arXiv subjects

Kaushik Dayal

Publications and source records attributed to Kaushik Dayal.

At least 19 recordsLinked to original sources

arXiv2026

Compressive Splitting in Brittle Solids: The Inverse of Wrinkling in Sheets

Axial splitting is the dominant failure mode of brittle solids under compression, yet its mechanical origin remains unclear. We show that clamped loading platens suppress lateral Poisson expansion, generating boundary-induced tensile stresses at the specimen interior -- the compressive analog of wrinkling in stretched sheets. This mechanism provides a predictive strength law, relating axial splitting to tensile strength, geometry, and confinement pressure. This is validated against diverse materials ranging from rocks to ceramics, establishing axial splitting as a geometry-controlled elastic process rather than a stochastic flaw problem.

cond-mat.mtrl-sci↗

arXiv2026

Continuum Limit of Nonlocal Electrostatics in Random Media

We derive a two-scale continuum limit for the electrostatic energy of random charge density fields that are stationary and ergodic under lattice translations. Each microscopic cell is charge neutral in every realization, while its dipole moment may fluctuate and have a nonzero mean. Under assumptions on the stationary microscopic potential and the finite-volume fields, the local and nonlocal energies converge almost surely to deterministic limits. The local limit consists of the ensemble-averaged microscopic Coulomb energy and a cell-depolarization term, whereas the effective polarization determines the nonlocal limit. The cell-depolarization terms cancel in the total energy, which consists of the ensemble-averaged microscopic cell energy and the macroscopic electrostatic field energy. The deterministic specialization recovers the periodic two-scale limit. For an independent-cell random-displacement model, we verify the assumptions of the continuum-limit theorem and show that centered microscopic fluctuations can change the local energy without changing the effective polarization or the nonlocal energy.

cond-mat.mes-hall↗

arXiv2026

Anisotropic Thermalization in Far-from-Equilibrium Flows

We present a deterministic discontinuous Galerkin (DG) finite-element solution of the Boltzmann equation, without moment-closure approximations, under a class of far-from-equilibrium deformations. Specifically, we consider affine flows which reduce the Boltzmann equation to a purely velocity-space problem for the reduced distribution function in a reduced velocity field. We solve the reduced equation using a tensor-product Lagrange DG discretization for four representative flows: simple shear, pressure shear, bi-directional shear, and a vortex flow. Our principal finding is that the velocity distribution is well-approximated by an anisotropic Gaussian throughout the evolution, despite the non-equilibrium conditions. Further, we show the evolution of the covariance tensor of the Gaussian distribution is equal to the inverse of the right Cauchy-Green tensor in the free-streaming limit without collisions. This prediction compares very well with the numerical solution at short times; at longer times, they grow apart, reflecting the influence of particle collisions.

physics.flu-dyn↗

arXiv2026

Nonlocal Linear Instability Drives the Initiation of Motion of Rational and Irrational Twin Interfaces

Twin boundaries play a central role in the functional behavior of martensitic materials, yet the mechanisms governing the initiation of their motion remain poorly understood for twins lying along irrational crystallographic directions. Here we present an atomistic investigation of the onset of motion of both rational and irrational twin interfaces in a two-dimensional model lattice with rectangular unit cells. Using quasistatic shear loading and full linear stability analysis, we show that the initiation of twin boundary motion is signaled by a nonlocal linear instability, marked by the vanishing of the lowest eigenvalue of the Hessian; the corresponding eigenmode predicts the atomic displacements that initiate motion. We find that irrational twin boundaries have significantly lower critical shear stress to initiate motion compared to rational twin boundaries. Further, we find that they display unusual mechanisms to initiate motion such as the formation of microtwins in directions orthogonal to the overall twin boundary. Finally, we compare various local measures against the nonlocal stability analysis, and find that the former do not capture that irrational twin boundaries initiate their motion at lower stresses compared to rational boundaries.

cond-mat.mtrl-sci↗

arXiv2026

Stress Asymmetry in Hard Magnetic Soft Materials

Hard magnetic soft materials -- soft polymers embedded with hard magnetic particles -- are modeled using continuum magnetomechanical formulations in which the deformation and the magnetization field are the primary kinematic variables. A recent question in such formulations is whether the Cauchy stress is symmetric, which is directly related to frame invariance and angular momentum balance. This note discusses energetically equivalent formulations, related by a change of variables between referential and current descriptions of the magnetization, and shows that they generally yield different Cauchy stresses, including a change in their symmetry. Specifically, the formulation based on a referential magnetization produces a symmetric Cauchy stress, while that based on a current magnetization generally yields an asymmetric Cauchy stress. We highlight that when the internal variable (magnetization field) is at the energy-minimizing equilibrium configuration, the divergences of these stresses are the same, and both stresses are symmetric.

cond-mat.mtrl-sci↗

arXiv2026

Aeroacoustic signatures reveal fast transient dynamics of vapor-jet-driven cavity oscillations in metallic additive manufacturing

Aeroacoustic emissions from intense evaporation are widely measured yet often treated as noisy byproducts and used mainly in empirical monitoring. Here, we show that airborne sound encodes physics-governed sub-millisecond fingerprints of vapor-jet dynamics in excessive vaporization, exemplified by vapor keyholes in laser metal processing. From first principles, we develop a vapor-jet-cavity oscillation framework and incorporate it into an aeroacoustic formulation, thereby coupling measured sound to transient cavity depth and oscillation frequency. Reconciled with synchronized multimodal in-situ data, airborne acoustics enable accurate tracking of vapor-cavity properties within tens to hundreds of microseconds. Combined with newly discovered correlations, cavity-jet-acoustic theory recasts the transition from steady, pore-free to pore-shedding vaporizations as a critical-frequency event. Aeroacoustic emissions thus become scalable, physics-guided, and cost-efficient probes of rapidly evolving liquid-vapor systems.

physics.app-ph↗

arXiv2026

A Kinetic Phase-Field Model of Diffusion Bonding: A Nonlocal Approach to Interface Coalescence

Conventional phase-field models often drive solid-solid interfaces to coalesce when in close proximity. This feature limits their use for processes like diffusion bonding, where the interfaces might need to remain distinct under certain thermodynamic conditions. We develop a kinetic phase-field model to address this problem, using an evolution equation based on a geometric conservation law for interfaces, rather than the gradient descent evolution that is typical in phase-field modeling. This formulation enables us to specify complex kinetic laws, and we use this to incorporate a physically-motivated geometric criterion to control interface merging. This criterion, based on nonlocal higher-derivative curvature invariants of the phase field, can be temperature-dependent, allows for a range of behaviors from complete coalescence to the preservation of distinct boundaries. Simulations show controlled bonding kinetics, demonstrating capabilities that are not available with existing methods for modeling interfaces that must remain distinct under given thermodynamic conditions.

cond-mat.mtrl-sci↗

arXiv2026

Two-Scale Analysis of the Electrostatics of Dielectric Crystals: Emergence of Polarization Density and Boundary Charges

Ionic crystals, such as solid electrolytes and complex oxides, are central to modern technologies for energy storage, sensing, actuation, and other functional applications. An important fundamental issue in the atomic and quantum-scale modeling of these materials is defining the macroscopic polarization. In a periodic crystal, the usual definition of the polarization as the first moment of the charge density in a unit cell is found to depend qualitatively - allowing even a change in the sign - and quantitatively on the choice of unit cell. We examine this issue using a rigorous approach based on the framework of 2-scale convergence. By examining the continuum limit of when the lattice spacing is much smaller than the characteristic dimensions of the body, we show that the 2-scale limit provides both a bulk polarization as well as a surface charge density supported on the boundary of the body. Further, different choices of the periodic unit cell of the body lead to correspondingly different partial unit cells at the boundary; these choices give to different bulk polarization and surface charges but compensate such that the electric field and energy are independent of the choice of unit cell.

cond-mat.mtrl-sci↗

arXiv2025

Emergent Electronic Flat Bands Through Dislocation Defect Phase Patterning: Effective One-Dimensional Model

Recent theoretical work has predicted that dislocation patterning induces anisotropic flat bands in the electronic band diagram, which can lead to unusual effects such as unconventional superconductivity. This work develops a reduced-dimensional framework to provide insights into their origin. An effective one-dimensional dislocation potential is constructed by averaging over the spatial distributions of dislocations along a singular direction. The resulting model introduces a parameter that quantifies the strain modulation, thereby providing a transparent approach to analyze the role of dislocation strain in leading to flat band formation.

cond-mat.str-el↗

arXiv2025

Nonlocal Electrostatics and Boundary Charges in Continuum Limits of Two-Dimensional Materials

Two-dimensional (2D) electronic materials are of significant technological interest due to their exceptional properties and broad applicability in engineering. The transition from nanoscale physics, that dictates their stable configurations, to macroscopic engineering applications requires the use of multiscale methods to systematically capture their electronic properties at larger scales. A key challenge in coarse-graining is the rapid and near-periodic variation of the charge density, which exhibits significant spatial oscillations at the atomic scale. Therefore, the polarization density field -- the first moment of the charge density over the periodic unit cell -- is used as a multiscale mediator that enables efficient coarse-graining by exploiting the almost-periodic nature of the variation. Unlike the highly oscillatory charge density, the polarization varies over lengthscales that are much larger than the atomic, making it suitable for continuum modeling. In this paper, we investigate the electrostatic potential arising from the charge distribution of 2D materials. Specifically, we consider a sequence of problems wherein the underlying lattice spacing vanishes and thus obtain the continuum limit. We consider 3 distinct limits: where the thickness is much smaller than, comparable to, and much larger than the in-plane lattice spacing. These limiting procedures provide the homogenized potential expressed in terms of the boundary charge and dipole distribution, subject to the appropriate boundary conditions that are also obtained through the limit process. Further, we demonstrate that despite the intrinsic non-uniqueness in the definition of polarization, accounting for the boundary charges ensures that the total electrostatic potential, the associated electric field, and the corresponding energy of the homogenized system are uniquely determined.

math.AP↗

arXiv2025

Dipolar Self-Interactions Drive Polymer Chain Collapse

We report that a dielectric polymer chain, constrained at both ends, sharply collapses when exposed to a high electric field. The chain collapse is driven by nonlocal dipolar interactions and anisotropic polarization of monomers, a characteristic of real polymers that prior theories were unable to incorporate. Once collapsed, a large number of chain monomers accumulate at the center location between the chain ends, locally increasing the electric field and polarization by orders of magnitude. The chain collapse is sensitive to the orientation of the applied electric field and chain stretch. Our findings not only offer new ways for rapid actuation and sensing but also provide a pathway to discover the critical physics behind instabilities and electrical breakdown in dielectric polymers.

cond-mat.soft↗

arXiv2025

Impact of gas/liquid phase change of CO$_2$ during injection for sequestration

CO$_2$ sequestration in deep saline formations is an effective and important process to control the rapid rise in CO$_2$ emissions. The process of injecting CO$_2$ requires reliable predictions of the stress in the formation and the fluid pressure distributions -- particularly since monitoring of the CO$_2$ migration is difficult -- to mitigate leakage, prevent induced seismicity, and analyze wellbore stability. A key aspect of CO$_2$ is the gas-liquid phase transition at the temperatures and pressures of relevance to leakage and sequestration, which has been recognized as being critical for accurate predictions but has been challenging to model without \textit{ad hoc} empiricisms. This paper presents a robust multiphase thermodynamics-based poromechanics model to capture the complex phase transition behavior of CO$_2$ and predict the stress and pressure distribution under super- and sub- critical conditions during the injection process. A finite element implementation of the model is applied to analyze the behavior of a multiphase porous system with CO$_2$ as it displaces the fluid brine phase. We find that if CO$_2$ undergoes a phase transition in the geologic reservoir, the spatial variation of the density is significantly affected, and the migration mobility of CO$_2$ decreases in the reservoir. A key feature of our approach is that we do not \textit{a priori} assume the location of the CO$_2$ gas/liquid interface -- or even if it occurs at all -- but rather, this is a prediction of the model, along with the spatial variation of the phase of CO$_2$ and the change of the saturation profile due to the phase change.

physics.geo-ph↗

arXiv2025

Soft Electromechanical Elastomers Impervious to Instability

Soft dielectric elastomers that can exhibit extremely large deformations under the action of an electric field enable applications such as soft robotics, biomedical devices, energy harvesting among others. A key impediment in the use of dielectric elastomers is failure through instability mechanisms or dielectric breakdown. In this work, using a group-theory based approach, we provide a closed-form solution to the bifurcation problem of a paradigmatical elastomer actuator and discover an interesting result: at a critical electric field, the elastomer becomes impervious to Treloar-Kearsley instability. This limit is reached prior to the typical dielectric breakdown threshold. Our results thus establish a regime of electrical and mechanical loads where the dielectric elastomer is invulnerable to all common failure modes.

cond-mat.soft↗

arXiv2025

Crack Face Contact Modeling is Essential to Predict Crack-Parallel Stresses

Phase-field fracture models provide a powerful approach to modeling fracture, potentially enabling the unguided prediction of crack growth in complex patterns. To ensure that only tensile stresses and not compressive stresses drive crack growth, several models have been proposed that aim to distinguish between compressive and tensile loads. However, these models have a critical shortcoming: they do not account for the crack direction, and hence they cannot distinguish between crack-normal tensile stresses that drive crack growth and crack-parallel stresses that do not. In this study, we apply a phase-field fracture model, developed in our earlier work, that uses the crack direction to distinguish crack-parallel stresses from crack-normal stresses. This provides a transparent energetic formulation that drives cracks to grow in when crack faces open or slide past each other, while the cracks respond like the intact solid when the crack faces contact under normal compressive loads. We compare our approach against two widely used approaches, Spectral splitting and the Volumetric-Deviatoric splitting, and find that these predict unphysical crack growth and unphysical stress concentrations under loading conditions in which these should not occur. Specifically, we show that the splitting models predict spurious crack growth and stress concentration under pure crack-parallel normal stresses. However, our formulation, which resolves the crack-parallel stresses from the crack-normal stresses, predicts these correctly.

cond-mat.mtrl-sci↗

arXiv2025

Dislocation Patterning as a Mechanism for Flat Band Formation

We compute the second-order correction to the electronic dispersion relation of a free electron gas interacting with an effective electron-dislocation potential, derived from a modern quantized theory of dislocations. Our results demonstrate that dislocation patterning induces anisotropic flat bands in the electronic dispersion under specific strain fields and directions, referred to as ``magic'' parameters. These flat bands acquire non-zero curvature as the strain or direction deviates from these magic parameters.

cond-mat.str-el↗

arXiv2025

The Roles of Size, Packing, and Cohesion in the Emergence of Force Chains in Granular Packings

This study investigates computationally the impact of particle size disparity and cohesion on force chain formation in granular media. The granular media considered in this study are bi-disperse systems under uniaxial compression, consisting of spherical, frictionless particles that interact through a modified Hookean model. Force chains in granular media are characterized as networks of particles that meet specific criteria for particle stress and inter-particle forces. The computational setup decouples the effects of particle packing on force chain formations, ensuring an independent assessment of particle size distribution and cohesion on force chain formation. The decoupling is achieved by characterizing particle packing through the radial density function, which enables the identification of systems with both regular and irregular packing. The fraction of particles in the force chains network is used to quantify the presence of the force chains. The findings show that particle size disparity promotes force chain formation in granular media with nearly-regular packing (i.e., an almost-ordered system). However, as particle size disparities grow, it promotes irregular packing (i.e., a disordered systems), leading to fewer force chains carrying larger loads than in ordered systems. Further, it is observed that the increased cohesion in granular systems leads to fewer force chains irrespective of particle size or packing.

cond-mat.soft↗

arXiv2025

Accretion and Ablation in Deformable Solids using an Eulerian Formulation: A Finite Deformation Numerical Method

Surface growth, i.e., the addition or removal of mass from the boundary of a solid body, occurs in a wide range of processes, including the growth of biological tissues, solidification and melting, and additive manufacturing. To understand nonlinear phenomena such as failure and morphological instabilities in these systems, accurate numerical models are required to study the interaction between mass addition and stress in complex geometrical and physical settings. Despite recent progress in the formulation of models of surface growth of deformable solids, current numerical approaches require several simplifying assumptions. This work formulates a method that couples an Eulerian surface growth description to a phase-field approach. It further develops a finite element implementation to solve the model numerically using a fixed computational domain with a fixed discretization. This approach bypasses the challenges that arise in a Lagrangian approach, such as having to construct a four-dimensional reference configuration, remeshing, and/or changing the computational domain over the course of the numerical solution. It also enables the modeling of several settings -- such as non-normal growth of biological tissues and stress-induced growth -- which can be challenging for available methods. The numerical approach is demonstrated on a model problem that shows non-normal growth, wherein growth occurs by the motion of the surface in a direction that is not parallel to the normal of the surface, that can occur in hard biological tissues such as nails, horns, etc. Next, a thermomechanical model is formulated and used to investigate the kinetics of freezing and melting in ice under complex stress states, particularly to capture regelation which is a key process in frost heave and basal slip in glaciers.

math.AP↗

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↗