arXiv subjects

Kaushik Dayal

Publications and source records attributed to Kaushik Dayal.

At least 55 records · Page 3Linked to original sources

arXiv2021

Energetic Formulation of Large-Deformation Poroelasticity

The modeling of coupled fluid transport and deformation in a porous medium is essential to predict the various geomechanical process such as CO2 sequestration, hydraulic fracturing, and so on. Current applications of interest, for instance, that include fracturing or damage of the solid phase, require a nonlinear description of the large deformations that can occur. This paper presents a variational energy-based continuum mechanics framework to model large-deformation poroelasticity. The approach begins from the total free energy density that is additively composed of the free energy of the components. A variational procedure then provides the balance of momentum, fluid transport balance, and pressure relations. A numerical approach based on finite elements is applied to analyze the behavior of saturated and unsaturated porous media using a nonlinear constitutive model for the solid skeleton. Examples studied include the Terzaghi and Mandel problems; a gas-liquid phase-changing fluid; multiple immiscible gases; and unsaturated systems where we model injection of fluid into soil. The proposed variational approach can potentially have advantages for numerical methods as well as for combining with data-driven models in a Bayesian framework.

math.AP↗

arXiv2021

Phase-Field Modeling and Peridynamics for Defect Dynamics, and an Augmented Phase-Field Model with Viscous Stresses

This work begins by applying peridynamics and phase-field modeling to predict 1-d interface motion with inertia in an elastic solid with a non-monotone stress-strain response. In classical nonlinear elasticity, it is known that subsonic interfaces require a kinetic law, in addition to momentum balance, to obtain unique solutions; in contrast, for supersonic interfaces, momentum balance alone is sufficient to provide unique solutions. This work finds that peridynamics agrees with this classical result, in that different choices of regularization parameters provide different kinetics for subsonic motion but the same kinetics for supersonic motion. In contrast, conventional phase-field models coupled to elastodynamics are unable to model, even qualitatively, the supersonic motion of interfaces. This work identifies the shortcomings in the physics of standard phase-field models to be: (1) the absence of higher-order stress to balance unphysical stress singularities, and (2) the ability of the model to access unphysical regions of the energy landscape. Based on these observations, this work proposes an augmented phase-field model to introduce the missing physics. The augmented model adds: (1) a viscous stress to the momentum balance, in addition to the dissipative phase-field evolution, to regularize singularities; and (2) an augmented driving force that models the physical mechanism that keeps the system out of unphysical regions of the energy landscape. When coupled to elastodynamics, the augmented model correctly describes both subsonic and supersonic interface motion. The augmented model has essentially the same computational expense as conventional phase-field models and requires only minor modifications of numerical methods, and is therefore proposed as a replacement to the conventional phase-field models.

math.AP↗

arXiv2021

Surface Growth in Deformable Solids using an Eulerian Formulation

Accretion and ablation, i.e. the addition and removal of mass at the surface, is important in a wide range of physical processes including solidification, growth of biological tissues, environmental processes, and additive manufacturing. The description of accretion requires the addition of new continuum particles to the body, and is therefore challenging for standard continuum formulations for solids that require a reference configuration. Recent work has proposed an Eulerian approach to this problem, enabling the side-stepping of the issue of constructing the reference configuration. However, this raises the complementary challenge of determining the stress response of the solid, which typically requires the deformation gradient that is not immediately available in the Eulerian formulation. To resolve this, the approach introduced the elastic deformation as an additional kinematic descriptor of the added material, and its evolution has been shown to be governed by a transport equation. In this work, the method of characteristics is applied to solve concrete simplified problems motivated by biomechanics and manufacturing. Specifically, (1) for a problem with both ablation and accretion in a fixed domain, and (2) for a problem with a time-varying domain, the closed-form solution is obtained in the Eulerian framework using the method of characteristics without explicit construction of the reference configuration.

math.AP↗

arXiv2021

Statistical mechanics of a dielectric polymer chain in the force ensemble

Constitutive modeling of dielectric elastomers has been of long standing interest in mechanics. Over the last two decades rigorous constitutive models have been developed that couple the electrical response of these polymers with large deformations characteristic of soft solids. A drawback of these models is that unlike classic models of rubber elasticity they do not consider the coupled electromechanical response of single polymer chains which must be treated using statistical mechanics. The objective of this paper is to compute the stretch and polarization of single polymer chains subject to a fixed force and fixed electric field using statistical mechanics. We assume that the dipoles induced by the applied electric field at each link do not interact with each other and compute the partition function using standard techniques. We then calculate the stretch and polarization by taking appropriate derivatives of the partition function and obtain analytical results in various limits. We also perform Markov chain Monte Carlo simulations using the Metropolis and umbrella sampling methods, as well as develop a new sampling method which improves convergence by exploiting a symmetry inherent in dielectric polymer chains. The analytical expressions are shown to agree with the Monte Carlo results over a range of forces and electric fields. Our results complement recent work on the statistical mechanics of electro-responsive chains which obtains analytical expressions in a different ensemble.

cond-mat.soft↗

arXiv2021

Surface Growth in Deformable Solids using an Eulerian Formulation

Growth occurs in a wide range of systems ranging from biological tissue to additive manufacturing. This work considers surface growth, in which mass is added to the boundary of a continuum body from the ambient medium or from within the body. In contrast to bulk growth in the interior, the description of surface growth requires the addition of new continuum particles to the body. This is challenging for standard continuum formulations for solids that are meant for situations with a fixed amount of material. Recent approaches to handle this have used time-evolving reference configurations. In this work, an Eulerian approach to this problem is formulated, enabling the side-stepping of the issue of constructing the reference configuration. However, this raises the complementary challenge of determining the stress response of the solid, which typically requires the deformation gradient that is not immediately available in the Eulerian formulation. To resolve this, the approach introduces additional kinematic descriptors, namely the relaxed zero-stress deformation and the elastic deformation; in contrast to the deformation gradient, these have the important advantage that they are not required to satisfy kinematic compatibility. The resulting model has only the density, velocity, and elastic deformation as variables in the Eulerian setting. The introduction in this formulation of the relaxed deformation and the elastic deformation provides a description of surface growth whereby the added material can bring in its own kinematic information. Loosely, the added material "brings in its own reference configuration" through the specification of the relaxed deformation and the elastic deformation of the added material. This kinematic description enables, e.g., modeling of non-normal growth using a standard normal growth velocity and a simple approach to prescribing boundary conditions.

math.AP↗

arXiv2021

Nonlinear Statistical Mechanics Drives Intrinsic Electrostriction and Volumetric Torque in Polymer Networks

Statistical mechanics is an important tool for understanding polymer electroelasticity because the elasticity of polymers is primarily due to entropy. However, a common approach for the statistical mechanics of polymer chains, the Gaussian chain approximation, misses key physics. By considering the nonlinearities of the problem, we show a strong coupling between the deformation of a polymer chain and its dielectric response; that is, its net dipole. When chains with this coupling are cross-linked in an elastomer network and an electric field is applied, the field breaks the symmetry of the elastomer's elastic properties, and, combined with electrostatic torque and incompressibility, leads to intrinsic electrostriction. Conversely, deformation can break the symmetry of the dielectric response leading to volumetric torque (i.e., a couple stress or torque per unit volume) and asymmetric actuation. Both phenomena have important implications for designing high-efficiency soft actuators and soft electroactive materials; and the presence of mechanisms for volumetric torque, in particular, can be used to develop higher degree of freedom actuators and to achieve bioinspired locomotion.

cond-mat.soft↗

arXiv2020

The interplay between symmetry-breaking and symmetry-preserving bifurcations in soft dielectric films and the emergence of giant electro-actuation

Soft elastomers that can exhibit extremely large deformations under the action of an electric field are essential for applications such as soft robotics, stretchable and flexible electronics, energy harvesting among others. The critical limiting factor in conventional electro-actuation of such materials is the occurrence of the so-called pull-in instability. In this work, we demonstrate an extraordinarily simple way to coax a dielectric thin film towards a symmetry-breaking pitchfork bifurcation state while avoiding pull-in instability. Through the nonlinear interplay between the two bifurcation modes, we predict electro-actuation strains that exceed what is conventionally possible by 200$\%$, and at significantly lower applied electric fields.

cond-mat.soft↗

arXiv2020

Architected Elastomer Networks for Optimal Electromechanical Response

Dielectric elastomers (DEs) that couple deformation and electrostatics have the potential for use in soft sensors and actuators with applications ranging from robotic, biomedical, energy, aerospace and automotive technologies. However, currently available DEs are limited by weak electromechanical coupling and require large electric fields for significant actuation. In this work, a statistical mechanics-based model of DE chains is applied to elucidate the role of a polymer network architecture in the performance of the bulk material. Given a polymer network composed of chains that are cross-linked, the paper examines the role of cross-link density, orientational density of chains, and other network parameters in determining the material properties of interest including elastic modulus, electrical susceptibility, and the electromechanical coupling. From this analysis, a practical strategy is presented to increase the deformation and usable work derived from (anisotropic) dielectric elastomer actuators by as much as $75-100\%$.

cond-mat.soft↗

arXiv2020

Symmetry-Adapted Tight-Binding Electronic Structure Analysis of Carbon Nanotubes with Defects, Kinks, Twist, and Stretch

This paper applies a symmetry-adapted method to examine the influence of deformation and defects on the electronic structure and band structure in carbon nanotubes. First, the symmetry-adapted approach is used to develop the analog of Bloch waves. Building on this, the technique of perfectly-matched layers is applied to develop a method to truncate the computational domain of electronic structure calculations without spurious size effects. This provides an efficient and accurate numerical approach to compute the electronic structure and electromechanics of defects in nanotubes. The computational method is applied to study the effect of twist, stretch, and bending, with and without various types of defects, on the band structure of nanotubes. Specifically, the effect of stretch and twist on band structure in defect-free conducting and semiconducting nanotubes is examined, and the interaction with vacancy defects is elucidated. Next, the effect of localized bending or kinking on the electronic structure is studied. Finally, the paper examines the effect of 5-8-5 Stone-Wales defects. In all of these settings, the perfectly-matched layer method enables the calculation of localized non-propagating defect modes with energies in the bandgap of the defect-free nanotube.

cond-mat.mes-hall↗

arXiv2020

Statistical Mechanical Analysis of the Electromechanical Coupling in an Electrically-Responsive Polymer Chain

Polymeric materials that couple deformation and electrostatics have the potential for use in soft sensors and actuators with potential applications ranging from robotic, biomedical, energy, aerospace and automotive technologies. In contrast to the mechanics of polymers that has been studied using statistical mechanics approaches for decades, the coupled response under deformation and electrical field has largely been modeled only phenomenologically at the continuum scale. In this work, we examine the physics of the coupled deformation and electrical response of an electrically-responsive polymer chain using statistical mechanics. We begin with a simple anisotropic model for the electrostatic dipole response to electric field of a single monomer, and use a separation of energy scales between the electrostatic field energy and the induced dipole field energy to reduce the nonlocal and infinite-dimensional statistical averaging to a simpler local finite-dimensional averaging. In this simplified setting, we derive the equations of the most likely monomer orientation density using the maximum term approximation, and a chain free energy is derived using this approximation. These equations are investigated numerically and the results provide insight into the physics of electro-mechanically coupled elastomer chains. Closed-form approximations are also developed in the limit of small electrical energy with respect to thermal energy; in the limit of small mechanical tension force acting on the chain; and using asymptotic matching for general chain conditions.

cond-mat.soft↗

arXiv2020

Effective Response of Heterogeneous Materials using the Recursive Projection Method

This paper applies the Recursive Projection Method (RPM) to the problem of finding the effective mechanical response of a periodic heterogeneous solid. Previous works apply the Fast Fourier Transform (FFT) in combination with various fixed-point methods to solve the problem on the periodic unit cell. These have proven extremely powerful in a range of problems ranging from image-based modeling to dislocation plasticity. However, the fixed-point iterations can converge very slowly, or not at all, if the elastic properties have high contrast, such as in the case of voids. The paper examines the reasons for slow, or lack of convergence, in terms of a variational perspective. In particular, when the material contains regions with zero or very small stiffness, there is lack of uniqueness, and the energy landscape has flat or shallow directions. Therefore, in this work, the fixed-point iteration is replaced by the RPM iteration. The RPM uses the fixed-point iteration to adaptively identify the subspace on which fixed-point iterations are unstable, and performs Newton iterations only on the unstable subspace, while fixed-point iterations are performed on the complementary stable subspace. This combination of efficient fixed-point iterations where possible, and expensive but well-convergent Newton iterations where required, is shown to lead to robust and efficient convergence of the method. In particular, RPM-FFT converges well for a wide range of choices of the reference medium, while usual fixed-point iterations are usually sensitive to this choice.

cs.CE↗

arXiv2019

A 3D phase field dislocation dynamics model for body-centered cubic crystals

In this work, we present a 3D Phase Field Dislocation Dynamics (PFDD) model for body-centered cubic (BCC) metals. The model formulation is extended to account for the dependence of the Peierls barrier on the line-character of the dislocation. Simulations of the expansion of a dislocation loop belonging to the $\left\{110\right\} \left<111\right>$ slip system are presented with direct comparison to Molecular Statics (MS) simulations. The extended PFDD model is able to capture the salient features of dislocation loop expansion predicted by MS simulations. The model is also applied to simulate the motion of a straight screw dislocation through kink-pair motion.

cond-mat.mtrl-sci↗

arXiv2016

Coherent motion of monolayer sheets under confinement and its pathological implications

Coherent angular rotation of epithelial cells is thought to contribute to many vital physiological processes including tissue morphogenesis and glandular formation. However, factors regulating this motion, and the implications of this motion if perturbed remain incompletely understood. In the current study, we address these questions using a cell-center based model in which cells are polarized, motile, and interact with the neighboring cells via harmonic forces. We demonstrate that, a simple evolution rule in which the polarization of any cell tends to orient with its velocity vector can induce coherent motion in geometrically confined environments. In addition to recapitulating coherent rotational motion observed in experiments, our results also show the presence of radial movements and tissue behavior that can vary between solid-like and fluid-like. We show that the pattern of coherent motion is dictated by the combination of different physical parameters including number density, cell motility, system size, bulk cell stiffness and stiffness of cell-cell adhesions. We further observe that, perturbations in the form of cell division can induce a reversal in the direction of motion when cell division occurs synchronously. Moreover, when the confinement is removed, we see that the existing coherent motion leads to cell scattering, with bulk cell stiffness and stiffness of cell-cell contacts dictating the invasion pattern. In summary, our study provides an in-depth understanding of the origin of coherent rotation in confined tissues, and extracts useful insights into the influence of various physical parameters on the pattern of such movements

q-bio.CB↗

arXiv2014

A Dynamic Multiscale Phase-field Model for Structural Transformations and Twinning: Regularized Interfaces with Transparent Prescription of Complex Kinetics and Nucleation

The motion of microstructural interfaces is important in modeling materials that undergo twinning and structural phase transformations. Continuum models fall into two classes: sharp-interface models, where interfaces are singular surfaces; and regularized-interface models, such as phase-field models, where interfaces are smeared out. The former are challenging for numerical solutions because the interfaces need to be explicitly tracked, but have the advantage that the kinetics of existing interfaces and the nucleation of new interfaces can be transparently and precisely prescribed. In contrast, phase-field models do not require explicit tracking of interfaces, thereby enabling relatively simple numerical calculations, but the specification of kinetics and nucleation is both restrictive and extremely opaque. This prevents straightforward calibration of phase-field models to experiment and/or molecular simulations, and breaks the multiscale hierarchy of passing information from atomic to continuum. We present the formulation of a phase-field model -- i.e., a model with regularized interfaces that do not require explicit numerical tracking -- that allows for easy and transparent prescription of complex interface kinetics and nucleation. The key ingredients are a re-parametrization of the energy density to clearly separate nucleation from kinetics; and an evolution law that comes from a conservation statement for interfaces. This enables clear prescription of nucleation through the source term of the conservation law and of kinetics through an interfacial velocity field. A formal limit of the kinetic driving force recovers the classical continuum sharp-interface driving force, providing confidence in both the re-parametrized energy and the evolution statement. We present a number of numerical calculations in one and two dimensions to characterize and demonstrate the formulation.

cond-mat.mtrl-sci↗

arXiv2013

Atomistic-to-Continuum Multiscale Modeling with Long-Range Electrostatic Interactions in Ionic Solids

We present a multiscale atomistic-to-continuum method for ionic crystals with defects. Defects often play a central role in ionic and electronic solids, not only to limit reliability, but more importantly to enable the functionalities that make these materials of critical importance. Examples include solid electrolytes that conduct current through the motion of charged point defects, and complex oxide ferroelectrics that display multifunctionality through the motion of domain wall defects. Therefore, it is important to understand the structure of defects and their response to electrical and mechanical fields. A central hurdle, however, is that interactions in ionic solids include both short-range atomic interactions as well as long-range electrostatic interactions. Existing atomistic-to-continuum multi-scale methods, such as the Quasicontinuum method, are applicable only when the atomic interactions are short-range. In addition, empirical reductions of quantum mechanics to density functional models are unable to capture key phenomena of interest in these materials. To address this open problem, we develop a multiscale atomistic method to coarse-grain the long-range electrical interactions in ionic crystals with defects. In these settings, the charge density is rapidly varying, but in an almost-periodic manner. The key idea is to use the polarization density field as a multiscale mediator that enables efficient coarse-graining by exploiting the almost-periodic nature of the variation. In regions far from the defect, where the crystal is close-to-perfect, the polarization field serves as a proxy that enables us to avoid accounting for the details of the charge variation. We combine this approach for long-range electrostatics with the standard Quasicontinuum method for short-range interactions to achieve an efficient multiscale atomistic-to-continuum method.

cond-mat.mes-hall↗

arXiv2013

Anomalous phonon behavior of carbon nanotubes: First-order influence of external load

External loads typically have a indirect influence on phonon curves, i.e., they influence the phonon curves by changing the state about which linearization is performed. In this paper, we show that in nanotubes, the axial load has a direct first-order influence on the long-wavelength behavior of the transverse acoustic (TA) mode. In particular, when the tube is force-free the TA mode frequencies vary quadratically with wave number and have curvature (second derivative) proportional to the square-root of the nanotube's bending stiffness. When the tube has non-zero external force, the TA mode frequencies vary linearly with wave number and have slope proportional to the square-root of the axial force. Therefore, the TA phonon curves -- and associated transport properties -- are not material properties but rather can be directly tuned by external loads. In addition, we show that the out-of-plane shear deformation does {\em not} contribute to this mode and the unusual properties of the TA mode are exclusively due to bending. Our calculations consist of 3 parts: first, we use a linear chain of atoms as an illustrative example that can be solved in close-form; second, we use our recently-developed symmetry-adapted phonon analysis method to present direct numerical evidence; and finally, we present a simple mechanical model that captures the essential physics of the geometric nonlinearity in slender nanotubes that couples the axial load directly to the phonon curves. We also compute the Density of States and show the significant effect of the external load.

cond-mat.mtrl-sci↗

arXiv2012

A fundamental improvement to Ericksen-Leslie kinematics

We demonstrate theory and computations for finite-energy line defect solutions in an improvement of Ericksen-Leslie liquid crystal theory. Planar director fields are considered in two and three space dimensions, and we demonstrate straight as well as loop disclination solutions. The possibility of static balance of forces in the presence of a disclination and in the absence of flow and body forces is discussed. The work exploits an implicit conceptual connection between the Weingarten-Volterra characterization of possible jumps in certain potential fields and the Stokes-Helmholtz resolution of vector fields. The theoretical basis of our work is compared and contrasted with the theory of Volterra disclinations in elasticity. Physical reasoning precluding a gauge-invariant structure for the model is also presented.

cond-mat.soft↗

arXiv2012

Symmetry-Adapted Phonon Analysis of Nanotubes

The characteristics of phonons, i.e. linearized normal modes of vibration, provide important insights into many aspects of crystals, e.g. stability and thermodynamics. In this paper, we use the Objective Structures framework to make concrete analogies between crystalline phonons and normal modes of vibration in non-crystalline but highly symmetric nanostructures. Our strategy is to use an intermediate linear transformation from real-space to an intermediate space in which the Hessian matrix of second derivatives is block-circulant. The block-circulant nature of the Hessian enables us to then follow the procedure to obtain phonons in crystals: namely, we use the Discrete Fourier Transform from this intermediate space to obtain a block-diagonal matrix that is readily diagonalizable. We formulate this for general Objective Structures and then apply it to study carbon nanotubes of various chiralities that are subjected to axial elongation and torsional deformation. We compare the phonon spectra computed in the Objective Framework with spectra computed for armchair and zigzag nanotubes. We also demonstrate the approach by computing the Density of States. In addition to the computational efficiency afforded by Objective Structures in providing the transformations to almost-diagonalize the Hessian, the framework provides an important conceptual simplification to interpret the phonon curves.

cond-mat.mtrl-sci↗