arXiv subjects

Kaushik Dayal

Publications and source records attributed to Kaushik Dayal.

At least 37 records · Page 2Linked to original sources

arXiv2025

Exploiting Instabilities to Enable Large Shape Transformations in Dielectric Elastomers

Dielectric elastomers have significant potential for new technologies ranging from soft robots to biomedical devices, driven by their ability to display complex shape changes in response to electrical stimulus. However, an important shortcoming of current realizations is that large voltages are required for useful actuation strains. This work proposes, and demonstrates through theory and numerical simulations, a strategy to achieve large and controlled actuation by exploiting the electromechanical analog of the Treloar-Kearsley (TK) instability. The key idea is to use the fact that the TK instability is a symmetry-breaking bifurcation, which implies the existence of a symmetry-driven constant-energy region in the energy landscape. This provides for nonlinear soft modes with large deformations that can be accessed with very small external stimulus, which is achieved here by applying a small in-plane electric field. First, the bifurcation and post-bifurcation behavior of the electromechanical TK instability are established theoretically in the idealized setting of uniform deformation and electric field. Next, building on this, a finite element analysis of a realistic geometry with patterned top and bottom electrodes is applied to demonstrate large and soft shape changes driven by small voltage differences across the electrodes.

cond-mat.soft↗

arXiv2024

Phase-Field Modeling of Fracture under Compression and Confinement in Anisotropic Geomaterials

Strongly anisotropic geomaterials undergo fracture under compressive loading. This paper applies a phase-field fracture model to study this fracture process. While phase-field fracture models have several advantages, they provide unphysical predictions when the stress state is complex and includes compression that can cause crack faces to contact. Building on a phase-field model that accounts for compressive traction across the crack face, this paper extends the model to anisotropic fracture. The key features include: (1) a homogenized anisotropic elastic response and strongly-anisotropic model for the work to fracture; (2) an effective damage response that accounts consistently for compressive traction across the crack face, that is derived from the anisotropic elastic response; (3) a regularized crack normal field that overcomes the shortcomings of the isotropic setting, and enables the correct crack response, both across and transverse to the crack face. To test the model, we first compare the predictions to phase-field fracture evolution calculations in a fully-resolved layered specimen with spatial inhomogeneity, and show that it captures the overall patterns of crack growth. We then apply the model to previously-reported experimental observations of fracture evolution in laboratory specimens of shales under compression with confinement, and find that it predicts well the observed crack patterns in a broad range of loading conditions. We further apply the model to predict the growth of wing cracks under compression and confinement. The effective crack response model enables us to treat the initial crack simply as a non-singular damaged zone within the computational domain, thereby allowing for easy and general computations.

cond-mat.mtrl-sci↗

arXiv2024

Impact of grain boundary energy anisotropy on grain growth

A threshold dynamics model of grain growth that accounts for the anisotropy in the grain boundary energy has been used to simulate experimentally observed grain growth of polycrystalline Ni. The simulation reproduces several aspects of the observed microstructural evolution that are not found in the results of simulations assuming isotropic properties. For example, the relative areas of the lowest-energy twin boundaries increase as the grains grow and the average grain boundary energy decreases with grain growth. This decrease in energy occurs because the population of higher-energy grain boundaries decreases while the population of lower-energy boundaries increases as the total grain boundary area decreases. This phenomenon emerges from the assumption of anisotropic grain boundary energies without modification of the energy minimizing algorithm. These findings are consistent with the observation that, in addition to the decrease in grain boundary area, additional energy is dissipated during grain growth by a decrease in the average grain boundary energy.

cond-mat.mtrl-sci↗

arXiv2024

Interplay between Nucleation and Kinetics in Dynamic Twinning

In this work, we apply a phase-field modeling framework to elucidate the interplay between nucleation and kinetics in the dynamic evolution of twinning interfaces. The key feature of this phase-field approach is the ability to transparently and explicitly specify nucleation and kinetic behavior in the model, in contrast to other regularized interface models. We use this to study 2 distinct problems where it is essential to explicitly specify the kinetic and nucleation behavior governing twin evolution. First, we study twinning interfaces in 2-d. When these interfaces are driven to move, we find that significant levels of twin nucleation occur ahead of the moving interface. Essentially, the finite interface velocity and the relaxation time of the stresses ahead of the interface allows for nucleation to occur before the interface is able to propagate to that point. Second, we study the growth of needle twins in antiplane elasticity. We show that both nucleation and anisotropic kinetics are essential to obtain predictions of needle twins. While standard regularized interface approaches do not permit the transparent specification of anisotropic kinetics, this is readily possible with the phase-field approach that we have used here.

cond-mat.mtrl-sci↗

arXiv2024

Nonuniqueness in Defining the Polarization: Nonlocal Surface Charges and the Electrostatic, Energetic, and Transport Perspectives

Ionic crystals play a central role in functional applications. Mesoscale descriptions of these crystals are based on the continuum polarization density field to represent the effective physics of charge distribution at the scale of the atomic lattice. However, a long-standing difficulty is that the classical electrostatic definition of the macroscopic polarization -- as the dipole or first moment of the charge density in a unit cell -- is not unique. This unphysical non-uniqueness has been shown to arise from starting directly with an infinite system rather than starting with a finite body and taking appropriate limits. This limit process shows that the electrostatic description requires not only the bulk polarization density, but also the surface charge density, as the effective macroscopic descriptors; that is, a nonlocal effective description. Other approaches to resolve this difficulty include relating the change in polarization to the transport of charge; or, to define the polarization as the energy-conjugate to the electric field. This work examines the relation between the classical electrostatic definition of polarization, and the transport and energy-conjugate definitions of polarization. We show the following: (1) The transport of charge does not correspond to the change in polarization in general; instead, one requires additional simplifying assumptions on the electrostatic definition of polarization for these approaches to give rise to the same macroscopic electric fields. Thus, the electrostatic definition encompasses the transport definition as a special case. (2) The energy-conjugate definition has both bulk and surface contributions; while traditional approaches neglect the surface contribution, we find that accounting for the nonlocal surface contributions is essential to obtain the correct macroscopic electric fields.

cond-mat.mes-hall↗

arXiv2024

Statistical Field Theory of Polarizable Polymer Chains with Nonlocal Dipolar Interactions

The electromechanical response of polymeric soft matter to applied electric fields is of fundamental scientific interest as well as relevant to technologies for sensing and actuation. Several existing theoretical and numerical approaches for polarizable polymers subject to a combined applied electric field and stretch are based on discrete monomer models. In these models, accounting for the interactions between the induced dipoles on monomers is challenging due to the nonlocality of these interactions. On the other hand, the framework of statistical field theory provides a continuous description of polymer chains that potentially enables a tractable way to account for these interactions. However, prior formulations using this framework have been restricted to the case of weak anisotropy of the monomer polarizability. This paper formulates a general approach based in the framework of statistical field theory to account for the nonlocal nature of the dipolar interactions without any restrictions on the anisotropy or nonlinearity of the polarizability of the monomer. The approach is based on 3 key elements: (1) the statistical field theory framework, in which the discrete monomers are regularized to a continuous dipole distribution; (2) a replacement of the nonlocal dipole-dipole interactions by the local electrostatics PDE with the continuous dipole distribution as the forcing; (3) the use of a completely general relation between the polarization and the local electric field. Rather than treat the dipole-dipole interactions directly, the continuous description in the field theory enables the computationally-tractable nonlocal-to-local transformation. Further, it enables the use of a realistic statistical-mechanical ensemble wherein the average far-field applied electric field is prescribed, rather than prescribing the applied field at every point in the polymer domain.

cond-mat.soft↗

arXiv2023

Grain boundary migration in polycrystalline $α$-Fe

High energy x-ray diffraction microscopy was used to image the microstructure of $α$-Fe before and after a 600 $^\circ$C anneal. These data were used to determine the areas, curvatures, energies, and velocities of approximately 40,000 grain boundaries. The measured grain boundary properties depend on the five macroscopic grain boundary parameters. The velocities are not correlated with the product of the mean boundary curvature and grain boundary energy, usually assumed to be the driving force. Boundary migration is made up of area changes (lateral motion) and translation (normal motion) and both contribute to the total migration. Through the lateral motion component of the migration, low energy boundaries tend to expand in area while high energy boundaries shrink, reducing the average energy through grain boundary replacement. The driving force for this process is not related to curvature and might disrupt the expected curvature-velocity relationship.

cond-mat.mtrl-sci↗

arXiv2023

A Dimensionally-Reduced Nonlinear Elasticity Model for Liquid Crystal Elastomer Strips with Transverse Curvature

Liquid Crystalline Elastomers (LCEs) are active materials that are of interest due to their programmable response to various external stimuli such as light and heat. When exposed to these stimuli, the anisotropy in the response of the material is governed by the nematic director, which is a continuum parameter that is defined as the average local orientation of the mesogens in the liquid crystal phase. This nematic director can be programmed to be heterogeneous in space, creating a vast design space that is useful for applications ranging from artificial ligaments to deployable structures to self-assembling mechanisms. Even when specialized to long and thin strips of LCEs -- the focus of this work -- the vast design space has required the use of numerical simulations to aid in experimental discovery. To mitigate the computational expense of full 3-d numerical simulations, several dimensionally-reduced rod and ribbon models have been developed for LCE strips, but these have not accounted for the possibility of initial transverse curvature, like carpenter's tape spring. Motivated by recent experiments showing that transversely-curved LCE strips display a rich variety of configurations, this work derives a dimensionally-reduced 1-d model for pre-curved LCE strips. The 1-d model is validated against full 3-d finite element calculations, and it is also shown to capture experimental observations, including tape-spring-like localizations, in activated LCE strips.

cond-mat.soft↗

arXiv2023

Deformation Decomposition versus Energy Decomposition for Chemo- and Poro- Mechanics

We briefly compare the structure of two classes of popular models used to describe poro- and chemo- mechanics wherein a fluid phase is transported within a solid phase. The multiplicative deformation decomposition has been successfully used to model permanent inelastic shape change in plasticity, solid-solid phase transformation, and thermal expansion, which has motivated its application to poro- and chemo- mechanics. However, the energetic decomposition provides a more transparent structure and advantages, such as to couple to phase-field fracture, for models of poro- and chemo- mechanics.

cond-mat.soft↗

arXiv2023

Statistical field theory for nonlinear elasticity of polymer networks with excluded volume interactions

Polymer networks formed by cross linking flexible polymer chains are ubiquitous in many natural and synthetic soft-matter systems. Current micromechanics models generally do not account for excluded volume interactions except, for instance, through imposing a phenomenological incompressibility constraint at the continuum scale. This work aims to examine the role of excluded volume interactions on the mechanical response. The approach is based on the framework of the self-consistent statistical field theory of polymers, which provides an efficient mesoscale approach that enables the accounting of excluded volume effects without the expense of large-scale molecular modeling. A mesoscale representative volume element is populated with multiple interacting chains, and the macroscale nonlinear elastic deformation is imposed by mapping the end-to-end vectors of the chains by this deformation. In the absence of excluded volume interactions, it recovers the closed-form results of the classical theory of rubber elasticity. With excluded volume interactions, the model is solved numerically in three dimensions using a finite element method to obtain the energy, stresses, and linearized moduli under imposed macroscale deformation. Highlights of the numerical study include: (i) the linearized Poisson's ratio is very close to the incompressible limit without a phenomenological imposition of incompressibility; (ii) despite the harmonic Gaussian chain as a starting point, there is an emergent strain-softening and strain-stiffening response that is characteristic of real polymer networks, driven by the interplay between the entropy and the excluded volume interactions; and (iii) the emergence of a deformation-sensitive localization instability at large excluded volumes.

cond-mat.soft↗

arXiv2023

Discrete-to-Continuum Limits of Long-Range Electrical Interactions in Nanostructures

We consider electrostatic interactions in two classes of nanostructures embedded in a three dimensional space: (1) helical nanotubes, and (2) thin films with uniform bending (i.e., constant mean curvature). Starting from the atomic scale with a discrete distribution of dipoles, we obtain the continuum limit of the electrostatic energy; the continuum energy depends on the geometric parameters that define the nanostructure, such as the pitch and twist of the helical nanotubes and the curvature of the thin film. We find that the limiting energy is local in nature. This can be rationalized by noticing that the decay of the dipole kernel is sufficiently fast when the lattice sums run over one and two dimensions, and is also consistent with prior work on dimension reduction of continuum micromagnetic bodies to the thin film limit. However, an interesting contrast between the discrete-to-continuum approach and the continuum dimension reduction approaches is that the limit energy in the latter depends only on the normal component of the dipole field, whereas in the discrete-to-continuum approach, both tangential and normal components of the dipole field contribute to the limit energy.

cond-mat.mes-hall↗

arXiv2023

Hessian-informed Hamiltonian Monte Carlo for high-dimensional problems

We investigate the effect of using local and non-local second derivative information on the performance of Hamiltonian Monte Carlo (HMC) sampling methods, for high-dimension non-Gaussian distributions, with application to Bayesian inference and nonlinear inverse problems. The Riemannian Manifold Hamiltonian Monte Carlo (RMHMC) method uses second and third derivative information to improve the performance of the HMC approach. We propose using the local Hessian information at the start of each iteration, instead of re-calculating the higher order derivatives in all sub-steps of the leapfrog updating algorithm. We compare the result of Hessian-informed HMC method using the local and nonlocal Hessian information, in a test bed of a high-dimensional log-normal distribution, related to a problem of inferring soil properties.

stat.CO↗

arXiv2023

High-dimensional Nonlinear Bayesian Inference of Poroelastic Fields from Pressure Data

We investigate solution methods for large-scale inverse problems governed by partial differential equations (PDEs) via Bayesian inference. The Bayesian framework provides a statistical setting to infer uncertain parameters from noisy measurements. To quantify posterior uncertainty, we adopt Markov Chain Monte Carlo (MCMC) approaches for generating samples. To increase the efficiency of these approaches in high-dimension, we make use of local information about gradient and Hessian of the target potential, also via Hamiltonian Monte Carlo (HMC). Our target application is inferring the field of soil permeability processing observations of pore pressure, using a nonlinear PDE poromechanics model for predicting pressure from permeability. We compare the performance of different sampling approaches in this and other settings. We also investigate the effect of dimensionality and non-gaussianity of distributions on the performance of different sampling methods.

stat.AP↗

arXiv2023

Distal and non-symmetrical crack nucleation in delamination of plates via dimensionally-reduced peridynamics

Exploiting the framework of peridynamics, a dimensionally-reduced plate formulation is developed that allows for the through-thickness nucleation and growth of fracture surfaces, enabling the treatment of delamination in a lower-dimensional model. Delamination fracture nucleation and propagation are treated by choosing the kinematics to be composed of an absolutely continuous part and a zone where jumps in the displacements are allowed. This assumption allows the explicit derivation of the dimensionally-reduced elastic energy, which shows a hierarchy of terms characterising the stored energy in the plane element. An interpretation of the various terms of the reduced energy is shown by means of the most straightforward paradigm of bond-based peridynamics. A striking feature of the reduced energy is that, despite the small-displacement assumption, there is a coupling between the membrane and bending terms. Semi-analytical solutions for simplified settings are obtained through a minimization procedure, and a range of nonstandard behaviours such as \textit{distal} crack nucleation and curved crack path are captured by the model. Finally, convergence of the proposed peridynamic reduced model to a local elastic theory for vanishing nonlocal lengthscale is determined, giving a local cohesive model for fracture.

physics.app-ph↗

arXiv2022

Phase-Field Finite Deformation Fracture with an Effective Energy for Regularized Crack Face Contact

Phase-field models are a leading approach for realistic fracture problems. They treat the crack as a second phase and use gradient terms to smear out the crack faces, enabling the use of standard numerical methods for simulations. This regularization causes cracks to occupy a finite volume in the reference, and leads to the inability to appropriately model the closing or contacting -- without healing -- of crack faces. Specifically, the classical idealized crack face tractions are that the shear component is zero, and that the normal component is zero when the crack opens and identical to the intact material when the crack closes. Phase-field fracture models do not replicate this behavior. This work addresses this shortcoming by introducing an effective crack energy density that endows the regularized (finite volume) phase-field crack with the effective properties of an idealized sharp crack. The approach is based on applying the QR (upper triangular) decomposition of the deformation gradient tensor in the basis of the crack, enabling a transparent identification of the crack deformation modes. By then relaxing over those modes that do not cost energy, an effective energy is obtained that has the intact response when the crack faces close and zero energy when the crack faces are open. A highlight of this approach is that it lies completely in the setting of finite deformation, enabling potential application to soft materials and other settings with large deformation or rotations. The model is applied to numerically study representative complex loadings, including (1) cyclic loading on a cavity in a soft solid that shows the growth and closing of cracks in complex stress states; and (2) cyclic shear that shows a complex pattern of crack branching driven by the closure of cracks.

math.AP↗

arXiv2022

Multiband homogenization of metamaterials in real-space: Higher-order nonlocal models and scattering at external surfaces

This work develops a dynamic homogenization approach for metamaterials. It finds an approximate macroscopic homogenized equation with constant coefficients posed in space and time; however, the resulting homogenized equation is higher order in space and time. The homogenized equation can be used to solve initial-boundary-value problems posed on arbitrary non-periodic macroscale geometries with macroscopic heterogeneity, such as bodies composed of several different metamaterials or with external boundaries. First, considering a single band, the higher-order space derivatives lead to additional continuity conditions at the boundary between a homogeneous material and a metamaterial. These provide predictions of wave scattering in 1-d and 2-d that match well with the exact fine-scale solution; compared to alternative approaches, they provide a single equation that is valid over a broad range of frequencies, are easy to apply, and are much faster to compute. Next, the setting of two bands with a bandgap is considered. The homogenized equation has also higher-order time derivatives. Notably, the homogenized model provides a single equation that is valid over both bands and the bandgap. The continuity conditions are applied to wave scattering at a boundary, and show good agreement with the exact fine-scale solution. Using that the order of the highest time derivative is proportional to the number of bands considered, a nonlocal-in-time structure is conjectured for the homogenized equation in the limit of infinite bands. This suggests that homogenizing over finer length and time scales -- with the temporal homogenization being carried out through the consideration of higher bands in the dispersion relation -- is a mechanism for the emergence of macroscopic spatial and temporal nonlocality, with the extent of temporal nonlocality being related to the number of bands considered.

math.AP↗

arXiv2022

Comparison of simulated and measured grain volume changes during grain growth

The three-dimensional microstructure of Ni, observed after five annealing intervals, was compared to simulations of grain growth using the threshold dynamics method with the assumption of capillarity as the only driving force. A grain-by-grain comparison made it possible to identify the sources of differences between the simulation and experiment. The most significant difference was for grains of the smallest sizes, which the simulation predicted would lose volume and disappear at a greater rate than observed in the experiment. The loss of grains created errors in the numbers of neighbors of the remaining grains, and it was found that errors in the simulated grain volume were correlated to errors in the number of near neighbors. While anisotropic grain boundary properties likely play a role in the differences, the size dependence of the errors suggest that it might be necessary to include a size dependence in the model for grain boundary migration kinetics.

cond-mat.mtrl-sci↗

arXiv2022

Predicting Peak Stresses In Microstructured Materials Using Convolutional Encoder-Decoder Learning

This work presents a machine learning approach to predict peak-stress clusters in heterogeneous polycrystalline materials. Prior work on using machine learning in the context of mechanics has largely focused on predicting the effective response and overall structure of stress fields. However, their ability to predict peak stresses -- which are of critical importance to failure -- is unexplored, because the peak-stress clusters occupy a small spatial volume relative to the entire domain, and hence requires computationally expensive training. This work develops a deep-learning based Convolutional Encoder-Decoder method that focuses on predicting peak-stress clusters, specifically on the size and other characteristics of the clusters in the framework of heterogeneous linear elasticity. This method is based on convolutional filters that model local spatial relations between microstructures and stress fields using spatially weighted averaging operations. The model is first trained against linear elastic calculations of stress under applied macroscopic strain in synthetically-generated microstructures, which serves as the ground truth. The trained model is then applied to predict the stress field given a (synthetically-generated) microstructure and then to detect peak-stress clusters within the predicted stress field. The accuracy of the peak-stress predictions is analyzed using the cosine similarity metric and by comparing the geometric characteristics of the peak-stress clusters against the ground-truth calculations. It is observed that the model is able to learn and predict the geometric details of the peak-stress clusters and, in particular, performed better for higher (normalized) values of the peak stress as compared to lower values of the peak stress. These comparisons showed that the proposed method is well-suited to predict the characteristics of peak-stress clusters.

math.AP↗