhou', 'given': 'Hao'}}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'Kaushik'}, 'orcid': '0000-0003-2908-5469'}]}
Year: 2021
DOI: 10.1016/j.jmps.2021.104470
We present an approach to solving problems in computational micromechanics that is amenable to massively parallel calculations through the use of graphical processing units (GPUs) and other accelerators. We apply it to study microstructure evolution in polydomain liquid crystal elastomers (LCEs). LCEs are rubber-like solids where rod-like nematic molecules are incorporated into the main or a side polymer chain. They undergo isotropic to nematic phase transition accompanied by spontaneous deformation which can be exploited for actuation. Further, they display a soft behavior at low temperatures due to the reorientation of the nematic directors. The problem of understanding nematic reorientation in the presence of realistic defects (non-ideality) is computationally expensive, and we address this by efficiently exploiting GPUs. The approach is broadly applicable to various phenomena including crystal plasticity and phase transitions that are described by internal variable theories. We verify the approach against previous calculations and establish its performance by studying long wavelength instability of finite elasticity. Our numerical studies of LCEs provide insights into the director distribution and reorientation in polydomain specimens, and how these lead to soft behavior under multiaxial loading. The results show good agreement with experimental observations.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/r1n9a-4ag27Neural Operator: Learning Maps Between Function Spaces
https://resolver.caltech.edu/CaltechAUTHORS:20210831-204010794
Authors: {'items': [{'id': 'Kovachki-Nikola-B', 'name': {'family': 'Kovachki', 'given': 'Nikola'}, 'orcid': '0000-0002-3650-2972'}, {'id': 'Li-Zongyi', 'name': {'family': 'Li', 'given': 'Zongyi'}, 'orcid': '0000-0003-2081-9665'}, {'id': 'Liu-Burigede', 'name': {'family': 'Liu', 'given': 'Burigede'}, 'orcid': '0000-0002-6518-3368'}, {'id': 'Azizzadenesheli-Kamyar', 'name': {'family': 'Azizzadenesheli', 'given': 'Kamyar'}, 'orcid': '0000-0001-8507-1868'}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'Kaushik'}, 'orcid': '0000-0003-2908-5469'}, {'id': 'Stuart-A-M', 'name': {'family': 'Stuart', 'given': 'Andrew'}, 'orcid': '0000-0001-9091-7266'}, {'id': 'Anandkumar-A', 'name': {'family': 'Anandkumar', 'given': 'Anima'}}]}
Year: 2021
DOI: 10.48550/arXiv.2108.08481
The classical development of neural networks has primarily focused on learning mappings between finite dimensional Euclidean spaces or finite sets. We propose a generalization of neural networks tailored to learn operators mapping between infinite dimensional function spaces. We formulate the approximation of operators by composition of a class of linear integral operators and nonlinear activation functions, so that the composed operator can approximate complex nonlinear operators. Furthermore, we introduce four classes of operator parameterizations: graph-based operators, low-rank operators, multipole graph-based operators, and Fourier operators and describe efficient algorithms for computing with each one. The proposed neural operators are resolution-invariant: they share the same network parameters between different discretizations of the underlying function spaces and can be used for zero-shot super-resolutions. Numerically, the proposed models show superior performance compared to existing machine learning based methodologies on Burgers' equation, Darcy flow, and the Navier-Stokes equation, while being several order of magnitude faster compared to conventional PDE solvers.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/h5ry0-fsp13Simple deformation measures for discrete elastic rods and ribbons
https://resolver.caltech.edu/CaltechAUTHORS:20210809-205939039
Authors: {'items': [{'id': 'Korner-Kevin', 'name': {'family': 'Korner', 'given': 'K.'}, 'orcid': '0000-0002-2967-9657'}, {'id': 'Audoly-Basile', 'name': {'family': 'Audoly', 'given': 'B.'}, 'orcid': '0000-0002-0534-1467'}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'K.'}, 'orcid': '0000-0003-2908-5469'}]}
Year: 2021
DOI: 10.1098/rspa.2021.0561
The discrete elastic rod method (Bergou et al. 2008 ACM Trans. Graph. 27, 63:1–63:12. (doi:10.1145/1360612.1360662)) is a numerical method for simulating slender elastic bodies. It works by representing the centreline as a polygonal chain, attaching two perpendicular directors to each segment and defining discrete stretching, bending and twisting deformation measures and a discrete strain energy. Here, we investigate an alternative formulation of this model based on a simpler definition of the discrete deformation measures. Both formulations are equally consistent with the continuous rod model. Simple formulae for the first and second gradients of the discrete deformation measures are derived, making it easy to calculate the Hessian of the discrete strain energy. A few numerical illustrations are given. The approach is also extended to inextensible ribbons described by the Wunderlich model, and both the developability constraint and the dependence of the energy on the strain gradients are handled naturally.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/nrbae-qk103Machine-learned prediction of the electronic fields in a crystal
https://resolver.caltech.edu/CaltechAUTHORS:20210412-100652607
Authors: {'items': [{'id': 'Teh-Ying-Shi', 'name': {'family': 'Teh', 'given': 'Ying Shi'}, 'orcid': '0000-0003-1743-4158'}, {'id': 'Ghosh-Swarnava', 'name': {'family': 'Ghosh', 'given': 'Swarnava'}, 'orcid': '0000-0003-3800-5264'}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'Kaushik'}, 'orcid': '0000-0003-2908-5469'}]}
Year: 2021
DOI: 10.1016/j.mechmat.2021.104070
We propose an approach for exploiting machine learning to approximate electronic fields in crystalline solids subjected to deformation. Strain engineering is emerging as a widely used method for tuning the properties of materials, and this requires repeated density functional theory calculations of the unit cell subjected to strain. Repeated unit cell calculations are also required for multi-resolution studies of defects in crystalline solids. We propose an approach that uses data from such calculations to train a carefully architected machine learning approximation. We demonstrate the approach on magnesium, a promising light-weight structural material: we show that we can predict the energy and electronic fields to the level of chemical accuracy, and even capture lattice instabilities.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/bakha-jp029Accurate approximations of density functional theory for large systems with applications to defects in crystalline solids
https://resolver.caltech.edu/CaltechAUTHORS:20220119-233956787
Authors: {'items': [{'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'Kaushik'}, 'orcid': '0000-0003-2908-5469'}, {'id': 'Gavini-Vikram', 'name': {'family': 'Gavini', 'given': 'Vikram'}, 'orcid': '0000-0002-9451-2300'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'Michael'}, 'orcid': '0000-0001-5877-4824'}, {'id': 'Ponga-Mauricio', 'name': {'family': 'Ponga', 'given': 'Mauricio'}, 'orcid': '0000-0001-5058-1454'}, {'id': 'Suryanarayana-Phanish', 'name': {'family': 'Suryanarayana', 'given': 'Phanish'}, 'orcid': '0000-0001-5172-0049'}]}
Year: 2021
DOI: 10.48550/arXiv.2112.06016
This chapter presents controlled approximations of Kohn-Sham density functional theory (DFT) that enable very large scale simulations. The work is motivated by the study of defects in crystalline solids, though the ideas can be used in other applications. The key idea is to formulate DFT as a minimization problem over the density operator, and to cast spatial and spectral discretization as systematically convergent approximations. This enables efficient and adaptive algorithms that solve the equations of DFT with no additional modeling, and up to desired accuracy, for very large systems, with linear and sublinear scaling. Various approaches based on such approximations are presented, and their numerical performance demonstrated through selected examples. These examples also provide important insight about the mechanics and physics of defects in crystalline solids.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/gb81e-r3t46Imposing equilibrium on experimental 3-D stress fields using Hodge decomposition and FFT-based optimization
https://resolver.caltech.edu/CaltechAUTHORS:20211105-145214759
Authors: {'items': [{'id': 'Zhou-Hao', 'name': {'family': 'Zhou', 'given': 'Hao'}}, {'id': 'Lebensohn-Ricardo-A', 'name': {'family': 'Lebensohn', 'given': 'Ricardo A.'}, 'orcid': '0000-0002-3152-9105'}, {'id': 'Reischig-Péter', 'name': {'family': 'Reischig', 'given': 'Péter'}}, {'id': 'Ludwig-Wolfgang', 'name': {'family': 'Ludwig', 'given': 'Wolfgang'}, 'orcid': '0000-0002-3256-3831'}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'Kaushik'}, 'orcid': '0000-0003-2908-5469'}]}
Year: 2022
DOI: 10.1016/j.mechmat.2021.104109
We present a methodology to impose micromechanical constraints, i.e. stress equilibrium at grain and sub-grain scale, to an arbitrary (non-equilibrated) voxelized stress field obtained, for example, by means of synchrotron X-ray diffraction techniques. The method consists in finding the equilibrated stress field closest (in L²-norm sense) to the measured non-equilibrated stress field, via the solution of an optimization problem. The extraction of the divergence-free (equilibrated) part of a general (non-equilibrated) field is performed using the Hodge decomposition of a symmetric matrix field, which is the generalization of the Helmholtz decomposition of a vector field into the sum of an irrotational field and a solenoidal field. The combination of: a) the Euler–Lagrange equations that solve the optimization problem, and b) the Hodge decomposition, gives a differential expression that contains the bi-harmonic operator and two times the curl operator acting on the experimental stress field. These high-order derivatives can be efficiently performed in Fourier space. The method is applied to filter the non-equilibrated parts of a synthetic piecewise constant stress fields with a known ground truth, and stress fields in Gum Metal, a beta-Ti-based alloy measured in-situ using Diffraction Contrast Tomography (DCT). In both cases, the largest corrections were obtained near grain boundaries.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/en67q-akj15A learning-based multiscale method and its application to inelastic impact problems
https://resolver.caltech.edu/CaltechAUTHORS:20210225-132721680
Authors: {'items': [{'id': 'Liu-Burigede', 'name': {'family': 'Liu', 'given': 'Burigede'}, 'orcid': '0000-0002-6518-3368'}, {'id': 'Kovachki-Nikola-B', 'name': {'family': 'Kovachki', 'given': 'Nikola'}, 'orcid': '0000-0002-3650-2972'}, {'id': 'Li-Zongyi', 'name': {'family': 'Li', 'given': 'Zongyi'}}, {'id': 'Azizzadenesheli-Kamyar', 'name': {'family': 'Azizzadenesheli', 'given': 'Kamyar'}, 'orcid': '0000-0001-8507-1868'}, {'id': 'Anandkumar-A', 'name': {'family': 'Anandkumar', 'given': 'Anima'}}, {'id': 'Stuart-A-M', 'name': {'family': 'Stuart', 'given': 'Andrew M.'}, 'orcid': '0000-0001-9091-7266'}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'Kaushik'}, 'orcid': '0000-0003-2908-5469'}]}
Year: 2022
DOI: 10.1016/j.jmps.2021.104668
The macroscopic properties of materials that we observe and exploit in engineering application result from complex interactions between physics at multiple length and time scales: electronic, atomistic, defects, domains etc. Multiscale modeling seeks to understand these interactions by exploiting the inherent hierarchy where the behavior at a coarser scale regulates and averages the behavior at a finer scale. This requires the repeated solution of computationally expensive finer-scale models, and often a priori knowledge of those aspects of the finer-scale behavior that affect the coarser scale (order parameters, state variables, descriptors, etc.). We address this challenge in a two-scale setting where we learn the fine-scale behavior from off-line calculations and then use the learnt behavior directly in coarse scale calculations. The approach builds on the recent success of deep neural networks by combining their approximation power in high dimensions with ideas from model reduction. It results in a neural network approximation that has high fidelity, is computationally inexpensive, is independent of the need for a priori knowledge, and can be used directly in the coarse scale calculations. We demonstrate the approach on problems involving the impact of magnesium, a promising light-weight structural and protective material.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/j2js9-txr69Phase-Field Modeling of Deformation Twinning and Dislocation Slip Interaction in Polycrystalline Solids
https://resolver.caltech.edu/CaltechAUTHORS:20220207-702194000
Authors: {'items': [{'id': 'Ocegueda-Eric', 'name': {'family': 'Ocegueda', 'given': 'Eric'}, 'orcid': '0000-0001-7845-6890'}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'Kaushik'}, 'orcid': '0000-0003-2908-5469'}]}
Year: 2022
DOI: 10.1007/978-3-030-92533-8_51
Mechanical twinning is a form of inelastic deformation in magnesium and other hexagonal close-packed (hcp) metals, which has a significant effect on material behavior. Magnesium's high strength-to-weight ratio has led to its interest in structural, automotive, and armor applications, requiring a comprehensive understanding of twinning's effect on material response. Past studies have taken either a microscopic approach, through atomistic simulations, or a macroscopic approach, through simplified pseudo-slip models. However, twins interact across the mesoscale, forming collectively across grains with complex local morphology propagating into bulk behavior. With the goal of describing twinning's mesoscale behavior, we propose a model where twinning is treated using a phase-field approach, while slip is considered using crystal plasticity, with lattice reorientation, twinning length scale, and twin-slip interactions all accounted. We present GPU accelerated simulations on polycrystalline solids and summarize the insights gained from these studies and the implications on the macroscale behavior of hcp materials.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/cf6q7-pvq59Multiscale modeling of materials: Computing, data science, uncertainty and goal-oriented optimization
https://resolver.caltech.edu/CaltechAUTHORS:20220121-968309000
Authors: {'items': [{'id': 'Kovachki-Nikola-B', 'name': {'family': 'Kovachki', 'given': 'Nikola'}, 'orcid': '0000-0002-3650-2972'}, {'id': 'Liu-Burigede', 'name': {'family': 'Liu', 'given': 'Burigede'}, 'orcid': '0000-0002-6518-3368'}, {'id': 'Sun-Xingsheng', 'name': {'family': 'Sun', 'given': 'Xingsheng'}, 'orcid': '0000-0003-1527-789X'}, {'id': 'Zhou-Hao', 'name': {'family': 'Zhou', 'given': 'Hao'}, 'orcid': '0000-0002-6011-6422'}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'Kaushik'}, 'orcid': '0000-0003-2908-5469'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'Michael'}, 'orcid': '0000-0001-5877-4824'}, {'id': 'Stuart-A-M', 'name': {'family': 'Stuart', 'given': 'Andrew'}, 'orcid': '0000-0001-9091-7266'}]}
Year: 2022
DOI: 10.1016/j.mechmat.2021.104156
The recent decades have seen various attempts at accelerating the process of developing materials targeted towards specific applications. The performance required for a particular application leads to the choice of a particular material system whose properties are optimized by manipulating its underlying microstructure through processing. The specific configuration of the structure is then designed by characterizing the material in detail, and using this characterization along with physical principles in system level simulations and optimization. These have been advanced by multiscale modeling of materials, high-throughput experimentations, materials data-bases, topology optimization and other ideas. Still, developing materials for extreme applications involving large deformation, high strain rates and high temperatures remains a challenge. This article reviews a number of recent methods that advance the goal of designing materials targeted by specific applications.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/cjvbg-kbb29Interaction between deformation twinning and dislocation slip in polycrystalline solids
https://resolver.caltech.edu/CaltechAUTHORS:20220304-171248075
Authors: {'items': [{'id': 'Ocegueda-Eric', 'name': {'family': 'Ocegueda', 'given': 'Eric'}, 'orcid': '0000-0001-7845-6890'}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'Kaushik'}, 'orcid': '0000-0003-2908-5469'}]}
Year: 2022
DOI: 10.48550/arXiv.2202.02908
Deformation twinning is a form of permanent deformation that is commonly observed in low symmetry crystals such as hexagonal close-packed (hcp) metals. With recent increased interest in using hcp metals, such as magnesium, in structural, automotive, and armor applications due to their high strength to weight ratio, there is a need for a comprehensive understanding of deformation twinning and its interaction with dislocation slip. A great deal has been learned at the microscopic level where individual dislocations interact with twin boundaries through atomistic simulations, and at the macroscopic level by ignoring morphology and treating twinning as `pseudo-slip'. However, twins form collectively across multiple grains with complex morphology that affects the bulk behavior. These mesoscale aspects have been less studied and are the focus of this paper. We present a model that describes the twin and slip morphology, its evolution, and interactions in a unified manner at the scale of several grains and use it to study the implications on macroscopic behavior. The key ideas are to combine a phase-field model of twinning with a crystal plasticity model of slip, and to implement it in parallel on graphic processing units for fast computations.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/4dsdm-4y873Optimal design of responsive structures
https://resolver.caltech.edu/CaltechAUTHORS:20210831-203942317
Authors: {'items': [{'id': 'Akerson-Andrew', 'name': {'family': 'Akerson', 'given': 'Andrew'}, 'orcid': '0000-0002-4382-1226'}, {'id': 'Bourdin-Blaise', 'name': {'family': 'Bourdin', 'given': 'Blaise'}, 'orcid': '0000-0002-1312-9175'}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'Kaushik'}, 'orcid': '0000-0003-2908-5469'}]}
Year: 2022
DOI: 10.1007/s00158-022-03200-5
With recent advances in both responsive materials and fabrication techniques, it is now possible to construct integrated functional structures, composed of both structural and active materials. We investigate the robust design of such structures through topology optimization. By applying a typical interpolation scheme and filtering technique, we prove existence of an optimal design to a class of objective functions which depend on the compliances of the stimulated and unstimulated states. In particular, we consider the actuation work and the blocking load as objectives, both of which may be written in terms of compliances. We study numerical results for the design of a 2D rectangular lifting actuator for both of these objectives, and discuss some intuition behind the features of the converged designs. We formulate the optimal design of these integrated responsive structures with the introduction of voids or holes in the domain, and show that our existence result holds in this setting. We again consider the design of the 2D lifting actuator now with voids. Finally, we investigate the optimal design of an integrated 3D torsional actuator for maximum blocking torque.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/k9d4a-mhq95DIC Challenge 2.0: Developing Images and Guidelines for Evaluating Accuracy and Resolution of 2D Analyses
https://resolver.caltech.edu/CaltechAUTHORS:20220202-403160900
Authors: {'items': [{'id': 'Reu-P-L', 'name': {'family': 'Reu', 'given': 'P. L.'}}, {'name': {'family': 'Blaysat', 'given': 'B.'}, 'orcid': '0000-0002-4642-7451'}, {'name': {'family': 'Andó', 'given': 'E.'}}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'K.'}, 'orcid': '0000-0003-2908-5469'}, {'name': {'family': 'Couture', 'given': 'C.'}}, {'name': {'family': 'Couty', 'given': 'V.'}}, {'name': {'family': 'Deb', 'given': 'D.'}}, {'name': {'family': 'Fayad', 'given': 'S. S.'}}, {'name': {'family': 'Iadicola', 'given': 'M. A.'}}, {'name': {'family': 'Jaminion', 'given': 'S.'}}, {'name': {'family': 'Klein', 'given': 'M.'}}, {'name': {'family': 'Landauer', 'given': 'A. K.'}}, {'name': {'family': 'Lava', 'given': 'P.'}}, {'name': {'family': 'Liu', 'given': 'M.'}}, {'name': {'family': 'Luan', 'given': 'L. K.'}}, {'name': {'family': 'Olufsen', 'given': 'S. N.'}}, {'name': {'family': 'Réthoré', 'given': 'J.'}}, {'name': {'family': 'Roubin', 'given': 'E.'}}, {'name': {'family': 'Seidl', 'given': 'D. T.'}}, {'name': {'family': 'Siebert', 'given': 'T.'}}, {'name': {'family': 'Stamati', 'given': 'O.'}}, {'name': {'family': 'Toussaint', 'given': 'E.'}}, {'name': {'family': 'Turner', 'given': 'D.'}}, {'name': {'family': 'Vemulapati', 'given': 'C. S. R.'}}, {'name': {'family': 'Weikert', 'given': 'T.'}}, {'name': {'family': 'Witz', 'given': 'J. F.'}}, {'name': {'family': 'Witzel', 'given': 'O.'}}, {'name': {'family': 'Yang', 'given': 'J.'}}]}
Year: 2022
DOI: 10.1007/s11340-021-00806-6
Background: The DIC Challenge 2.0 follows on from the work accomplished in the first Digital Image Correlation (DIC) Challenge Reu et al. (Experimental Mechanics 58(7):1067, 1). The second challenge was required to better quantify the spatial resolution of 2D-DIC codes.
Objective: The goal of this paper is to outline the methods and images for the 2D-DIC community to use to evaluate the performance of their codes and improve the implementation of 2D-DIC.
Methods: This paper covers the creation of the new challenge images and the analysis and discussion of the results. It proposes a method of unambiguously defining spatial resolution for 2D-DIC and explores the tradeoff between displacement and strain noise (or measurement noise) and spatial resolution for a wide variety of DIC codes by a combination of the images presented here and a performance factor called Metrological Efficiency Indicator (MEI).
Results: The performance of the 2D codes generally followed the expected theoretical performance, particularly in the measurement of the displacement. The comparison did however show that even with fairly uniform displacement performance, the calculation of the strain spatial resolution varied widely.
Conclusions: This work provides a useful framework for understanding the tradeoff and analyzing the performance of the DIC software using the provided images. It details some of the unique errors associated with the analysis of these images, such as the Pattern Induced Bias (PIB) and imprecision introduced through the strain calculation method. Future authors claiming improvements in 2D accuracy are encouraged to use these images for an unambiguous comparison.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/dcdce-2c712Spectral quadrature for the first principles study of crystal defects: Application to magnesium
https://resolver.caltech.edu/CaltechAUTHORS:20210729-195436164
Authors: {'items': [{'id': 'Ghosh-Swarnava', 'name': {'family': 'Ghosh', 'given': 'Swarnava'}, 'orcid': '0000-0003-3800-5264'}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'Kaushik'}, 'orcid': '0000-0003-2908-5469'}]}
Year: 2022
DOI: 10.1016/j.jcp.2022.111035
We present an accurate and efficient finite-difference formulation and parallel implementation of Kohn-Sham Density (Operator) Functional Theory (DFT) for non periodic systems embedded in a bulk environment. Specifically, employing non-local pseudopotentials, local reformulation of electrostatics, and truncation of the spatial Kohn-Sham Hamiltonian, and the Linear Scaling Spectral Quadrature method to solve for the pointwise electronic fields in real-space and the non-local component of the atomic force, we develop a parallel finite difference framework suitable for distributed memory computing architectures to simulate non-periodic systems embedded in a bulk environment. Choosing examples from magnesium-aluminum alloys, we first demonstrate the convergence of energies and forces with respect to spectral quadrature polynomial order, and the width of the spatially truncated Hamiltonian. Next, we demonstrate the parallel scaling of our framework, and show that the computation time and memory scale linearly with respect to the number of atoms. Next, we use the developed framework to simulate isolated point defects and their interactions in magnesium-aluminum alloys. Our findings conclude that the binding energies of divacancies, Al solute-vacancy and two Al solute atoms are anisotropic and are dependent on cell size. Furthermore, the binding is favorable in all three cases.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/57b8v-e0y47Light-induced swirling and locomotion
https://resolver.caltech.edu/CaltechAUTHORS:20221128-491790500.1
Authors: {'items': [{'id': 'Maghsoodi-Ameneh', 'name': {'family': 'Maghsoodi', 'given': 'Ameneh'}, 'orcid': '0000-0002-8250-8734'}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'Kaushik'}, 'orcid': '0000-0003-2908-5469'}]}
Year: 2022
DOI: 10.1098/rspa.2022.0545
The design of remotely activated, untethered devices without onboard power is a continuing challenge in soft robotics. This work describes a method of generating a whirling motion in pre-stressed photomechanical liquid crystal elastomer fibres using steady illumination that can be exploited for propulsion and mixing. Photomechanical liquid crystal elastomers (LCEs) can convert light directly into mechanical deformation, making them attractive candidates for soft actuators capable of remote and multi-mode actuation. We propose a three-dimensional multi-scale model of the nonlinear and non-local dynamics of fibres of photomechanical LCEs under illumination. We use the model to show that pre-stressed helix-like fibres immersed in a fluid can undergo a periodic whirling motion under steady illumination. We analyse the photo-driven spatio-temporal pattern and stability of the whirling deformation, and provide a parametric study. Unlike previous work on photo-driven periodic motion, this whirling motion does not exploit instabilities in the form of snap-through phenomena, or unilateral constraints as in rolling. More broadly, our work provides an unusual example of a physical system capable of periodic motion under steady stimulus that does not exploit instabilities. We finally show that such motion can be exploited in developing remote controlled bioinspired microswimmers and novel micromixers.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/8nygz-pj377Leaping liquid crystal elastomers
https://resolver.caltech.edu/CaltechAUTHORS:20230512-806563000.1
Authors: {'items': [{'id': 'Hebner-Tayler-S', 'name': {'family': 'Hebner', 'given': 'Tayler S.'}, 'orcid': '0000-0003-2723-3835'}, {'id': 'Korner-Kevin', 'name': {'family': 'Korner', 'given': 'Kevin'}, 'orcid': '0000-0002-2967-9657'}, {'id': 'Bowman-Christopher-N', 'name': {'family': 'Bowman', 'given': 'Christopher N.'}, 'orcid': '0000-0001-8458-7723'}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'Kaushik'}, 'orcid': '0000-0003-2908-5469'}, {'id': 'White-Timothy-J', 'name': {'family': 'White', 'given': 'Timothy J.'}, 'orcid': '0000-0001-8006-7173'}]}
Year: 2023
DOI: 10.1126/sciadv.ade1320
PMCID: PMC9848472
Snap-through mechanisms are pervasive in everyday life in biological systems, engineered devices, and consumer products. Snap-through transitions can be realized in responsive materials via stimuli-induced mechanical instability. Here, we demonstrate a rapid and powerful snap-through response in liquid crystalline elastomers (LCEs). While LCEs have been extensively examined as material actuators, their deformation rate is limited by the second-order character of their phase transition. In this work, we locally pattern the director orientation of LCEs and fabricate mechanical elements with through-thickness (functionally graded) modulus gradients to realize stimuli-induced responses as fast as 6 ms. The rapid acceleration and associated force output of the LCE elements cause the elements to leap to heights over 200 times the material thickness. The experimental examination in functionally graded LCE elements is complemented with computational evaluation of the underlying mechanics. The experimentally validated model is then exercised as a design tool to guide functional implementation, visualized as directional leaping.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/2k2dy-yd945Low energy fold paths in multistable origami structures
https://resolver.caltech.edu/CaltechAUTHORS:20230227-87934600.11
Authors: {'items': [{'id': 'Zhou-Hao', 'name': {'family': 'Zhou', 'given': 'Hao'}, 'orcid': '0000-0002-6011-6422'}, {'id': 'Grasinger-Matthew', 'name': {'family': 'Grasinger', 'given': 'Matthew'}, 'orcid': '0000-0001-7188-0736'}, {'id': 'Buskohl-Philip', 'name': {'family': 'Buskohl', 'given': 'Philip'}, 'orcid': '0000-0001-5517-1956'}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'Kaushik'}, 'orcid': '0000-0003-2908-5469'}]}
Year: 2023
DOI: 10.1016/j.ijsolstr.2023.112125
Origami design concepts are finding pervasive utility in engineering applications due to their ability to map complex shape transformations into a series of folding actions. The interplay between stretching, folding, and facet bending modes in origami structures also generates a complex energy landscape of multistable states to leverage for engineering applications. However, identifying rigid and deformable folding paths in this high-dimensional and non-convex energy landscape remains a challenge. To help address this challenge, we first introduce a global, constraint-based approach to modeling origami that uses a redundant kinematic description of the facets and nodes, and treats the kinematic compatibility between these redundant descriptors as a constraint. This approach allows for complex facet shapes without increasing the dimensionality of the system, as would be necessary in truss-based and other node-based formulations in order to stiffen the facet. Secondly, we adopt the nudged elastic band method, that is widely used in computational chemistry, to identify minimum energy folding paths. This strategy addresses, from a global perspective, the difficulty of piecing together sequences of local folding steps in order to connect two different points in configuration space. We implement this path finding approach on both the kinematic constraint formulation and a truss-based model, and compare their behaviors on a series of folding and multistable origami examples.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/153ej-mpr91Learning Markovian Homogenized Models in Viscoelasticity
https://resolver.caltech.edu/CaltechAUTHORS:20230613-155502989
Authors: {'items': [{'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'Kaushik'}, 'orcid': '0000-0003-2908-5469'}, {'id': 'Liu-Burigede', 'name': {'family': 'Liu', 'given': 'Burigede'}, 'orcid': '0000-0002-6518-3368'}, {'id': 'Stuart-A-M', 'name': {'family': 'Stuart', 'given': 'Andrew'}, 'orcid': '0000-0001-9091-7266'}, {'id': 'Trautner-Margaret', 'name': {'family': 'Trautner', 'given': 'Margaret'}, 'orcid': '0000-0001-9937-8393'}]}
Year: 2023
DOI: 10.1137/22M1499200
Fully resolving dynamics of materials with rapidly varying features involves expensive fine-scale computations which need to be conducted on macroscopic scales. The theory of homogenization provides an approach for deriving effective macroscopic equations which eliminates the small scales by exploiting scale separation. An accurate homogenized model avoids the computationally expensive task of numerically solving the underlying balance laws at a fine scale, thereby rendering a numerical solution of the balance laws more computationally tractable. In complex settings, homogenization only defines the constitutive model implicitly, and machine learning can be used to learn the constitutive model explicitly from localized fine-scale simulations. In the case of one-dimensional viscoelasticity, the linearity of the model allows for a complete analysis. We establish that the homogenized constitutive model may be approximated by a recurrent neural network that captures the memory. The memory is encapsulated in the evolution of an appropriate finite set of hidden variables, which are discovered through the learning process and dependent on the history of the strain. Simulations are presented which validate the theory. Guidance for the learning of more complex models, such as arise in plasticity, using similar techniques, is given.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/tsw3z-9yb69Accurate Approximations of Density Functional Theory for Large Systems with Applications to Defects in Crystalline Solids
https://authors.library.caltech.edu/records/nc59f-2jz76
Authors: {'items': [{'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'Kaushik'}, 'orcid': '0000-0003-2908-5469'}, {'id': 'Gavini-Vikram', 'name': {'family': 'Gavini', 'given': 'Vikram'}, 'orcid': '0000-0002-9451-2300'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'Michael'}, 'orcid': '0000-0001-5877-4824'}, {'id': 'Ponga-Mauricio', 'name': {'family': 'Ponga', 'given': 'Mauricio'}, 'orcid': '0000-0001-5058-1454'}, {'id': 'Suryanarayana-Phanish', 'name': {'family': 'Suryanarayana', 'given': 'Phanish'}, 'orcid': '0000-0001-5172-0049'}]}
Year: 2023
DOI: 10.1007/978-3-031-22340-2_12
<p>This chapter presents controlled approximations of Kohn–Sham density functional theory (DFT) that enable very large scale simulations. The work is motivated by the study of defects in crystalline solids, though the ideas can be used in other applications. The key idea is to formulate DFT as a minimization problem over the density operator, and to cast spatial and spectral discretization as systematically convergent approximations. This enables efficient and adaptive algorithms that solve the equations of DFT with no additional modeling, and up to desired accuracy, for very large systems, with linear and sublinear scaling. Various approaches based on such approximations are presented, and their numerical performance is demonstrated through selected examples. These examples also provide important insights into the mechanics and physics of defects in crystalline solids.</p>https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/nc59f-2jz76