Book Section records
https://feeds.library.caltech.edu/people/Bhattacharya-K/book_section.rss
A Caltech Library Repository Feedhttp://www.rssboard.org/rss-specificationpython-feedgenenFri, 12 Apr 2024 23:17:59 +0000Effective 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.edu/records/nc8b8-t0911A 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.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.edu/records/p07ke-5fs22The 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.edu/records/mt9x9-7x492Energy 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.edu/records/09na0-3ex49Mechanics 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.edu/records/g7p4f-bgb71Electromechanical 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.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.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.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.edu/records/bqwwv-zrz35Observation 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.edu/records/ypr41-9rp58A 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.edu/records/ekbmw-1r826Modeling 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.edu/records/x20qz-19897Interaction 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.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.edu/records/r4jat-6pe58Investigation 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.edu/records/byq2z-wba47Deformation 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.edu/records/yhgba-w7z71Linear 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.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.edu/records/jb1tn-mtd29Measuring 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.edu/records/p1yq5-1fh78Investigating 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.edu/records/n9jzn-v0q21Cohesive 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.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.edu/records/bbwxj-tj840Multipole 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.edu/records/gqmwj-t9b36Phase-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.edu/records/cf6q7-pvq59Accurate 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.edu/records/nc59f-2jz76