Article records
https://feeds.library.caltech.edu/people/Kochmann-D-M/article.rss
A Caltech Library Repository Feedhttp://www.rssboard.org/rss-specificationpython-feedgenenThu, 30 Nov 2023 18:09:21 +0000Composite Materials with Viscoelastic Stiffness Greater Than Diamond
https://resolver.caltech.edu/CaltechAUTHORS:20131001-082855007
Authors: Jaglinski, T.; Kochmann, D. M.; Stone, D.; Lakes, R. S.
Year: 2007
DOI: 10.1126/science.1135837
We show that composite materials can exhibit a viscoelastic modulus (Young's modulus) that is far greater than that of either constituent. The modulus, but not the strength, of the composite was observed to be substantially greater than that of diamond. These composites contain bariumtitanate inclusions, which undergo a volume-change phase transformation if they are not constrained. In the composite, the inclusions are partially constrained by the surrounding metal matrix. The constraint stabilizes the negative bulk modulus (inverse compressibility) of the inclusions. This negative modulus arises from stored elastic energy in the inclusions, in contrast to periodic composite metamaterials that exhibit negative refraction by inertial resonant effects. Conventional composites with positive-stiffness constituents have aggregate properties bounded by a weighted average of constituent properties; their modulus cannot exceed that of the stiffest constituent.https://authors.library.caltech.edu/records/v29w4-53g90Dislocation pile-ups in bicrystals within continuum dislocation theory
https://resolver.caltech.edu/CaltechAUTHORS:20131001-082855438
Authors: Kochmann, D. M.; Le, K. C.
Year: 2008
DOI: 10.1016/j.ijplas.2008.03.007
Within continuum dislocation theory the plastic deformation of bicrystals under a mixed deformation of plane constrained uniaxial extension and shear is investigated with regard to the nucleation of dislocations and the dislocation pile-up near the phase boundaries of a model bicrystal with one active slip system within each single crystal. For plane uniaxial extension, we present a closed-form analytical solution for the evolution of the plastic distortion and of the dislocation network in the case of symmetric slip planes (i.e. for twins), which exhibits an energetic as well as a dissipative threshold for the dislocation nucleation. The general solution for non-symmetric slip systems is obtained numerically. For a combined deformation of extension and shear, we analyze the possibility of linearly superposing results obtained for both loading cases independently. All solutions presented in this paper also display the Bauschinger effect of translational work hardening and a size effect typical to problems of crystal plasticity.https://authors.library.caltech.edu/records/n7e88-0xr39A continuum model for initiation and evolution of deformation twinning
https://resolver.caltech.edu/CaltechAUTHORS:20131001-082855691
Authors: Kochmann, Dennis M.; Le, Khanh C.
Year: 2009
DOI: 10.1016/j.jmps.2009.03.001
Within continuum dislocation theory the plastic deformation of a single crystal with one active slip system under plane-strain constrained shear is investigated. By introducing a twinning shear into the energy of the crystal, we show that in a certain range of straining the formation of deformation twins becomes energetically preferable. An energetic threshold for the onset of twinning is determined. A rough analysis qualitatively describes not only the evolving volume fractions of twins but also their number during straining. Finally, we analyze the evolution of deformation twins and of the dislocation network at non-zero dissipation. We present the corresponding stress–strain hysteresis, the evolution of the plastic distortion, the twin volume fractions and the dislocation densities.https://authors.library.caltech.edu/records/12dt7-xc085Dynamic stability analysis of an elastic composite material having a negative-stiffness phase
https://resolver.caltech.edu/CaltechAUTHORS:20131001-082855204
Authors: Kochmann, D. M.; Drugan, W. J.
Year: 2009
DOI: 10.1016/j.jmps.2009.03.002
The rigorous classical bounds of elastic composite materials theory provide limits on the achievable composite stiffnesses in terms of the properties and arrangements of the composite's constituents. These bounds result from the assumption, presumably made for stability reasons, that each constituent material must have positive-definite elastic moduli. If this assumption is relaxed, recently published elasticity analyses and experimental measurements show these bounds can be greatly exceeded, resulting in new materials of enormous potential. The key question is whether a composite material having a non-positive-definite constituent can be stable overall in the practically useful situation of applied traction boundary conditions. Drugan 2007. Elastic composite materials having a negative-stiffness phase can be stable. Phys. Rev. Lett. 98 (5), article no. 055502 first proved the answer is yes, by applying the energy criterion of elastic stability to the basic two- and three-dimensional composites consisting of a cylinder or sphere having non-positive-definite (but strongly elliptic) moduli with a thin positive-definite coating and proving overall stability provided the coating is sufficiently stiff. Here, we perform a complete and direct dynamic stability analysis of the plane strain fundamental elastic composite consisting of a circular cylinder of non-positive-definite material firmly bonded to a positive-definite concentric coating, for the full range of coating thicknesses (i.e., volume fractions). We determine quantitatively the full permissible range of inclusion and coating moduli, as a function of coating thickness, for which the overall composite is stable under dead traction boundary conditions. Among the results, we show that in the thin-coating case, the present dynamic stability analysis leads to precisely the same analytical stability requirements as those derived via the energy criterion by Drugan 2007. Elastic composite materials having a negative-stiffness phase can be stable. Phys. Rev. Lett. 98 (5), article no. 055502, and we derive new analytical stability requirements that are valid for a wider range of coating thickness. At the other extreme, we show that in the case of very thick coatings (corresponding to the dilute case of a matrix-inclusion composite), even an inclusion with merely strongly elliptic moduli can be stabilized by a positive-definite matrix satisfying weak requirements, for which we derive analytical expressions. Overall, our results show that surprisingly weak restrictions on the moduli and thickness of the positive-definite coating are sufficient to stabilize a non-positive-definite inclusion, even one whose moduli are merely strongly elliptic. These results legitimize expanding the search for novel materials with extreme properties to those incorporating a non-positive-definite constituent, and they provide quantitative restrictions on the constituent materials' moduli and volume fractions, for the geometry examined here, that ensure overall stability of such composite materials.https://authors.library.caltech.edu/records/ydjzp-f1d11A simple model for dynamic recrystallization during severe plastic deformation
https://resolver.caltech.edu/CaltechAUTHORS:20131001-082855589
Authors: Le, K. C.; Kochmann, D. M.
Year: 2009
DOI: 10.1007/s00419-008-0280-z
During severe plastic deformation at elevated temperature dynamic recrystallization governs the microstructural evolution in natural geological processes as well as in industrial processing of metals, e.g. during equal channel angular extrusion (ECAE). Microstructure changes into almost dislocation-free grains of an average diameter of a few hundred nanometers yielding materials with excellent room-temperature strength. In this paper, we present a thermodynamically consistent model for the dynamic recrystallization during severe plastic deformation which provides explicit evolution equations for grain size and dislocation density.https://authors.library.caltech.edu/records/a3azw-hdz57Plastic Deformation of Bicrystals Within Continuum Dislocation Theory
https://resolver.caltech.edu/CaltechAUTHORS:20131001-082855322
Authors: Kochmann, D. M.; Le, K. C.
Year: 2009
DOI: 10.1177/1081286507087322
Within continuum dislocation theory the plastic deformation of bicrystals under plane strain constrained shear is considered. An analytical solution is found in the symmetric case (for twins) which exhibits the energetic and dissipative thresholds for dislocation nucleation, the Bauschinger translational work hardening, and the size effect. Similar features hold true also for the numerical solution in the general case.https://authors.library.caltech.edu/records/x3aeg-00p06The evolution of laminates in finite crystal plasticity: a variational approach
https://resolver.caltech.edu/CaltechAUTHORS:20110303-095336775
Authors: Kochmann, D. M.; Hackl, K.
Year: 2011
DOI: 10.1007/s00161-010-0174-5
The analysis and simulation of microstructures in solids has gained crucial importance, virtue of the
influence of all microstructural characteristics on a material's macroscopic, mechanical behavior. In particular,
the arrangement of dislocations and other lattice defects to particular structures and patterns on the microscale
as well as the resultant inhomogeneous distribution of localized strain results in a highly altered stress–strain
response. Energetic models predicting the mechanical properties are commonly based on thermodynamic
variational principles. Modeling the material response in finite strain crystal plasticity very often results in a
non-convex variational problem so that the minimizing deformation fields are no longer continuous but exhibit
small-scale fluctuations related to probability distributions of deformation gradients to be calculated via energy
relaxation. This results in fine structures that can be interpreted as the observed microstructures. In this paper,
we first review the underlying variational principles for inelastic materials. We then propose an analytical
partial relaxation of a Neo-Hookean energy formulation, based on the assumption of a first-order laminate
microstructure, thus approximating the relaxed energy by an upper bound of the rank-one-convex hull. The
semi-relaxed energy can be employed to investigate elasto-plastic models with a single as well as multiple
active slip systems. Based on the minimization of a Lagrange functional (consisting of the sum of energy rate
and dissipation potential), we outline an incremental strategy to model the time-continuous evolution of the
laminate microstructure, then present a numerical scheme by means of which the microstructure development
can be computed, and show numerical results for particular examples in single- and double-slip plasticity.We
discuss the influence of hardening and of slip system orientations in the present model. In contrast to many
approaches before, we do not minimize a condensed energy functional. Instead, we incrementally solve the
evolution equations at each time step and account for the actual microstructural changes during each time
step. Results indicate a reduction in energy when compared to those theories based on a condensed energy
functional.https://authors.library.caltech.edu/records/wcb91-gq812Infinitely stiff composite via a rotation-stabilized negative-stiffness phase
https://resolver.caltech.edu/CaltechAUTHORS:20110802-154144027
Authors: Kochmann, D. M.; Drugan, W. J.
Year: 2011
DOI: 10.1063/1.3609328
We show that an elastic composite material having a component with sufficiently negative stiffness to produce positive-infinite composite stiffness can be stabilized by the gyroscopic forces produced by composite rotation.https://authors.library.caltech.edu/records/9y938-fzc78From atomistics to the continuum: a mesh-free quasicontinuum formulation based on local max-ent approximation schemes
https://resolver.caltech.edu/CaltechAUTHORS:20180223-110852480
Authors: Kochmann, Dennis M.; Amelang, Jeffrey S.; Español, Malena I.; Ortiz, Michael
Year: 2011
DOI: 10.1002/pamm.201110188
A novel quasicontinuum formulation based on mesh-free local maximum-entropy approximation schemes is presented, whose accuracy (compared to full atomistic simulations) is tunable and, in particular, can be designed superior to conventional affine approximation schemes.https://authors.library.caltech.edu/records/9amaf-hvv63Generation and evolution of inelastic microstructures - an overview
https://resolver.caltech.edu/CaltechAUTHORS:20120914-075526590
Authors: Hackl, Klaus; Hoppe, Ulrich; Kochmann, Dennis M.
Year: 2012
DOI: 10.1002/gamm.201210007
In this paper we give an overview on the modeling of inelastic microstructures using variational methods. We start by discussing the underlying variational principles for inelastic materials, derive evolution equations for internal variables, and introduce the concept of condensed energy. As a mathematical prerequisite we review the variational calculus of nonconvex potentials and the notion of relaxation. We use these instruments in order to study the initiation of plastic microstructures. Here we focus on a model of single-slip crystal plasticity. Afterwards we move on to model the evolution of microstructures. We introduce the concept of essential microstructures and the corresponding relaxed energies and dissipation potentials, and derive evolution equations for microstructure parameters. We then present a numerical scheme by means of which the microstructure development can be computed, and show numerical results for particular examples.https://authors.library.caltech.edu/records/sv69m-msw76Stability criteria for continuous and discrete elastic composites and the influence of geometry on the stability of a negative-stiffness phase
https://resolver.caltech.edu/CaltechAUTHORS:20120810-140037087
Authors: Kochmann, Dennis M.
Year: 2012
DOI: 10.1002/pssb.201084213
Recent experimental findings and theoretical analyses have confirmed the bound-exceeding performance of composite materials with one constituent of so-called negative stiffness (i.e., with non-positive-definite elastic moduli): the overall elastic properties greatly exceed those of the composite constituents, when the negative-stiffness phase's properties are appropriately tuned. However, the stability of such composite materials has remained a key open question. It has been shown, e.g., that a spherical particle of a negative-stiffness material can be stabilized when embedded in a sufficiently stiff and thick coating to impose a geometrical constraint on the negative-stiffness phase. For general composite geometries (as those arising from actual manufacturing processes), no such investigation has been reported. We review the classical stability conditions for homogeneous linear elastic solids and outline methods to determine the sufficient stability conditions for elastic composites. In addition, a numerical technique to obtain the stability restrictions on the elastic moduli of a composite with, in principle, arbitrary geometry is presented. Based on this method, we investigate the stability of simple elastic two-phase composites consisting of an inclusion (having non-positive-definite elastic moduli) embedded in a different coating material. In particular, the influence of the geometry of the encapsulated particles and the surrounding matrix is shown to considerably affect the overall stability. Our results compare the stability limits for two- (2D) and three-dimensional (3D) composite arrangements and provide design guidelines for optimal stability.https://authors.library.caltech.edu/records/2wm9y-0wv81Analytical stability conditions for elastic composite materials with a non-positive-definite phase
https://resolver.caltech.edu/CaltechAUTHORS:20120801-093547662
Authors: Kochmann, D. M.; Drugan, W. J.
Year: 2012
DOI: 10.1098/rspa.2011.0546
Elastic multi-phase materials with a phase having appropriately tuned non-positive-definite elastic moduli have been shown theoretically to permit extreme increases in multiple desirable material properties. Stability analyses of such composites were only recently initiated. Here, we provide a thorough stability analysis for general composites when one phase violates positive-definiteness. We first investigate the dynamic deformation modes leading to instability in the fundamental two-phase solids of a coated cylinder (two dimensions) and a coated sphere (three dimensions), from which we derive closed-form analytical sufficient stability conditions for the full range of coating thicknesses. Next, we apply the energy method to derive a general correlation between composite stability limit and composite bulk modulus that enables determination of closed-form analytical sufficient stability conditions for arbitrary multi-phase materials by employing effective modulus formulas coupled with a numerical finite-element stability analysis. We demonstrate and confirm this new approach by applying it to (i) the two basic two-phase solids already analysed dynamically; and (ii) a more geometrically complex matrix/distributed-inclusions composite. The specific new analytical stability results, and new methods presented, provide a basis for creation of novel, stable composite materials.https://authors.library.caltech.edu/records/j9h06-9z352Homogenized mechanical properties of auxetic composite materials in finite-strain elasticity
https://resolver.caltech.edu/CaltechAUTHORS:20130829-144736932
Authors: Kochmann, Dennis M.; Venturini, Gabriela N.
Year: 2013
DOI: 10.1088/0964-1726/22/8/084004
Careful microstructural design can result in materials with counterintuitive effective
(macroscale) mechanical properties such as a negative Poisson's ratio, commonly referred to
as auxetic behavior. One specific approach to achieving auxetic behavior is to elastically
connect structural elements with rotational degrees of freedom to result in elastic structures
that unfold under uniaxial loading in specific directions, thereby giving rise to bi- or triaxial
expansion, i.e. auxetic behavior (transverse expansion under uniaxial extension). This concept
has been applied successfully to elastically coupled two-dimensional rigid rotational elements
(such as rotating rectangles and triangles) which exhibit a negative effective in-plane Poisson's
ratio under uniaxial (ex)tension. Here, we adopt this fundamental design principle but take it
to the next level by achieving auxetic behavior in finitely strained composites made of stiff
inclusions in a hyperelastic matrix, and we study the resulting elastic properties under in-plane
strain by numerical homogenization. Our results highlight the emergence of auxetic behavior
based on geometric arrangement and properties of the base material and demonstrate a path
towards simple inclusion–matrix composites with auxetic behavior.https://authors.library.caltech.edu/records/dee7z-31q25A Γ-Convergence Analysis of the Quasicontinuum Method
https://resolver.caltech.edu/CaltechAUTHORS:20131104-155146267
Authors: Español, Malena I.; Kochmann, Dennis M.; Conti, Sergio; Ortiz, Michael
Year: 2013
DOI: 10.1137/120895354
We present a Γ-convergence analysis of the quasicontinuum method focused on the behavior of the approximate energy functionals in the continuum limit of a harmonic and defect-free crystal. The analysis shows that, under general conditions of stability and boundedness of the energy, the continuum limit is attained provided that the continuum---e.g., finite-element---approximation spaces are strongly dense in an appropriate topology and provided that the lattice size converges to zero more rapidly than the mesh size. The equicoercivity of the quasicontinuum energy functionals is likewise established with broad generality, which, in conjunction with Γ-convergence, ensures the convergence of the minimizers. We also show under rather general conditions that, for interatomic energies having a clusterwise additive structure, summation or quadrature rules that suitably approximate the local element energies do not affect the continuum limit. Finally, we propose a discrete patch test that provides a practical means of assessing the convergence of quasicontinuum approximations. We demonstrate the utility of the discrete patch test by means of selected examples of application.https://authors.library.caltech.edu/records/fdqeb-pty38A negative-stiffness phase in elastic composites can produce stable extreme effective dynamic but not static stiffness
https://resolver.caltech.edu/CaltechAUTHORS:20131204-142341321
Authors: Wojnar, Charles S.; Kochmann, Dennis M.
Year: 2013
DOI: 10.1080/14786435.2013.857795
We investigate the effective elastic properties and overall stability of four specific two-phase elastic composite systems having a non-positive-definite phase (often referred to as a negative-stiffness phase) to determine whether or not the presence of the negative-stiffness phase can lead to stable extreme overall stiffness. We start with an instructive spring-mass model to illustrate the underlying physical mechanisms before proceeding to the two- and three-dimensional two-phase solids of coated cylindrical and coated spherical inclusions, and we finally study a general particle-matrix composite. For all examples, we correlate effective stiffness with overall stability to demonstrate that the static effective stiffness measures can never reach extreme values due to the inclusion of a negative-stiffness phase in a stable manner, while dynamic loading indeed permits resonance-induced extreme effective stiffness.https://authors.library.caltech.edu/records/vebc1-kry49Stability of extreme static and dynamic bulk moduli of an elastic two-phase composite due to a non-positive-definite phase
https://resolver.caltech.edu/CaltechAUTHORS:20140228-133546855
Authors: Wojnar, Charles S.; Kochmann, Dennis M.
Year: 2014
DOI: 10.1002/pssb.201384241
Elastic composite materials having phases that violate elastic positive-definiteness (so-called negative-stiffness phases) have been reported to, in principle, realize extreme values of overall elastic moduli such as the effective bulk modulus, if the composite geometry and the constituents' elastic properties are appropriately tuned. In addition, previous studies have confirmed the stabilizing effect of the geometric constraints on the individual phases within a composite material: a non-positive-definite phase can be stabilized by a constraining matrix that is sufficiently stiff and sufficiently thick. However, to date no analysis has correlated the predicted extreme elastic response to the regime of stability. Therefore, it has remained an open question whether or not the inclusion of a non-positive-definite phase in an elastic composite can lead to stable extreme overall moduli. In this contribution we aim to close this gap by investigating the effective static and time-harmonic dynamic response of the simple elastic two-phase system of a coated spherical inclusion, and we report the results of its stability analysis. We show that the predicted extreme effective static bulk modulus of the two-phase system cannot be stable, whereas time-harmonic dynamic conditions indicate potential for considerable increases of the effective dynamic bulk stiffness in a resonant-like fashion due to the negative-stiffness induced low-frequency resonance.https://authors.library.caltech.edu/records/s1f0v-qwz36A meshless quasicontinuum method based on local maximum-entropy interpolation
https://resolver.caltech.edu/CaltechAUTHORS:20140613-133404451
Authors: Kochmann, Dennis M.; Venturini, Gabriela N.
Year: 2014
DOI: 10.1088/0965-0393/22/3/034007
Coarse-graining atomistic ensembles can overcome the practical limitations of molecular statics and dynamics in order to facilitate simulations at much larger length scales than accessible by discrete atomistic techniques due to computational expense. The quasicontinuum (QC) method was introduced to reduce the number of degrees of freedom in crystalline solids by choosing a set of representative atoms from the fully atomistic ensemble and obtaining the positions and momenta of all remaining lattice sites by interpolation. Here, we present a new energy-based nonlocal meshless version of the QC method based on local maximum-entropy (max-ent) interpolation schemes instead of the traditional polynomial interpolation, which particularly promises advantages in model adaptation to tie atomistic resolution to crystal defects while efficiently coarse-graining away from these. To this end, we formulate the meshless QC representation and analyze its performance. One-dimensional chain problems allow for clean mathematical treatment and provide interesting insight, which allow us to quantify the approximation error as a function of representative atom distribution and support of meshless shape functions. A fully three-dimensional implementation then demonstrates the applicability of the new QC scheme and highlights its features. Overall, we show that local max-ent interpolation offers a number of advantages over previous QC realizations.https://authors.library.caltech.edu/records/01z61-x4p273D Auxetic Microlattices with Independently Controllable Acoustic Band Gaps and Quasi-Static Elastic Moduli
https://resolver.caltech.edu/CaltechAUTHORS:20140613-093542107
Authors: Krödel, Sebastian; Delpero, Tommaso; Bergamini, Andrea; Ermanni, Paolo; Kochmann, Dennis M.
Year: 2014
DOI: 10.1002/adem.201300264
Mechanical metamaterials offer unique possibilities to tune their mechanical response by adjusting their geometry, without the complexity that the thermodynamics and kinetics of materials synthesis otherwise impose. In this work, the tuning of the quasi-static and wave propagation properties of micro-lattice structures are explored using numerical methods. The ability to independently modify the elastic moduli and the dispersion properties of the material by appropriately placing micro-inertia elements is demonstrated. The numerical methods used for this investigation are also presented.https://authors.library.caltech.edu/records/2rp11-5ec34Stable extreme damping in viscoelastic two-phase composites with non-positive-definite phases close to the loss of stability
https://resolver.caltech.edu/CaltechAUTHORS:20140724-153508138
Authors: Kochmann, Dennis M.
Year: 2014
DOI: 10.1016/j.mechrescom.2013.09.003
By investigating the effective response of linear viscoelastic composites, we demonstrate that stiff systems can exhibit stable extreme increases in overall damping if one of the composite phases loses positive-definiteness of its elasticities. While non-positive-definite elastic moduli (often referred to as negative stiffness) are thermodynamically unstable in unconstrained homogeneous solids, the geometric constraints among constituents in a composite can provide sufficient stabilization. Allowing for negative-stiffness phases in principle expands the range of attainable composite properties and promises extremely high composite stiffness and damping (significantly beyond those of the composite base materials) if the composite is appropriately tuned. This, however, raises questions of stability. In particular, the resulting high damping in stiff composites so far has only been shown to be stable in simple structural and elementary spring-dashpot systems, and therefore has remained a key open question for general composite materials. Studying successively the examples of a spring-dashpot model, a two-phase solid, and a general particle–matrix composite, we demonstrate that a non-positive-definite phase may indeed result in stable extreme damping, which is in line with recent experimental findings.https://authors.library.caltech.edu/records/zg2ek-8n697Microstructural pattern formation in finite-deformation single-slip crystal plasticity under cyclic loading: Relaxation vs. gradient plasticity
https://resolver.caltech.edu/CaltechAUTHORS:20140911-085738194
Authors: Klusemann, Benjamin; Kochmann, Dennis M.
Year: 2014
DOI: 10.1016/j.cma.2014.05.015
We investigate microstructure formation and evolution during cyclic loading in rate-dependent crystal plasticity at finite strains. The non-quasiconvex free energy density in multiplicative single-slip crystal plasticity leads to fine-scale microstructure whose characteristics and resulting effective stress–strain response are studied by two independent approaches: (i) using an incremental formulation based on variational constitutive updates we approximate the quasiconvex hull by lamination, i.e. by constructing an energy-minimizing first-order laminate microstructure, and (ii) a strain-gradient plasticity model applied to a representative unit cell whose effective properties are obtained from homogenization. In the lamination model, three different formulations for updating the accumulated plastic strains are compared and discussed with a specific focus on identifying a suitable description to account for hardening due to changes of the laminate volume fractions. The gradient-plasticity model also predicts a first-order laminate microstructure to form at a comparable stress level upon microstructure initiation. However, the energy associated with the dislocation network is shown to affect the microstructure evolution, leading to considerably higher strain levels at laminate initiation and a stress overshoot. In both models, cyclic loading leads to a degeneration of the stress–strain hysteresis which ultimately experiences elastic shakedown. The amount of work hardening significantly depends on how fast the degeneration occurs. To allow for a comparison, we consider cyclic loading after pre-deformation in the gradient model which delays the degeneration of the stress–strain hysteresis. For low hardening, the two models predict differences in the stress–strain hysteresis, mainly owing to laminate migration in the gradient-plasticity model. As work hardening increases, this phenomenon is restricted and the agreement of the effective stress–strain response between the two models is excellent. Accounting for the energy stored in the domain walls leads to a delayed lamination which is in agreement with the gradient plasticity model.https://authors.library.caltech.edu/records/2abvh-kz893Dynamics of periodic mechanical structures containing bistable elastic elements: From elastic to solitary wave propagation
https://resolver.caltech.edu/CaltechAUTHORS:20140926-083716624
Authors: Nadkarni, Neel; Daraio, Chiara; Kochmann, Dennis M.
Year: 2014
DOI: 10.1103/PhysRevE.90.023204
We investigate the nonlinear dynamics of a periodic chain of bistable elements consisting of masses connected by elastic springs whose constraint arrangement gives rise to a large-deformation snap-through instability. We show that the resulting negative-stiffness effect produces three different regimes of (linear and nonlinear) wave propagation in the periodic medium, depending on the wave amplitude. At small amplitudes, linear elastic waves experience dispersion that is controllable by the geometry and by the level of precompression. At moderate to large amplitudes, solitary waves arise in the weakly and strongly nonlinear regime. For each case, we present closed-form analytical solutions and we confirm our theoretical findings by specific numerical examples. The precompression reveals a class of wave propagation for a partially positive and negative potential. The presented results highlight opportunities in the design of mechanical metamaterials based on negative-stiffness elements, which go beyond current concepts primarily based on linear elastic wave propagation. Our findings shed light on the rich effective dynamics achievable by nonlinear small-scale instabilities in solids and structures.https://authors.library.caltech.edu/records/e5rjy-sq679Broadband control of the viscoelasticity of ferroelectrics via domain switching
https://resolver.caltech.edu/CaltechAUTHORS:20141204-083203819
Authors: Wojnar, C. S.; le Graverend, J.-B.; Kochmann, D. M.
Year: 2014
DOI: 10.1063/1.4899055
We show that the viscoelastic properties of polycrystalline ferroelectric ceramics can be significantly altered over a wide range of mechanical frequencies when domain switching is controlled by cyclic electric fields. The dynamic stiffness of lead zirconate titanate is shown to vary by more than 30%, while damping increases by an order of magnitude. Experimental results are interpreted by the aid of a continuum-mechanics model that captures the nonlinear electro-mechanically coupled material response for the full electric hysteresis.https://authors.library.caltech.edu/records/gwge8-tza30Rigorous bounds on the effective moduli of composites and inhomogeneous bodies with negative-stiffness phases
https://resolver.caltech.edu/CaltechAUTHORS:20141120-133810593
Authors: Kochmann, Dennis M.; Milton, Graeme W.
Year: 2014
DOI: 10.1016/j.jmps.2014.06.010
We review the theoretical bounds on the effective properties of linear elastic inhomogeneous solids (including composite materials) in the presence of constituents having non-positive-definite elastic moduli (so-called negative-stiffness phases). Using arguments of Hill and Koiter, we show that for statically stable bodies the classical displacement-based variational principles for Dirichlet and Neumann boundary problems hold but that the dual variational principle for traction boundary problems does not apply. We illustrate our findings by the example of a coated spherical inclusion whose stability conditions are obtained from the variational principles. We further show that the classical Voigt upper bound on the linear elastic moduli in multi-phase inhomogeneous bodies and composites applies and that it imposes a stability condition: overall stability requires that the effective moduli do not surpass the Voigt upper bound. This particularly implies that, while the geometric constraints among constituents in a composite can stabilize negative-stiffness phases, the stabilization is insufficient to allow for extreme overall static elastic moduli (exceeding those of the constituents). Stronger bounds on the effective elastic moduli of isotropic composites can be obtained from the Hashin–Shtrikman variational inequalities, which are also shown to hold in the presence of negative stiffness.https://authors.library.caltech.edu/records/dym2r-5qn27Material instability-induced extreme damping in composites: A computational study
https://resolver.caltech.edu/CaltechAUTHORS:20141120-103844047
Authors: Fritzen, Felix; Kochmann, Dennis M.
Year: 2014
DOI: 10.1016/j.ijsolstr.2014.07.028
We investigate the effective viscoelastic performance of particle-reinforced composite materials whose particulate phase undergoes a material instability resulting in temporarily non-positive-definite elastic moduli. Recent experiments have shown that phase transitions in geometrically-constrained composite phases (such as in particles embedded in a stiff matrix) can lead to stable non-positive-definite elastic moduli, and they hinted at strong damping increases that can be achieved from such metastable composite phases. All previous theoretical efforts to explain such phenomena have used simplistic one-dimensional models or they were based on composite bounds and specific two-phase solids. Here, we study particle–matrix composites with periodic randomized particle dispersion. A finite element discretization is used in combination with a sophisticated nonlinear solver in order to perform the numerous calculations in a feasible amount of computing time. Our computational analysis shows that stable non-positive-definite inclusion moduli can indeed lead to extreme damping increases (i.e. greatly exceeding the intrinsic damping of each composite phase) and that such extreme damping arises from a shift in microstructural mechanisms.https://authors.library.caltech.edu/records/ywwjq-h0916Broadband Electromechanical Spectroscopy: characterizing the dynamic mechanical response of viscoelastic materials under temperature and electric field control in a vacuum environment
https://resolver.caltech.edu/CaltechAUTHORS:20150420-132839490
Authors: le Graverend, J.-B.; Wojnar, C. S.; Kochmann, D. M.
Year: 2015
DOI: 10.1007/s10853-015-8928-x
The viscoelasticity of a variety of active materials is controllable, e.g., by the application of electric or thermal fields. However, their viscoelastic behavior cannot be fully explored by current methods due to limitations in their control of mechanical, electrical, and thermal fields simultaneously. To close this gap, we introduce Broadband Electromechanical Spectroscopy (BES). For the specific apparatus developed, specimens are subjected to bending and torsional moments with frequencies up to 4 kHz and amplitudes up to 10^(−4) Nm (the method is sufficiently general to allow for higher and wider frequency ranges). Deflection/twist is measured and moments are applied in a contactless fashion to minimize the influence of the apparatus compliance and of spurious damping. Electric fields are applied to specimens via surface electrodes at frequencies up to 10 Hz and amplitudes up to 5 MV/m. Experiments are performed under vacuum to remove noise from the surrounding air. Using BES, the dynamic stiffness and damping in bending and torsion of a ferroelectric ceramic, lead zirconate titanate, were measured at room temperature, while applying large, cyclic electric fields to induce domain switching. Results reveal large increases of the specimen's damping capacity and softening of the modulus during domain switching. The effect occurs over wide ranges of mechanical frequencies and permits lowering of the resonance frequencies. This promises potential for using ferroelectrics for active vibration control beyond linear piezoelectricity. More generally, BES helps improve current understanding of microstructure kinetics (such as during domain switching) and how it relates to the macroscopic viscoelastic response of materials.https://authors.library.caltech.edu/records/nrwhv-gtz83Summation rules for a fully nonlocal energy-based quasicontinuum method
https://resolver.caltech.edu/CaltechAUTHORS:20151023-142752873
Authors: Amelang, J. S.; Venturini, G. N.; Kochmann, D. M.
Year: 2015
DOI: 10.1016/j.jmps.2015.03.007
The quasicontinuum (QC) method coarse-grains crystalline atomic ensembles in order to bridge the scales from individual atoms to the micro- and mesoscales. A crucial cornerstone of all QC techniques, summation or quadrature rules efficiently approximate the thermodynamic quantities of interest. Here, we investigate summation rules for a fully nonlocal, energy-based QC method to approximate the total Hamiltonian of a crystalline atomic ensemble by a weighted sum over a small subset of all atoms in the crystal lattice. Our formulation does not conceptually differentiate between atomistic and coarse-grained regions and thus allows for seamless bridging without domain-coupling interfaces. We review traditional summation rules and discuss their strengths and weaknesses with a focus on energy approximation errors and spurious force artifacts. Moreover, we introduce summation rules which produce no residual or spurious force artifacts in centrosymmetric crystals in the large-element limit under arbitrary affine deformations in two dimensions (and marginal force artifacts in three dimensions), while allowing us to seamlessly bridge to full atomistics. Through a comprehensive suite of examples with spatially non-uniform QC discretizations in two and three dimensions, we compare the accuracy of the new scheme to various previous ones. Our results confirm that the new summation rules exhibit significantly smaller force artifacts and energy approximation errors. Our numerical benchmark examples include the calculation of elastic constants from completely random QC meshes and the inhomogeneous deformation of aggressively coarse-grained crystals containing nano-voids. In the elastic regime, we directly compare QC results to those of full atomistics to assess global and local errors in complex QC simulations. Going beyond elasticity, we illustrate the performance of the energy-based QC method with the new second-order summation rule by the help of nanoindentation examples with automatic mesh adaptation. Overall, our findings provide guidelines for the selection of summation rules for the fully nonlocal energy-based QC method.https://authors.library.caltech.edu/records/cq357-y5q98Resilient 3D hierarchical architected metamaterials
https://resolver.caltech.edu/CaltechAUTHORS:20150909-102806332
Authors: Meza, Lucas R.; Zelhofer, Alex J.; Clarke, Nigel; Mateos, Arturo J.; Kochmann, Dennis M.; Greer, Julia R.
Year: 2015
DOI: 10.1073/pnas.1509120112
PMCID: PMC4577192
Hierarchically designed structures with architectural features that span across multiple length scales are found in numerous hard biomaterials, like bone, wood, and glass sponge skeletons, as well as manmade structures, like the Eiffel Tower. It has been hypothesized that their mechanical robustness and damage tolerance stem from sophisticated ordering within the constituents, but the specific role of hierarchy remains to be fully described and understood. We apply the principles of hierarchical design to create structural metamaterials from three material systems: (i) polymer, (ii) hollow ceramic, and (iii) ceramic–polymer composites that are patterned into self-similar unit cells in a fractal-like geometry. In situ nanomechanical experiments revealed (i) a nearly theoretical scaling of structural strength and stiffness with relative density, which outperforms existing nonhierarchical nanolattices; (ii) recoverability, with hollow alumina samples recovering up to 98% of their original height after compression to ≥50% strain; (iii) suppression of brittle failure and structural instabilities in hollow ceramic hierarchical nanolattices; and (iv) a range of deformation mechanisms that can be tuned by changing the slenderness ratios of the beams. Additional levels of hierarchy beyond a second order did not increase the strength or stiffness, which suggests the existence of an optimal degree of hierarchy to amplify resilience. We developed a computational model that captures local stress distributions within the nanolattices under compression and explains some of the underlying deformation mechanisms as well as validates the measured effective stiffness to be interpreted as a metamaterial property.https://authors.library.caltech.edu/records/dgtwx-cmb47A variational constitutive model for slip-twinning interactions in hcp metals: application to single- and polycrystalline magnesium
https://resolver.caltech.edu/CaltechAUTHORS:20150602-100153291
Authors: Chang, Yingrui; Kochmann, Dennis M.
Year: 2015
DOI: 10.1016/j.ijplas.2015.03.008
We present a constitutive model for hcp metals which is based on variational constitutive updates of plastic slips and twin volume fractions and accounts for the related lattice reorientation mechanisms. The model is applied to single- and polycrystalline pure magnesium. We outline the finite-deformation plasticity model combining basal, pyramidal, and prismatic dislocation activity as well as a convexification-based approach for deformation twinning. A comparison with experimental data from single-crystal tension-compression experiments validates the model and serves for parameter identification. The extension to polycrystals via both Taylor-type modeling and finite element simulations shows a characteristic stress-strain response that agrees well with experimental observations for polycrystalline magnesium. The presented continuum model does not aim to represent the full details of individual twin-dislocation interactions; yet, it is sufficiently efficient to allow for finite element simulations while qualitatively capturing the underlying microstructural deformation mechanisms.https://authors.library.caltech.edu/records/a0cm4-m2y35Surface effects in nanoscale structures investigated by a fully-nonlocal energy-based quasicontinuum method
https://resolver.caltech.edu/CaltechAUTHORS:20151016-150338537
Authors: Amelang, Jeffrey S.; Kochmann, Dennis M.
Year: 2015
DOI: 10.1016/j.mechmat.2015.04.004
Surface effects in nanoscale mechanical systems such as nanoporous solids or small-scale structures can have a significant impact on the effective material response which deviates from the material behavior of bulk solids. Understanding such phenomena requires modeling techniques that locally retain atomistic information while transitioning to the relevant macroscopic length scales. We recently introduced a fully-nonlocal energy based quasicontinuum (QC) method equipped with new summation rules. This technique accurately bridges across scales from atomistics to the continuum through a thermodynamically-consistent coarse-graining scheme. Beyond minimizing energy approximation errors and spurious force artifacts, the new method also qualifies to describe free surfaces, which is reported here. Surfaces present a major challenge to coarse-grained atomistics, which has oftentimes been circumvented by costly ad hoc extensions of the traditional QC method. We show that our new coarse-graining scheme successfully and automatically reduces spurious force artifacts near free surfaces. After discussing the computational model, we demonstrate its benefits in the presence of free surfaces by several nanomechanical examples including surface energy calculations, elastic size effects in nano-rods and in plates with nano-sized holes. Overall, we demonstrate the importance of surface effects as well as a new strategy to accurately capture those computationally via coarse-grained atomistics.https://authors.library.caltech.edu/records/nhvgg-vwv75Universal energy transport law for dissipative and diffusive phase transitions
https://resolver.caltech.edu/CaltechAUTHORS:20160425-135937974
Authors: Nadkarni, Neel; Daraio, Chiara; Abeyaratne, Rohan; Kochmann, Dennis M.
Year: 2016
DOI: 10.1103/PhysRevB.93.104109
We present a scaling law for the energy and speed of transition waves in dissipative and diffusive media. By considering uniform discrete lattices and continuous solids, we show that—for arbitrary highly nonlinear many-body interactions and multistable on-site potentials—the kinetic energy per density transported by a planar transition wave front always exhibits linear scaling with wave speed and the ratio of energy difference to interface mobility between the two phases. We confirm that the resulting linear superposition applies to highly nonlinear examples from particle to continuum mechanics.https://authors.library.caltech.edu/records/zsnv4-3rd38Auxeticity in truss networks and the role of bending versus stretching deformation
https://resolver.caltech.edu/CaltechAUTHORS:20160602-155105420
Authors: Desmoulins, Albert; Zelhofer, Alex J.; Kochmann, Dennis M.
Year: 2016
DOI: 10.1088/0964-1726/25/5/054003
Auxetic behavior (i.e., a negative value of Poisson's ratio) has been reported for a variety of cellular networks including truss structures. Commonly, this implies that the geometric arrangement of truss members within a periodic unit cell is designed to achieve the negative Poisson effect, e.g., in the reentrant honeycomb configuration. Here, we show that elastic periodic truss lattices can be tuned to display auxeticity by controlling the ratio of bending to stretching stiffness. If the nodal stiffness (or the bending stiffness) is low compared to the stretching stiffness of individual truss members, then the lattice is expected to exhibit a positive Poisson's ratio, showing lateral expansion upon uniaxial compression. In contrast, if the nodal or bending stiffness is high (and buckling is prevented), the lattice may reveal auxetic behavior, contracting laterally under uniaxial compression. This effect is demonstrated in two dimensions for the examples of square and triangular lattices, and it is confirmed both analytically in the limit of small strains as well as numerically for finite elastic deformation. Under large deformation, instability additionally gives rise to auxetic behavior due to truss buckling.https://authors.library.caltech.edu/records/9zsww-c8f92Unidirectional Transition Waves in Bistable Lattices
https://resolver.caltech.edu/CaltechAUTHORS:20160613-102147574
Authors: Nadkarni, Neel; Arrieta, Andres F.; Chong, Christopher; Kochmann, Dennis M.; Daraio, Chiara
Year: 2016
DOI: 10.1103/PhysRevLett.116.244501
We present a model system for strongly nonlinear transition waves generated in a periodic lattice of bistable members connected by magnetic links. The asymmetry of the on-site energy wells created by the bistable members produces a mechanical diode that supports only unidirectional transition wave propagation with constant wave velocity. We theoretically justify the cause of the unidirectionality of the transition wave and confirm these predictions by experiments and simulations. We further identify how the wave velocity and profile are uniquely linked to the double-well energy landscape, which serves as a blueprint for transition wave control.https://authors.library.caltech.edu/records/bjhwj-pky76An infinitely-stiff elastic system via a tuned negative-stiffness component stabilized by rotation-produced gyroscopic forces
https://resolver.caltech.edu/CaltechAUTHORS:20160705-084725238
Authors: Kochmann, D. M.; Drugan, W. J.
Year: 2016
DOI: 10.1063/1.4954967
An elastic system containing a negative-stiffness element tuned to produce positive-infinite system stiffness, although statically unstable as is any such elastic system if unconstrained, is proved to be stabilized by rotation-produced gyroscopic forces at sufficiently high rotation rates. This is accomplished in possibly the simplest model of a composite structure (or solid) containing a negative-stiffness component that exhibits all these features, facilitating a conceptually and mathematically transparent, completely closed-form analysis.https://authors.library.caltech.edu/records/bvnsm-xyz88Stable propogation of mechanical signals in soft media using stored elastic energy
https://resolver.caltech.edu/CaltechAUTHORS:20160808-102406505
Authors: Raney, Jordan R.; Nadkarni, Neel; Daraio, Chiara; Kochmann, Dennis M.; Lewis, Jennifer A.; Bertoldi, Katia
Year: 2016
DOI: 10.1073/pnas.1604838113
PMCID: PMC5024640
Soft structures with rationally designed architectures capable of large, nonlinear deformation present opportunities for unprecedented, highly tunable devices and machines. However, the highly dissipative nature of soft materials intrinsically limits or prevents certain functions, such as the propagation of mechanical signals. Here we present an architected soft system composed of elastomeric bistable beam elements connected by elastomeric linear springs. The dissipative nature of the polymer readily damps linear waves, preventing propagation of any mechanical signal beyond a short distance, as expected. However, the unique architecture of the system enables propagation of stable, nonlinear solitary transition waves with constant, controllable velocity and pulse geometry over arbitrary distances. Because the high damping of the material removes all other linear, small-amplitude excitations, the desired pulse propagates with high fidelity and controllability. This phenomenon can be used to control signals, as demonstrated by the design of soft mechanical diodes and logic gates.https://authors.library.caltech.edu/records/tj534-f2818Stable propagation of mechanical signals in soft media using stored elastic energy
https://resolver.caltech.edu/CaltechAUTHORS:20161007-080044914
Authors: Raney, Jordan R.; Nadkarni, Neel; Daraio, Chiara; Kochmann, Dennis M.; Lewis, Jennifer A.; Bertoldi, Katia
Year: 2016
DOI: 10.1073/pnas.1604838113
PMCID: PMC5024640
Soft structures with rationally designed architectures capable of large, nonlinear deformation present opportunities for unprecedented, highly tunable devices and machines. However, the highly dissipative nature of soft materials intrinsically limits or prevents certain functions, such as the propagation of mechanical signals. Here we present an architected soft system composed of elastomeric bistable beam elements connected by elastomeric linear springs. The dissipative nature of the polymer readily damps linear waves, preventing propagation of any mechanical signal beyond a short distance, as expected. However, the unique architecture of the system enables propagation of stable, nonlinear solitary transition waves with constant, controllable velocity and pulse geometry over arbitrary distances. Because the high damping of the material removes all other linear, small-amplitude excitations, the desired pulse propagates with high fidelity and controllability. This phenomenon can be used to control signals, as demonstrated by the design of soft mechanical diodes and logic gates.https://authors.library.caltech.edu/records/szer5-zhq74Local and nonlocal continuum modeling of inelastic periodic networks applied to stretching-dominated trusses
https://resolver.caltech.edu/CaltechAUTHORS:20170119-082126733
Authors: Desmoulins, A.; Kochmann, D. M.
Year: 2017
DOI: 10.1016/j.cma.2016.09.027
We present a nonlocal continuum model and its numerical implementation to describe the macroscale response of periodic discrete networks via second-order homogenization. The scale-bridging technique is applied to the specific example of stretching-dominated elastic and inelastic periodic truss networks. Experiments on small-scale truss structures have highlighted the importance of nodal connections on the effective stiffness and strength. Therefore, we describe the mechanics of trusses by accounting for the stretching of truss members and the deformation of nodes. For the representative 2D examples of lattices having square and triangular architectures and for example bar and nodal constitutive laws, we show that a simple continuum model based on affinely deforming a representative unit cell is sufficient to reproduce the nonlinear elastic behavior of discrete trusses. By contrast, localization that arises, e.g., from inelastic deformation requires a refined model. This is where the presented nonlocal continuum model is capable of accurately capturing details of localized deformation. We illustrate the performance of the model by comparing the results of example finite element simulations using the continuum constitutive model to discrete lattice calculations with elastic–plastic bars. Optimal performance is achieved when the representative unit cell of the continuum model agrees with the actual size of the discrete truss unit cell, which accounts for size effects even in regimes where a separation of scales between finite element size and unit cell size does not strictly apply.https://authors.library.caltech.edu/records/5ka0j-sbj74Linking Internal Dissipation Mechanisms to the Effective Complex Viscoelastic Moduli of Ferroelectrics
https://resolver.caltech.edu/CaltechAUTHORS:20170331-094447825
Authors: Wojnar, Charles S.; Kochmann, Dennis M.
Year: 2017
DOI: 10.1115/1.4035033
Microstructural mechanisms such as domain switching in ferroelectric ceramics dissipate energy, the nature, and extent of which are of significant interest for two reasons. First, dissipative internal processes lead to hysteretic behavior at the macroscale (e.g., the hysteresis of polarization versus electric field in ferroelectrics). Second, mechanisms of internal friction determine the viscoelastic behavior of the material under small-amplitude vibrations. Although experimental techniques and constitutive models exist for both phenomena, there is a strong disconnect and, in particular, no advantageous strategy to link both for improved physics-based kinetic models for multifunctional rheological materials. Here, we present a theoretical approach that relates inelastic constitutive models to frequency-dependent viscoelastic parameters by linearizing the kinetic relations for the internal variables. This enables us to gain qualitative and quantitative experimental validation of the kinetics of internal processes for both quasistatic microstructure evolution and high-frequency damping. We first present the simple example of the generalized Maxwell model and then proceed to the case of ferroelectric ceramics for which we predict the viscoelastic response during domain switching and compare to experimental data. This strategy identifies the relations between microstructural kinetics and viscoelastic properties. The approach is general in that it can be applied to other rheological materials with microstructure evolution.https://authors.library.caltech.edu/records/8vn3r-k4542Band gap transmission in periodic bistable mechanical systems
https://resolver.caltech.edu/CaltechAUTHORS:20170106-151747130
Authors: Frazier, Michael J.; Kochmann, Dennis M.
Year: 2017
DOI: 10.1016/j.jsv.2016.10.041
We theoretically and numerically investigate the supratransmission phenomenon in discrete, nonlinear systems containing bistable elements. While linear waves cannot propagate within the band gaps of periodic structures, supratransmission allows large-amplitude waves to transmit energy through the band gap. For systems lacking bistability, the threshold amplitude for such energy transmission at a given frequency in the linear band gap is fixed. We show that the topological transitions due to bistability provide an avenue for switching the threshold amplitude between two well-separated values. Moreover, this versatility is achieved while leaving the linear dispersion properties of the system essentially unchanged. Interestingly, the behavior changes when an elastic chain is coupled to bistable resonators (in an extension of the well-studied linear locally resonant metamaterials). Here, we show that a fraction of the injected energy is confined near the boundary due to the resonators, providing a means of regulating the otherwise unrestrained energy flow due to supratransmission. Together, the results illustrate new means of controlling nonlinear wave propagation and energy transport in systems having multi-stable elements.https://authors.library.caltech.edu/records/9zfjb-hpy05Nonlinear ultrasound imaging of nanoscale acoustic biomolecules
https://resolver.caltech.edu/CaltechAUTHORS:20170221-114609641
Authors: Maresca, David; Lakshmanan, Anupama; Lee-Gosselin, Audrey; Melis, Johan M.; Ni, Yu-Li; Bourdeau, Raymond W.; Kochmann, Dennis M.; Shapiro, Mikhail G.
Year: 2017
DOI: 10.1063/1.4976105
PMCID: PMC5315666
Ultrasound imaging is widely used to probe the mechanical structure of tissues and visualize blood flow. However, the ability of ultrasound to observe specific molecular and cellular signals is limited. Recently, a unique class of gas-filled protein nanostructures called gas vesicles (GVs) was introduced as nanoscale (∼250 nm) contrast agents for ultrasound, accompanied by the possibilities of genetic engineering, imaging of targets outside the vasculature and monitoring of cellular signals such as gene expression. These possibilities would be aided by methods to discriminate GV-generated ultrasound signals from anatomical background. Here, we show that the nonlinear response of engineered GVs to acoustic pressure enables selective imaging of these nanostructures using a tailored amplitude modulation strategy. Finite element modeling predicted a strongly nonlinear mechanical deformation and acoustic response to ultrasound in engineered GVs. This response was confirmed with ultrasound measurements in the range of 10 to 25 MHz. An amplitude modulation pulse sequence based on this nonlinear response allows engineered GVs to be distinguished from linear scatterers and other GV types with a contrast ratio greater than 11.5 dB. We demonstrate the effectiveness of this nonlinear imaging strategy in vitro, in cellulo, and in vivo.https://authors.library.caltech.edu/records/fpz65-n5k62Modeling microstructure evolution in magnesium: Comparison of detailed and reduced-order kinematic models
https://resolver.caltech.edu/CaltechAUTHORS:20170518-080559393
Authors: Chang, Yingrui; Lloyd, Jeffrey T.; Becker, Richard; Kochmann, Dennis M.
Year: 2017
DOI: 10.1016/j.mechmat.2017.02.007
The inelastic behavior of hcp metals, such as magnesium (Mg) and its alloys, is dominated by the shortage of available slip systems and the resulting competition between dislocation slip and deformation twinning to accommodate large, irreversible deformation. A variety of models exist to describe the material behavior to varying degrees of accuracy and efficiency. Specifically, detailed crystal plasticity models account for the full set of slip and twin systems, thereby providing detailed microstructural insight at high computational costs. By contrast, reduced-order models aim to describe the same material response by a contracted set of phenomenological internal variables, resulting in significant efficiency gains at the cost of accuracy. Here, we contrast two such approaches for the example of pure Mg and apply those to model texture and yield surface evolution in applications including cold rolling and uniaxial compressions on textured Mg polycrystals. For the latter, we also compare simulated stress–strain predictions to experimental data. We highlight common features and key differences between the two models and compare their levels of accuracy and efficiency for the chosen applications. Our findings demonstrate that the efficient model agrees well with the full-detail calculations at lower levels of strain but shows deviations at large strains due to the missing account of lattice misorientation. We thus show that formulations employing differing kinematic assumptions can predict similar macroscopic behavior by altering material parameters (i.e., using a more detailed model to inform coarse-scale models).https://authors.library.caltech.edu/records/dwyey-eqy72Acoustic Behavior of Halobacterium salinarum Gas Vesicles in the High-Frequency Range: Experiments and Modeling
https://resolver.caltech.edu/CaltechAUTHORS:20170313-090300487
Authors: Cherin, Emmanuel; Melis, Johan M.; Bourdeau, Raymond W.; Yin, Melissa; Kochmann, Dennis M.; Foster, F. Stuart; Shapiro, Mikhail G.
Year: 2017
DOI: 10.1016/j.ultrasmedbio.2016.12.020
PMCID: PMC5385285
Gas vesicles (GVs) are a new and unique class of biologically derived ultrasound contrast agents with sub-micron size whose acoustic properties have not been fully elucidated. In this study, we investigated the acoustic collapse pressure and behavior of Halobacterium salinarum gas vesicles at transmit center frequencies ranging from 12.5 to 27.5 MHz. The acoustic collapse pressure was found to be above 550 kPa at all frequencies, nine-fold higher than the critical pressure observed under hydrostatic conditions. We illustrate that gas vesicles behave non-linearly when exposed to ultrasound at incident pressure ranging from 160 kPa to the collapse pressure and generate second harmonic amplitudes of −2 to −6 dB below the fundamental in media with viscosities ranging from 0.89 to 8 mPa·s. Simulations performed using a Rayleigh–Plesset-type model accounting for buckling and a dynamic finite-element analysis suggest that buckling is the mechanism behind the generation of harmonics. We found good agreement between the level of second harmonic relative to the fundamental measured at 20 MHz and the Rayleigh–Plesset model predictions. Finite-element simulations extended these findings to a non-spherical geometry, confirmed that the acoustic buckling pressure corresponds to the critical pressure under hydrostatic conditions and support the hypothesis of limited gas flow across the GV shell during the compression phase in the frequency range investigated. From simulations, estimates of GV bandwidth-limited scattering indicate that a single GV has a scattering cross section comparable to that of a red blood cell. These findings will inform the development of GV-based contrast agents and pulse sequences to optimize their detection with ultrasound.https://authors.library.caltech.edu/records/gxtxg-18j82Voltage-controlled complete stopbands in two-dimensional soft dielectrics
https://resolver.caltech.edu/CaltechAUTHORS:20170518-074455016
Authors: Getz, Roey; Kochmann, Dennis M.; Shmuel, Gal
Year: 2017
DOI: 10.1016/j.ijsolstr.2016.10.002
Dielectric elastomers deform and stiffen when subjected to voltage. This work demonstrates how fiber composites made of incompressible dielectric elastomers exhibit complete band gaps—frequency ranges in which elastic wave propagation is prohibited, irrespective of its polarization and direction. To this end, we first analytically determine the quasi-static response of a wide class of composites to an electric field along the fibers. We then formulate and calculate incremental motions of general polarization propagating in the deformed composite, using a plane wave expansion approach. We numerically explore the dependency of the motion on the composite properties and electric field. We show how complete band gaps are tuned by adjusting the electric field, owing to resultant geometrical and physical changes. These results suggest that soft dielectrics can serve as tunable waveguides and filters.https://authors.library.caltech.edu/records/py723-73q23Damage-induced mechanical damping in phase-transforming composites materials
https://resolver.caltech.edu/CaltechAUTHORS:20170518-075917401
Authors: Junker, Philipp; Kochmann, Dennis M.
Year: 2017
DOI: 10.1016/j.ijsolstr.2017.01.040
We investigate the influence of stress-induced damage on the effective viscoelastic response of two-phase composites having constituents that undergo solid-solid phase transitions. Such composites are prone to experience damage near the interfaces separating phase-transforming inclusions and the non-transforming matrix. By accounting for inelasticity, temperature-induced phase transitions, and damage in the individual constituents and applying techniques of computational homogenization, we numerically show that the observed damage and resulting decrease in matrix stiffness can lead to significant changes in the overall, frequency-dependent damping and dynamic stiffness of the composite under time-harmonic two-dimensional loading. This is of particular interest since recent experiments and simulations hinted at increased composite damping due to metastable states of phase-transforming inclusions when embedded in a stiff matrix (so-called negative stiffness). Experiments also reported signs of matrix degradation, the causal mechanisms and consequences of which have not been investigated. The homogenized material response reported here reveals the interplay of material viscosity, matrix degradation, and structural transition, and illustrates how phase transformation and localized damage may lead to pronounced effective damping and stiffness variations.https://authors.library.caltech.edu/records/x9x2n-9t683Atomimetic Mechanical Structures with Nonlinear Topological Domain Evolution Kinetics
https://resolver.caltech.edu/CaltechAUTHORS:20170324-095257081
Authors: Frazier, Michael J.; Kochmann, Dennis M.
Year: 2017
DOI: 10.1002/adma.201605800
A mechanical metamaterial, a simple, periodic mechanical structure, is reported, which reproduces the nonlinear dynamic behavior of materials undergoing phase transitions and domain switching at the structural level. Tunable multistability is exploited to produce switching and transition phenomena whose kinetics are governed by the same Allen–Cahn law commonly used to describe material-level, structural-transition processes. The reported purely elastic mechanical system displays several key features commonly found in atomic- or mesoscale physics of solids. The rotating-mass network shows qualitatively analogous features as, e.g., ferroic ceramics or phase-transforming solids, and the discrete governing equation is shown to approach the phase field equation commonly used to simulate the above processes. This offers untapped opportunities for reproducing material-level, dissipative and diffusive kinetic phenomena at the structural level, which, in turn, invites experimental realization and paves the road for new active, intelligent, or phase-transforming mechanical metamaterials bringing small-scale processes to the macroscopically observable scale.https://authors.library.caltech.edu/records/1f112-mmv97On acoustic wave beaming in two-dimensional structural lattices
https://resolver.caltech.edu/CaltechAUTHORS:20170526-080707035
Authors: Zelhofer, Alex J.; Kochmann, Dennis M.
Year: 2017
DOI: 10.1016/j.ijsolstr.2017.03.024
We discuss directional energy flow, often referred to as wave beaming, in two-dimensional periodic truss lattices under infinitesimal harmonic excitation. While the phenomenon of directional wave guiding is well-known and commonly treated in the context of dispersion relations, the theoretical and computational tools to predict beaming are limited, which is why a fundamental understanding for complex lattices is incomplete. Here, we present a new strategy to identify partial band gaps and wave beaming in a simple fashion, covering wide frequency ranges and distinguishing in-plane and out-of-plane vibrational modes in lattices composed of linear elastic Euler-Bernoulli beams. By calculating group velocities that provide insight into the frequency-dependent directional energy flow, we show that dispersion surfaces overlap in frequency and beaming direction, elucidating the need to consider multiple surfaces when predicting global system response – in contrast to many prior approaches that focused on the lowest surface(s) individually. These concepts are demonstrated for three examples of two-dimensional structural lattices (of rectangular, sheared, and hexagonal architecture), for each of which we study the influence of geometry on wave dispersion. Direct numerical simulations validate directional energy flow predictions, demonstrate directional frequency dispersion, and highlight conventional dispersion analysis limitations.https://authors.library.caltech.edu/records/2sspg-rdm95Automatic adaptivity in the fully nonlocal quasicontinuum method for coarse-grained atomistic simulations
https://resolver.caltech.edu/CaltechAUTHORS:20170503-094955128
Authors: Tembhekar, I.; Amelang, J. S.; Munk, L.; Kochmann, D. M.
Year: 2017
DOI: 10.1002/nme.5438
The quasicontinuum (QC) method is a concurrent scale-bridging technique that extends atomistic accuracy to significantly larger length scales by reducing the full atomic ensemble to a small set of representative atoms and using interpolation to recover the motion of all lattice sites where full atomistic resolution is not necessary. While traditional QC methods thereby create interfaces between fully resolved and coarse-grained regions, the recently introduced fully nonlocal QC framework does not fundamentally differentiate between atomistic and coarsened domains. Adding adaptive refinement enables us to tie atomistic resolution to evolving regions of interest such as moving defects. However, model adaptivity is challenging because large particle motion is described based on a reference mesh (even in the atomistic regions). Unlike in the context of, for example, finite element meshes, adaptivity here requires that (i) all vertices lie on a discrete point set (the atomic lattice), (ii) model refinement is performed locally and provides sufficient mesh quality, and (iii) Verlet neighborhood updates in the atomistic domain are performed against a Lagrangian mesh. With the suite of adaptivity tools outlined here, the nonlocal QC method is shown to bridge across scales from atomistics to the continuum in a truly seamless fashion, as illustrated for nanoindentation and void growth.https://authors.library.caltech.edu/records/p7w4t-gvz40An effective constitutive model for polycrystalline ferroelectric ceramics: Theoretical framework and numerical examples
https://resolver.caltech.edu/CaltechAUTHORS:20170531-103933351
Authors: Tan, Wei Lin; Kochmann, Dennis M.
Year: 2017
DOI: 10.1016/j.commatsci.2017.04.032
We present an efficient, physics-based constitutive model for bulk polycrystalline ferroelectric ceramics, which links domain switching mechanisms and phase transitions at the microscale to the observed electro-thermo-mechanically coupled material response at the macroscale. In particular, a convexified energy density is formulated based on domain volume fractions and extended to polycrystals via the common Taylor assumption of uniform strains (alternative descriptions are discussed as well). The chosen kinetic relations admit to account for differences in 90°- and 180°-domain wall motion and rate effects. The model is applied to tetragonal barium titanate (BaTiO_3) and we present results for both material point calculations and finite element simulations, which demonstrate good qualitative agreement with experiments. We deliberately target bulk polycrystalline ferroelectrics in contrast to thin films that have been studied extensively.https://authors.library.caltech.edu/records/k7pqd-e0997Predicting the effective response of bulk polycrystalline ferroelectric ceramics via improved spectral phase field methods
https://resolver.caltech.edu/CaltechAUTHORS:20170627-093545569
Authors: Vidyasagar, A.; Tan, W. L.; Kochmann, D. M.
Year: 2017
DOI: 10.1016/j.jmps.2017.05.017
Understanding the electromechanical response of bulk polycrystalline ferroelectric ceramics requires scale-bridging approaches. Recent advances in fast numerical methods to compute the homogenized mechanical response of materials with heterogeneous microstructure have enabled the solution of hitherto intractable systems. In particular, the use of a Fourier-based spectral method as opposed to the traditional finite element method has gained significant interest in the homogenization of periodic microstructures. Here, we solve the periodic, electro-mechanically-coupled boundary value problem at the mesoscale of polycrystalline ferroelectrics in order to extract the effective response of barium titanate (BaTiO3) and lead zirconate titanate (PZT) under applied electric fields. Results include the effective electric hysteresis and the associated butterfly curve of strain vs. electric field for mean stress-free electric loading. Computational predictions of the 3D polycrystalline response show convincing agreement with our experimental electric cycling and strain hysteresis data for PZT-5A. In addition to microstructure-dependent effective physics, we also show how finite-difference-based approximations in the spectral solution scheme significantly reduce instability and ringing phenomena associated with spectral techniques and lead to spatial convergence with h-refinement, which have been major challenges when modeling high-contrast systems such as polycrystals.https://authors.library.caltech.edu/records/j8gfm-e2n29Exploiting Microstructural Instabilities in Solids and Structures: From Metamaterials to Structural Transitions
https://resolver.caltech.edu/CaltechAUTHORS:20180103-134358139
Authors: Kochmann, Dennis M.; Bertoldi, Katia
Year: 2017
DOI: 10.1115/1.4037966
Instabilities in solids and structures are ubiquitous across all length and time scales, and engineering design principles have commonly aimed at preventing instability. However, over the past two decades, engineering mechanics has undergone a paradigm shift, away from avoiding instability and toward taking advantage thereof. At the core of all instabilities—both at the microstructural scale in materials and at the macroscopic, structural level—lies a nonconvex potential energy landscape which is responsible, e.g., for phase transitions and domain switching, localization, pattern formation, or structural buckling and snapping. Deliberately driving a system close to, into, and beyond the unstable regime has been exploited to create new materials systems with superior, interesting, or extreme physical properties. Here, we review the state-of-the-art in utilizing mechanical instabilities in solids and structures at the microstructural level in order to control macroscopic (meta)material performance. After a brief theoretical review, we discuss examples of utilizing material instabilities (from phase transitions and ferroelectric switching to extreme composites) as well as examples of exploiting structural instabilities in acoustic and mechanical metamaterials.https://authors.library.caltech.edu/records/grmqb-6h602Reexamining the mechanical property space of three-dimensional lattice architectures
https://resolver.caltech.edu/CaltechAUTHORS:20170828-140820883
Authors: Meza, Lucas R.; Phlipot, Gregory P.; Portela, Carlos M.; Maggi, Alessandro; Montemayor, Lauren C.; Comella, Andre; Kochmann, Dennis M.; Greer, Julia R.
Year: 2017
DOI: 10.1016/j.actamat.2017.08.052
Lightweight materials that are simultaneously strong and stiff are desirable for a range of applications from transportation to energy storage to defense. Micro- and nanolattices represent some of the lightest fabricated materials to date, but studies of their mechanical properties have produced inconsistent results that are not well captured by existing lattice models. We performed systematic nanomechanical experiments on four distinct geometries of solid polymer and hollow ceramic (Al_2O_3) nanolattices. All samples tested had a nearly identical scaling of strength (σy) and Young's modulus (E) with relative density (ρ¯), ranging from σy∝ρ¯1.45 to ρ¯1.92 and E∝ρ¯1.41 to ρ¯1.83, revealing that changing topology alone does not necessarily have a significant impact on nanolattice mechanical properties. Finite element analysis was performed on solid and hollow lattices with structural parameters beyond those realized experimentally, enabling the identification of transition regimes where solid-beam lattices diverge from existing analytical theories and revealing the complex parameter space of hollow-beam lattices. We propose a simplified analytical model for solid-beam lattices that provides insight into the mechanisms behind their observed stiffness, and we investigate different hollow-beam lattice parameters that give rise to their aberrant properties. These experimental, computational and theoretical results uncover how architecture can be used to access unique lattice mechanical property spaces while demonstrating the practical limits of existing beam-based models in characterizing their behavior.https://authors.library.caltech.edu/records/8zt06-95b70Deformation patterning in finite-strain crystal plasticity by spectral homogenization with application to magnesium
https://resolver.caltech.edu/CaltechAUTHORS:20180308-105420394
Authors: Vidyasagar, A.; Tutcuoglu, Abbas D.; Kochmann, Dennis M.
Year: 2018
DOI: 10.1016/j.cma.2018.03.003
Complex microstructural patterns arise as energy-minimizers in systems having non-convex energy landscapes such as those associated with phase transformations, deformation twinning, or finite-strain crystal plasticity. The prediction of such patterns at the microscale along with the resulting, effective material response at the macroscale is key to understanding a wide range of mechanical phenomena and has classically been dealt with by simplifying energy relaxation theory or by expensive finite element calculations. Here, we discuss a stabilized Fourier spectral technique for the homogenized response at the level of a representative volume element (RVE). We show that the FFT-based method admits sufficiently high resolution suitable to predict the emergence of energy-minimizing microstructures and the resulting effective response by computing the approximated quasiconvex energy hull. We test the method in the classical single-slip problem in single- and bicrystals. Especially the latter goes beyond the scope of traditional finite element and analytical relaxation treatments and hints at mechanisms of pattern formation in polycrystals. We also demonstrate that the chosen spectral finite-difference approximation, important for removing ringing artifacts in the presence of high contrasts, adds a natural regularization to the non-convex minimization. Finally, the technique is applied to polycrystalline pure magnesium, where we account for the competition between dislocation-mediated plasticity and deformation twinning. These inelastic deformation mechanisms result in complex texture evolution paths at the polycrystalline mesoscale and are simulated within RVEs of varying grain size and texture by a constitutive crystal plasticity model with an effective, volume fraction-based description of twinning.https://authors.library.caltech.edu/records/pjjpn-85149Impact of node geometry on the effective stiffness of non-slender three-dimensional truss lattice architectures
https://resolver.caltech.edu/CaltechAUTHORS:20180620-151712137
Authors: Portela, Carlos M.; Greer, Julia R.; Kochmann, Dennis M.
Year: 2018
DOI: 10.1016/j.eml.2018.06.004
Three-dimensional (3D), lattice-based micro- and nano-architected materials can possess desirable mechanical properties that are unattainable by homogeneous materials. Manufacturing these so-called structural metamaterials at the nano- and microscales typically results in non-slender architectures (e.g., struts with a high radius-to-length ratio r∕l), for which simple analytical and computational tools are inapplicable since they fail to capture the effects of nodes at strut junctions. We report a detailed analysis that quantifies the effect of nodes on the effective Young's modulus (E∗) of lattice architectures with different unit cell geometries through (i) simple analytical constructions, (ii) reduced-order computational models, and (iii) experiments at the milli- and micrometer scales. The computational models of variable-node lattice architectures match the effective stiffness obtained from experiments and incur computational cost that are three orders-of-magnitude lower than alternative, conventional methods. We highlight a difference in the contribution of nodes to rigid versus non-rigid architectures and propose an extension to the classical stiffness scaling laws of the form E∗∝C_1(r∕l)α+C_2(r∕l)^β, which holds for slender and non-slender beam-based architectures, where constants C_1 and C_2 change with lattice geometry. We find the optimal scaling exponents for rigid architectures to be α=2 and β=4, and α=4 and β=6 for non-rigid architectures. These analytical, computational, and experimental results quantify the specific contribution of nodes to the effective stiffness of beam-based architectures and highlight the necessity of incorporating their effects into calculations of the structural stiffness. This work provides new, efficient tools that accurately capture the mechanics and physics of strut junctions in 3D, beam-based architected materials.https://authors.library.caltech.edu/records/6r5gp-fna97Microstructural patterns with tunable mechanical anisotropy obtained by simulating anisotropic spinodal decomposition
https://resolver.caltech.edu/CaltechAUTHORS:20181115-073530554
Authors: Vidyasagar, A.; Krödel, S.; Kochmann, D. M.
Year: 2018
DOI: 10.1098/rspa.2018.0535
PMCID: PMC6237504
The generation of mechanical metamaterials with tailored effective properties through carefully engineered microstructures requires avenues to predict optimal microstructural architectures. Phase separation in heterogeneous systems naturally produces complex microstructural patterns whose effective response depends on the underlying process of spinodal decomposition. During this process, anisotropy may arise due to advection, diffusive chemical gradients or crystallographic interface energy, leading to anisotropic patterns with strongly directional effective properties. We explore the link between anisotropic surface energies during spinodal decomposition, the resulting microstructures and, ultimately, the anisotropic elastic moduli of the resulting medium. We simulate the formation of anisotropic patterns within representative volume elements, using recently developed stabilized spectral techniques that circumvent further regularization, and present a powerful alternative to current numerical techniques. The interface morphology of representative phase-separated microstructures is shown to strongly depend on surface anisotropy. The effective elastic moduli of the thus-obtained porous media are identified by periodic homogenization, and directionality is demonstrated through elastic surfaces. Our approach not only improves upon numerical tools to simulate phase separation; it also offers an avenue to generate tailored microstructures with tunable resulting elastic anisotropy.https://authors.library.caltech.edu/records/r9kx3-84886Stiffness-Independent Toughening of Beams through Coaxial Interfaces
https://resolver.caltech.edu/CaltechAUTHORS:20181204-082427046
Authors: Mueller, Jochen; Raney, Jordan R.; Kochmann, Dennis M.; Shea, Kristina
Year: 2018
DOI: 10.1002/advs.201800728
To be of engineering relevance, it is essential for stiff and strong materials to possess also high toughness. However, as these properties are typically mutually exclusive, they are rarely found in nature and synthetic replications are extremely limited. Here, an elegant albeit simple physical principle that enables ligaments in cellular networks to possess these mechanical properties simultaneously is presented. The underlying architecture consists of multiple, coaxially aligned layers separated by interfaces that prevent crack propagation, hence increasing the energy required for complete rupture. The results show that the fracture strain and toughness can be increased by over 100%, when compared to conventional reference struts, while fully maintaining the density, stiffness, and strength. The bioinspired and highly versatile approach is scale‐independent under the absence of shear, applicable to various geometries, and complementary to existing approaches. It can, therefore, significantly improve safety and reduce cost and environmental impact in numerous applications, such as packaging, sports equipment, and transportation.https://authors.library.caltech.edu/records/ajp0e-sgj05Stochastic modeling of discontinuous dynamic recrystallization at finite strains in hcp metals
https://resolver.caltech.edu/CaltechAUTHORS:20180926-083949101
Authors: Tutcuoglu, A. D.; Vidyasagar, A.; Bhattacharya, K.; Kochmann, D. M.
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.edu/records/4jenk-vdb24In-situ observation of evolving microstructural damage and associated effective electro-mechanical properties of PZT during bipolar electrical fatigue
https://resolver.caltech.edu/CaltechAUTHORS:20181107-112508653
Authors: Tan, Wei Lin; Faber, Katherine T.; Kochmann, Dennis M.
Year: 2019
DOI: 10.1016/j.actamat.2018.10.065
We investigate the fatigue behavior of bulk polycrystalline lead zirconate titanate (PZT) during bipolar electric field cycling. We characterize the frequency- and cycle-dependent degradation in both the effective electro-mechanical properties (specifically, the electrical hysteresis and the macroscopic viscoelastic stiffness and damping measured by Broadband Electromechanical Spectroscopy, BES) and the microstructural damage evolution (quantified via scanning electron microscopy). The BES setup enables the mechanical characterization while performing electrical cycling so as to measure the evolving viscoelasticity without remounting the sample; particularly measuring the viscoelastic damping allows us to gain insight into the ferroelectric domain wall activity across the full electric hysteresis and over the full range of cycles. A clear dependence on the electric cycling frequency is observed in the rates of degradation of all measured properties including an up to 10% increase in dynamic compliance and a 70% decrease in electric displacement magnitude. We quantify the evolving micro-crack density across wide ranges of numbers of cycles and compare with changes in the effective compliance. Interestingly, the observed strong degradation in the ferroelectric hysteresis is contrasted by relatively mild changes in the effective viscoelastic moduli, while samples clearly indicate increasing levels of micro-damage.https://authors.library.caltech.edu/records/p0bt6-4t124Enhanced local maximum-entropy approximation for stable meshfree simulations
https://resolver.caltech.edu/CaltechAUTHORS:20181030-105013107
Authors: Kumar, Siddhant; Danas, Kostas; Kochmann, Dennis M.
Year: 2019
DOI: 10.1016/j.cma.2018.10.030
We introduce an improved meshfree approximation scheme which is based on the local maximum-entropy strategy as a compromise between shape function locality and entropy in an information-theoretical sense. The improved version is specifically designed for severe, finite deformation and offers significantly enhanced stability as opposed to the original formulation. This is achieved by (i) formulating the quasistatic mechanical boundary value problem in a suitable updated-Lagrangian setting, (ii) introducing anisotropy in the shape function support to accommodate directional variations in nodal spacing with increasing deformation and eliminate tensile instability, (iii) spatially bounding and evolving shape function support to restrict the domain of influence and increase efficiency, (iv) truncating shape functions at interfaces in order to stably represent multi-component systems like composites or polycrystals. The new scheme is applied to benchmark problems of severe elastic and elastoplastic deformation that demonstrate its performance both in terms of accuracy (as compared to exact solutions and, where applicable, finite element simulations) and efficiency. Importantly, the presented formulation overcomes the classical tensile instability found in most meshfree interpolation schemes, as shown for stable simulations of, e.g., the inhomogeneous extension of a hyperelastic block up to 100% or the torsion of a hyperelastic cube by 200° –both in an updated Lagrangian setting and without the need for remeshing.https://authors.library.caltech.edu/records/s6mgk-21670A quasicontinuum theory for the nonlinear mechanical response of general periodic truss lattices
https://resolver.caltech.edu/CaltechAUTHORS:20181126-102125266
Authors: Phlipot, Gregory P.; Kochmann, Dennis M.
Year: 2019
DOI: 10.1016/j.jmps.2018.11.014
We present a framework for the efficient, yet accurate description of general periodic truss networks based on concepts of the quasicontinuum (QC) method. Previous research in coarse-grained truss models has focused either on simple bar trusses or on two-dimensional beam lattices undergoing small deformations. Here, we extend the truss QC methodology to nonlinear deformations, general periodic beam lattices, and three dimensions. We introduce geometric nonlinearity into the model by using a corotational beam description at the level of individual truss members. Coarse-graining is achieved by the introduction of representative unit cells and an affine interpolation analogous to traditional QC. General periodic lattices defined by the periodic assembly of a single unit cell are modeled by retaining all unique degrees of freedom of the unit cell (identified by a lattice decomposition into simple Bravais lattices) at each macroscopic point in the simulation, and interpolating each degree of freedom individually. We show that this interpolation scheme accurately captures the homogenized properties of periodic truss lattices for uniform deformations. In order to showcase the efficiency and accuracy of the method, we perform simulations to predict the brittle fracture toughness of multiple lattice architectures and compare them to results obtained from significantly more expensive discrete truss simulations. Finally, we demonstrate the applicability of the method for nonlinear elastic truss lattices undergoing finite deformations. Overall, the new technique shows convincing agreement with exact, discrete results for most lattice architectures, and offers opportunities to reduce computational expenses in structural lattice simulations and thus to efficiently extract the effective mechanical performance of discrete networks.https://authors.library.caltech.edu/records/1z1k1-egx67High- vs. low-fidelity models for dynamic recrystallization in copper
https://resolver.caltech.edu/CaltechAUTHORS:20190725-111817655
Authors: Tutcuoglu, A. D.; Hollenweger, Y.; Stoy, A.; Kochmann, D. M.
Year: 2019
DOI: 10.1016/j.mtla.2019.100411
We investigate the benefits and limitations of mesoscale models for discontinuous dynamic recrystallization (DDRX) in pure copper at elevated temperature with the two-fold aim of capturing microscale mechanisms and predicting the macroscale mechanical response during severe plastic deformation. Differing strongly in their computational expenses and the underlying constitutive assumptions, we introduce and compare an efficient Taylor model (which treats polycrystals as collections of spatially non-interacting grains) with a Field Monte-Carlo Potts (FMCP) model (which resolves spatially inhomogeneous deformation within grains by an FFT-based treatment). Both approaches are based on the same temperature-aware crystal plasticity model for pure copper and introduce only three model parameters for DDRX. The latter are fitted to stress-strain data from uniaxial compression experiments at elevated temperature levels where DDRX is prevalent. Both models capture grain refinement, texture evolution and the stress-strain history with convincing agreement with experiments. The fully-resolved model has highest accuracy, reveals pronounced texture formation, and captures the gradual formation of high-angle grain boundaries within grains as precursors to subgrain formation. The Taylor model, though being significantly more efficient, fails to capture spatially-correlated features including necklace formation and leads to comparatively high prediction errors. However, at temperatures where migration dominates the recrystallization behavior, we observe compelling agreement between the Taylor model and the FMCP model. Last, we demonstrate how reduced-order models facilitate identifying model parameters of the computationally more expensive models.https://authors.library.caltech.edu/records/rwnh5-3np05Electrochemically Reconfigurable Architected Materials
https://resolver.caltech.edu/CaltechAUTHORS:20190701-140145897
Authors: Xia, Xiaoxing; Afshar, Arman; Yang, Heng; Portela, Carlos M.; Kochmann, Dennis M.; Di Leo, Claudio V.; Greer, Julia R.
Year: 2019
DOI: 10.1038/s41586-019-1538-z
Architected materials can actively respond to external stimuli—such as mechanical forces, hydration and magnetic fields—by changing their geometries and thereby achieve novel functionalities. Such transformations are usually binary and volatile because they toggle between 'on' and 'off' states and require persistent external stimuli. Here we develop three-dimensional silicon-coated tetragonal microlattices that transform into sinusoidal patterns via cooperative beam buckling in response to an electrochemically driven silicon-lithium alloying reaction. In situ microscopy reveals a controllable, non-volatile and reversible structural transformation that forms multiple ordered buckling domains separated by distorted domain boundaries. We investigate the mechanical dynamics of individual buckling beams, cooperative coupling among neighbouring beams, and lithiation-rate-dependent distributions of domain sizes through chemo-mechanical modelling and statistical mechanics analysis. Our results highlight the critical role of defects and energy fluctuations in the dynamic response of architected materials. We further demonstrate that domain boundaries can be programmed to form particular patterns by pre-designing artificial defects, and that a variety of reconfigurational degrees of freedom can be achieved through micro-architecture design. This framework enables the design, fabrication, modelling, behaviour prediction and programming of electrochemically reconfigurable architected materials, and could open the way to beyond-intercalation battery electrodes, tunable phononic crystals and bio-implantable devices.https://authors.library.caltech.edu/records/2jjeb-8h075Continuum models for stretching- and bending-dominated periodic trusses undergoing finite deformations
https://resolver.caltech.edu/CaltechAUTHORS:20190415-151326350
Authors: Glaesener, Raphaël N.; Lestringant, Claire; Telgen, Bastian; Kochmann, Dennis M.
Year: 2019
DOI: 10.1016/j.ijsolstr.2019.04.022
Advances in additive manufacturing across scales have enabled the creation of random, periodic, or hierarchical truss networks containing millions and more of individual truss members. In order to significantly reduce computational costs while accurately capturing the dominant deformation mechanisms, we introduce a simple yet powerful homogenized continuum description of truss lattices, which is based on applying a multi-lattice Cauchy-Born rule to a representative unit cell (RUC). Beam theory applied at the level of the RUC introduces rotational degrees of freedom and leads to a generalized continuum model that depends on the effective deformation gradients, rotation, and curvature on the macroscale. While affinely deforming the RUC is shown to produce excellent results for simple Bravais lattices, a multi-lattice extension is required for general and especially bending-dominated lattices, which cannot be described by a pure Taylor expansion of the RUC deformation; the importance of the multi-lattice concept is demonstrated through analytical examples. The resulting method is a beneficial compromise between inefficient FE^2 techniques and micropolar theories with limited applicability. By implementing the model within a finite element framework, we solve and report several benchmark tests in 2D to illustrate the accuracy and efficiency of the model, which comes with only a small fraction of the computational costs associated with the full, discrete truss calculation. By using a corotational beam description, we also capture finite beam rotations. We further demonstrate that a second-gradient homogenization formulation is beneficial in examples involving localization, providing higher local accuracy at the RUC level than a first-gradient scheme, while affecting the global response only marginally.https://authors.library.caltech.edu/records/10x73-1by03Guided transition waves in multistable mechanical metamaterials
https://resolver.caltech.edu/CaltechAUTHORS:20200124-072110309
Authors: Jin, Lishuai; Khajehtourian, Romik; Mueller, Jochen; Rafsanjani, Ahmad; Tournat, Vincent; Bertoldi, Katia; Kochmann, Dennis M.
Year: 2020
DOI: 10.1073/pnas.1913228117
PMCID: PMC7007517
Transition fronts, moving through solids and fluids in the form of propagating domain or phase boundaries, have recently been mimicked at the structural level in bistable architectures. What has been limited to simple one-dimensional (1D) examples is here cast into a blueprint for higher dimensions, demonstrated through 2D experiments and described by a continuum mechanical model that draws inspiration from phase transition theory in crystalline solids. Unlike materials, the presented structural analogs admit precise control of the transition wave's direction, shape, and velocity through spatially tailoring the underlying periodic network architecture (locally varying the shape or stiffness of the fundamental building blocks, and exploiting interactions of transition fronts with lattice defects such as point defects and free surfaces). The outcome is a predictable and programmable strongly nonlinear metamaterial motion with potential for, for example, propulsion in soft robotics, morphing surfaces, reconfigurable devices, mechanical logic, and controlled energy absorption.https://authors.library.caltech.edu/records/cd2b8-53g53A meshless multiscale approach to modeling severe plastic deformation of metals: Application to ECAE of pure copper
https://resolver.caltech.edu/CaltechAUTHORS:20191202-153508281
Authors: Kumar, Siddhant; Tutcuoglu, Abbas D.; Hollenweger, Y.; Kochmann, D. M.
Year: 2020
DOI: 10.1016/j.commatsci.2019.109329
Severe plastic deformation (SPD), occurring ubiquitously across metal forming processes, has been utilized to significantly improve bulk material properties such as the strength of metals. The latter is achieved by ultra-fine grain refinement at the polycrystalline mesoscale via the application of large plastic strains on the macroscale. We here present a multiscale framework that aims at efficiently modeling SPD processes while effectively capturing the underlying physics across all relevant scales. At the level of the macroscale boundary value problem, an enhanced maximum-entropy (max-ent) meshless method is employed. Compared to finite elements and other meshless techniques, this method offers a stabilized finite-strain updated-Lagrangian setting for improved robustness with respect to mesh distortion arising from large plastic strains. At each material point on the macroscale, we describe the polycrystalline material response via a Taylor model at the mesoscale, which captures discontinuous dynamic recrystallization through the nucleation and growth/shrinkage of grains. Each grain, in turn, is modeled by a finite-strain crystal plasticity model at the microscale. We focus on equal-channel angular extrusion (ECAE) of polycrystalline pure copper as an application, in which severe strains are generated by extruding the specimen around a 90°-corner. Our framework describes not only the evolution of strain and stress distributions during the process but also grain refinement and texture evolution, while offering a computationally feasible treatment of the macroscale mechanical boundary value problem. Though we here focus on ECAE of copper, the numerical setup is sufficiently general for other applications including SPD and thermo-mechanical processes (e.g., rolling, high-pressure torsion, etc.) as well as other materials systems.https://authors.library.caltech.edu/records/hr97d-sx324Extreme mechanical resilience of self-assembled nanolabyrinthine materials
https://resolver.caltech.edu/CaltechAUTHORS:20200304-130419102
Authors: Portela, Carlos M.; Vidyasagar, A.; Krödel, Sebastian; Weissenbach, Tamara; Yee, Daryl W.; Greer, Julia R.; Kochmann, Dennis M.
Year: 2020
DOI: 10.1073/pnas.1916817117
PMCID: PMC7084143
Low-density materials with tailorable properties have attracted attention for decades, yet stiff materials that can resiliently tolerate extreme forces and deformation while being manufactured at large scales have remained a rare find. Designs inspired by nature, such as hierarchical composites and atomic lattice-mimicking architectures, have achieved optimal combinations of mechanical properties but suffer from limited mechanical tunability, limited long-term stability, and low-throughput volumes that stem from limitations in additive manufacturing techniques. Based on natural self-assembly of polymeric emulsions via spinodal decomposition, here we demonstrate a concept for the scalable fabrication of nonperiodic, shell-based ceramic materials with ultralow densities, possessing features on the order of tens of nanometers and sample volumes on the order of cubic centimeters. Guided by simulations of separation processes, we numerically show that the curvature of self-assembled shells can produce close to optimal stiffness scaling with density, and we experimentally demonstrate that a carefully chosen combination of topology, geometry, and base material results in superior mechanical resilience in the architected product. Our approach provides a pathway to harnessing self-assembly methods in the design and scalable fabrication of beyond-periodic and nonbeam-based nano-architected materials with simultaneous directional tunability, high stiffness, and unsurpassed recoverability with marginal deterioration.https://authors.library.caltech.edu/records/3rcma-cvw49A discrete, geometrically exact method for simulating nonlinear, elastic and inelastic beams
https://resolver.caltech.edu/CaltechAUTHORS:20191121-100451756
Authors: Lestringant, Claire; Audoly, Basile; Kochmann, Dennis M.
Year: 2020
DOI: 10.1016/j.cma.2019.112741
We present an extension of a discrete, geometrically exact beam formulation based on discrete framed curves and discrete parallel transport originally introduced in the computer graphics community. In combination with variational constitutive updates, our numerical scheme decouples the kinematics from the material behavior, and can handle finite rotations as well as a wide class of constitutive laws depending on the stretching, flexural and torsional strain and strain rates. We demonstrate its capabilities through a suite of benchmark problems involving elastic, viscous and visco-elastic beams. The method fits naturally in existing finite element frameworks and is well suited to engineering applications. It can efficiently and accurately simulate the nonlinear deformation of slender beams featuring complex material behavior, such as those found in the topical design of flexible structural metamaterials.https://authors.library.caltech.edu/records/rdvcv-ffr72An assessment of numerical techniques to find energy‐minimizing microstructures associated with nonconvex potentials
https://resolver.caltech.edu/CaltechAUTHORS:20200103-073712827
Authors: Kumar, Siddhant; Vidyasagar, A.; Kochmann, Dennis M.
Year: 2020
DOI: 10.1002/nme.6280
Microstructural patterns emerge ubiquitously during phase transformations, deformation twinning, or crystal plasticity. Challenges are the prediction of such microstructural patterns and the resulting effective material behavior. Mathematically, the experimentally observed patterns are energy‐minimizing sequences produced by an underlying non‐(quasi)convex strain energy. Therefore, identifying the microstructure and effective response is linked to finding the quasiconvex, relaxed energy. Due to its nonlocal nature, quasiconvexification has traditionally been limited to (semi‐)analytical techniques or has been dealt with by numerical techniques such as the finite element method (FEM). Both have been restricted to primarily simple material models. We here contrast three numerical techniques—FEM, a Fourier‐based spectral formulation, and a meshless maximum‐entropy (max‐ent) method. We demonstrate their performance by minimizing the energy of a representative volume element for both hyperelasticity and finite‐strain phase transformations. Unlike FEM, which fails to converge in most scenarios, the Fourier‐based spectral formulation (FFT) scheme captures microstructures of intriguingly high resolution, whereas max‐ent is superior at approximating the relaxed energy. None of the methods are capable of accurately predicting both microstructures and relaxed energy; yet, both FFT and max‐ent show significant advantages over FEM. Numerical errors are explained by the energy associated with microstructural interfaces in the numerical techniques compared here.https://authors.library.caltech.edu/records/83dn4-fjf46Roadmap on multiscale materials modeling
https://resolver.caltech.edu/CaltechAUTHORS:20200323-095145619
Authors: van der Giessen, Erik; Schultz, Peter A.; Bertin, Nicolas; Bulatov, Vasily V.; Cai, Wei; Csányi, Gábor; Foiles, Stephen M.; Geers, M. G. D.; González, Carlos; Hütter, Markus; Kim, Woo Kyun; Kochmann, Dennis M.; LLorca, Javier; Mattsson, Ann E.; Rottler, Jörg; Shluger, Alexander; Sills, Ryan B.; Steinbach, Ingo; Strachan, Alejandro; Tadmor, Ellad B
Year: 2020
DOI: 10.1088/1361-651x/ab7150
Modeling and simulation is transforming modern materials science, becoming an important tool for the discovery of new materials and material phenomena, for gaining insight into the processes that govern materials behavior, and, increasingly, for quantitative predictions that can be used as part of a design tool in full partnership with experimental synthesis and characterization. Modeling and simulation is the essential bridge from good science to good engineering, spanning from fundamental understanding of materials behavior to deliberate design of new materials technologies leveraging new properties and processes. This Roadmap presents a broad overview of the extensive impact computational modeling has had in materials science in the past few decades, and offers focused perspectives on where the path forward lies as this rapidly expanding field evolves to meet the challenges of the next few decades. The Roadmap offers perspectives on advances within disciplines as diverse as phase field methods to model mesoscale behavior and molecular dynamics methods to deduce the fundamental atomic-scale dynamical processes governing materials response, to the challenges involved in the interdisciplinary research that tackles complex materials problems where the governing phenomena span different scales of materials behavior requiring multiscale approaches. The shift from understanding fundamental materials behavior to development of quantitative approaches to explain and predict experimental observations requires advances in the methods and practice in simulations for reproducibility and reliability, and interacting with a computational ecosystem that integrates new theory development, innovative applications, and an increasingly integrated software and computational infrastructure that takes advantage of the increasingly powerful computational methods and computing hardware.https://authors.library.caltech.edu/records/y4kk3-7g478Inverse-designed spinodoid metamaterials
https://resolver.caltech.edu/CaltechAUTHORS:20200702-081435421
Authors: Kumar, Siddhant; Tan, Stephanie; Zheng, Li; Kochmann, Dennis M.
Year: 2020
DOI: 10.1038/s41524-020-0341-6
After a decade of periodic truss-, plate-, and shell-based architectures having dominated the design of metamaterials, we introduce the non-periodic class of spinodoid topologies. Inspired by natural self-assembly processes, spinodoid metamaterials are a close approximation of microstructures observed during spinodal phase separation. Their theoretical parametrization is so intriguingly simple that one can bypass costly phase-field simulations and obtain a rich and seamlessly tunable property space. Counter-intuitively, breaking with the periodicity of classical metamaterials is the enabling factor to the large property space and the ability to introduce seamless functional grading. We introduce an efficient and robust machine learning technique for the inverse design of (meta-)materials which, when applied to spinodoid topologies, enables us to generate uniform and functionally graded cellular mechanical metamaterials with tailored direction-dependent (anisotropic) stiffness and density. We specifically present biomimetic artificial bone architectures that not only reproduce the properties of trabecular bone accurately but also even geometrically resemble natural bone.https://authors.library.caltech.edu/records/jvgh3-7w842A phase-field approach to studying the temperature-dependent ferroelectric response of bulk polycrystalline PZT
https://resolver.caltech.edu/CaltechAUTHORS:20200722-102946779
Authors: Indergand, Roman; Vidyasagar, A.; Nadkarni, Neel; Kochmann, Dennis M.
Year: 2020
DOI: 10.1016/j.jmps.2020.104098
Ferroelectric ceramics are of interest for engineering applications because of their electro-mechanical coupling and the unique ability to permanently alter their atomic-level dipole structure (i.e., their polarization) and to induce large-strain actuation through applied electric fields. Although the underlying multiscale coupling mechanisms have been investigated by modeling strategies reaching from the atomic level across the polycrystalline mesoscale to the macroscopic device level, most prior work has neglected the important influence of temperature on the ferroelectric behavior. Here, we present a phase-field (diffuse-interface) constitutive model for ferroelectric ceramics, which is extended to account for the effects of finite temperature by considering thermal lattice vibrations based on statistical mechanics and by modifying the underlying Landau-Devonshire potential to depend on temperature. Results indicate that the chosen interpolation of the Landau energy coefficients is a suitable approach for predicting the temperature-dependent spontaneous polarization accurately over a broad temperature range. Lowering the energy barrier at finite temperature by the aforementioned methods also leads to better agreement with measurements of the bipolar hysteresis. Based on a numerical implementation via FFT spectral homogenization, we present simulation results of single- and polycrystals, which highlight the effect of temperature on the ferroelectric switching kinetics. We observe that thermal fluctuations (at the phase-field level realized by a thermalized stochastic noise term in the Allen-Cahn evolution equation) promote the nucleation of needle-like domains in regions of high heterogeneity or stress concentration such as grain boundaries. This, in turn, leads to a faster polarization reversal at low electric fields and a simulated domain pattern evolution comparable to experimental observations, stemming from the competition between nucleation and growth of domains. We discuss the development, implementation, validation, and application of the temperature-dependent phase-field framework for ferroelectric ceramics with a focus on tetragonal lead zirconate titanate (PZT), which we demonstrate to admit reasonable model predictions and comparison with experiments.https://authors.library.caltech.edu/records/w6taw-x4q63Nonequilibrium thermomechanics of Gaussian phase packet crystals: Application to the quasistatic quasicontinuum method
https://resolver.caltech.edu/CaltechAUTHORS:20210518-103040351
Authors: Gupta, Prateek; Ortiz, Michael; Kochmann, Dennis M.
Year: 2021
DOI: 10.1016/j.jmps.2021.104495
The quasicontinuum (QC) method was originally introduced to bridge across length scales by coarse-graining an atomistic ensemble to significantly larger continuum scales at zero temperature, thus overcoming the crucial length-scale limitation of classical atomic-scale simulation techniques while solely relying on atomic-scale input (in the form of interatomic potentials). An associated challenge lies in bridging across time scales to overcome the time-scale limitations of atomistics at finite temperature. To address the biggest challenge, bridging across both length and time scales, only a few techniques exist, and most of those are limited to conditions of constant temperature. Here, we present a new general strategy for the space–time coarsening of an atomistic ensemble, which introduces thermomechanical coupling. Specifically, we evolve the statistics of an atomistic ensemble in phase space over time by applying the Liouville equation to an approximation of the ensemble's probability distribution (which further admits a variational formulation). To this end, we approximate a crystalline solid as a lattice of lumped correlated Gaussian phase packets occupying atomic lattice sites, and we investigate the resulting quasistatics and dynamics of the system. By definition, phase packets account for the dynamics of crystalline lattices at finite temperature through the statistical variances of atomic momenta and positions. We show that momentum–space correlation allows for an exchange between potential and kinetic contributions to the crystal's Hamiltonian. Consequently, local adiabatic heating due to atomic site motion is captured. Moreover, in the quasistatic limit, the governing equations reduce to the minimization of thermodynamic potentials (similar to maximum-entropy formulation previously introduced for finite-temperature QC), and they yield the local equation of state, which we derive for isothermal, isobaric, and isentropic conditions. Since our formulation without interatomic correlations precludes irreversible heat transport, we demonstrate its combination with thermal transport models to describe realistic atomic-level processes, and we discuss opportunities for capturing atomic-level thermal transport by including interatomic correlations in the Gaussian phase packet formulation. Overall, our Gaussian phase packet approach offers a promising avenue for finite-temperature non-equilibrium quasicontinuum techniques, which may be combined with thermal transport models and extended to other approximations of the probability distribution as well as to exploit the variational structure.https://authors.library.caltech.edu/records/7njpe-mks78Supersonic impact resilience of nanoarchitected carbon
https://resolver.caltech.edu/CaltechAUTHORS:20210428-140642160
Authors: Portela, Carlos M.; Edwards, Bryce W.; Veysset, David; Sun, Yuchen; Nelson, Keith A.; Kochmann, Dennis M.; Greer, Julia R.
Year: 2021
DOI: 10.1038/s41563-021-01033-z
Architected materials with nanoscale features have enabled extreme combinations of properties by exploiting the ultralightweight structural design space together with size-induced mechanical enhancement at small scales. Apart from linear waves in metamaterials, this principle has been restricted to quasi-static properties or to low-speed phenomena, leaving nanoarchitected materials under extreme dynamic conditions largely unexplored. Here, using supersonic microparticle impact experiments, we demonstrate extreme impact energy dissipation in three-dimensional nanoarchitected carbon materials that exhibit mass-normalized energy dissipation superior to that of traditional impact-resistant materials such as steel, aluminium, polymethyl methacrylate and Kevlar. In-situ ultrahigh-speed imaging and post-mortem confocal microscopy reveal consistent mechanisms such as compaction cratering and microparticle capture that enable this superior response. By analogy to planetary impact, we introduce predictive tools for crater formation in these materials using dimensional analysis. These results substantially uncover the dynamic regime over which nanoarchitecture enables the design of ultralightweight, impact-resistant materials that could open the way to design principles for lightweight armour, protective coatings and blast-resistant shields for sensitive electronics.https://authors.library.caltech.edu/records/qtrkx-j6330Recrystallization mechanisms, grain refinement, and texture evolution during ECAE processing of Mg and its alloys
https://resolver.caltech.edu/CaltechAUTHORS:20211202-191330543
Authors: Kecskes, Laszlo J.; Krywopusk, Nicholas M.; Hollenweger, Yannick; Krynicki, Jenna N.; Eswarappa Prameela, Suhas; Yi, Peng; Liu, Burigede; Falk, Michael L.; Kochmann, Dennis M.; Weihs, Timothy P.
Year: 2021
DOI: 10.1016/j.mechmat.2021.104067
This article presents key findings from a study of the microstructural evolution and grain size refinement of equal-channel angular extrusion (ECAE)-processed Mg and Mg-based alloys. Firstly, we delineate the experimental trends and material characteristics of grain size distribution and texture of as-cast pure Mg and rolled AZ31B which were processed via ECAE. We then identify and describe the primary controlling mechanisms of dynamic recrystallization (DRX) and twinning and how their interaction affects the overall refinement process. Secondly, using preliminary results from ongoing studies of other Mg-based model binary and ternary systems, with access to precipitation hardening mechanisms, we present new opportunities and beneficial outcomes that could affect and control the material's microstructural properties. Thirdly, we provide a summary of prior and concurrent modeling and simulation efforts that capture and emulate the experimentally observed trends of DRX and illustrate their predictive capability. We then, within a Materials-by-Design and Optimization framework, conclude with implications for future developments in Mg alloy research.https://authors.library.caltech.edu/records/yftwy-b3j12