arXiv subjects

Mrityunjay Kothari

Publications and source records attributed to Mrityunjay Kothari.

11 recordsLinked to original sources

arXiv2026

Energetics of Nucleation in Finitely Deformed, Phase-Transforming Soft Solids

Classical nucleation theory describes the rate at which stable nuclei form within a metastable parent phase by crossing a free-energy barrier set by competing bulk and interfacial energies. In an elastic material, a pre-existing stress state modifies this barrier through an elastic contribution to the bulk driving force. This contribution is well characterized for linear elastic materials, but the corresponding finite-deformation result for soft solids remains less developed. The gap is computationally significant: in simulations that sample candidate nuclei throughout a stressed body, direct evaluation of the elastic contribution to free-energy change would require solving a new nonlinear elasticity boundary-value problem for each possible nucleus. Here, we derive an asymptotic expansion of the equilibrium elastic potential energy change for a hyperelastic body before and after formation of a small transformed region. The expansion is with respect to the amplitude of an isotropic transformation strain, while the pre-existing deformation and stress may be finite. At leading order, the elastic contribution to the formation energy is determined entirely by the known untransformed equilibrium fields, with additional terms accounting for stiffness contrast between the parent and transformed phases. Incorporating this into classical nucleation theory yields the stress-shifted transformation temperature, critical radius, and nucleation barrier. Representative results are shown for a compressible neo-Hookean solid under hydrostatic, uniaxial, and equibiaxial loading; tensile stresses promote nucleation and compressive stresses suppress it when transformation strain is expansive. Comparison with the corresponding linear-elastic result shows that finite-deformation effects can substantially change the predicted energy barrier at moderate stretches.

cond-mat.soft↗

arXiv2026

The effect of interactions on elastic cavitation

Cavitation refers to the sudden, unstable expansion of a defect or cavity within a material in response to applied loads, when the loads reach a critical threshold. It is widely recognized as a common failure nucleation mechanism in soft and biological materials. For an isolated cavity in the bulk of an incompressible neo-Hookean solid loaded by remote hydrostatic tension, the classical cavitation pressure is well established as $2.5 μ$, where $μ$ is the shear modulus. However, in realistic settings the cavitation threshold is influenced by interaction of the cavity with nearby interfaces and other cavities. Interface interaction effects are particularly relevant in multi-material systems and additively manufactured structures, where defects frequently occur near material boundaries. Meanwhile, cavity-cavity interactions become important in materials exhibiting finite porosity, such as foams, porous solids, and phase-separating polymers. Here, we characterize the effect of interactions on cavitation pressure for (i) a nearby rigid interface and (ii) a neighboring identical cavity. For cavities near a rigid interface, our analysis shows that the cavitation pressure increases as the initial cavity-interface distance decreases, starting from the bulk value for a distant cavity and approaching the cavitation pressure value for a defect situated at an interface ($\approx3.5μ$) as the cavity approaches the interface boundary. In contrast, interacting cavities exhibit a non-monotonic dependence of the cavitation pressure on the initial inter-cavity distance $d$: the threshold approaches the bulk value of $2.5μ$ for distant cavities and reaches a maximum of $\sim2.67μ$ at $d\sim3.8R$, where $R$ is the initial cavity radius.

cond-mat.soft↗

arXiv2025

A thermo-mechanically coupled finite deformation model for freezing-induced damage in soft materials

In the U.S., approximately 17 patients die each day awaiting an organ transplant, a crisis driven by the inability to store organs long-term via methods like cryopreservation. A primary failure mechanism is the severe thermo-mechanical damage tissues experience during freezing. A predictive understanding of this damage is hindered by the complex interplay between heat transfer, phase change, and large deformation mechanics. Motivated by this fundamental problem, we present a fully coupled, thermo-mechanical phase-field framework for modeling damage evolution in fluid-saturated soft materials under cryogenic conditions. The theoretical framework integrates heat transfer with solid-liquid phase transition, finite deformation nonlinear elasticity, and progressive mechanical damage. The governing equations are solved using \texttt{FEniCS} finite element package. The presentation will detail the theoretical framework and showcase representative simulations that capture the spatiotemporal evolution of temperature, freezing phase field, stress, and damage fields during representative freezing protocols. The developed framework serves as a powerful tool for understanding the fundamental mechanisms of freezing-induced injury and for designing improved cryopreservation strategies.

cond-mat.soft↗

arXiv2025

Push and Pull: Elastic Interaction Between Pressurized Spherical Cavities in Nonlinear Elastic Media

Elastic interaction of pressurized spherical cavities embedded in a three-dimensional hyperelastic medium is computationally analyzed. Using finite element analysis across several positive and negative pressure scenarios, we calculate the system's potential energy and configurational driving force for neo-Hookean, Mooney-Rivlin, and Arruda-Boyce material models. Our results show that while the interaction is always attractive for negative pressures, a non-monotonic energy landscape emerges for positive pressures above a critical value. In this regime, cavities attract at close range and repel when further apart. The critical separation distance for this transition is shown to be dependent on the material's strain-stiffening parameters. These findings are consolidated into phase diagrams, providing a clear map of interaction behaviors.

cond-mat.soft↗

arXiv2025

Elastic Interaction of Pressurized Cavities in Hyperelastic Media: Attraction and Repulsion

This study computationally investigates the elastic interaction of two pressurized cylindrical cavities in a 2D hyperelastic medium. Unlike linear elasticity, where interactions are exclusively attractive, nonlinear material models (neo-Hookean, Mooney-Rivlin, Arruda-Boyce) exhibit both attraction and repulsion between the cavities. A critical pressure-shear modulus ratio governs the transition, offering a pathway to manipulate cavity configurations through material and loading parameters. At low ratios, the interactions are always attractive; at higher ratios, both attractive and repulsive regimes exist depending on the separation between the cavities. Effect of strain stiffening on these interactions are also analyzed. These insights bridge theoretical and applied mechanics, with implications for soft material design and subsurface engineering.

cond-mat.soft↗

arXiv2023

On Hyperelastic Crease

We present analyses of crease-formation and stability criteria for incompressible hyperelastic solids. A generic singular perturbation over a laterally compressed half-space creates a far-field eigenmode of three energy-release angular sectors separated by two energy-elevating sectors of incremental deformation. The far-field eigenmode braces the energy-release field of the surface flaw against the transition to a self-similar crease field, and the braced-incremental-deformation (bid) field has a unique shape factor that determines the creasing stability. The shape factor, which is identified by two conservation integrals that represent a subsurface dislocation in the tangential manifold, is a monotonically increasing function of compressive strain. For Neo-Hookean material, when the shape factor is below unity, the bid field is configurationally stable. When the compressive strain is 0.356, the shape factor becomes unity, and the bid field undergoes a higher-order transition to a crease field. At the crease-limit point, we have two asymptotic solutions of the crease-tip folding field and the leading-order far field with two scaling parameters, the ratio of which is determined by matched asymptotes. Our analyses show that the surface is stable against singular perturbation up to the crease limit point and becomes unstable beyond the limit. However, the flat state is metastable against a regular perturbation between the crease limit point and wrinkle critical point, which is a first-order instability point. We introduced a novel finite element method for simulating the bid field with a finite domain size. For Gent model, the strain-stiffening alters the shape factor dependence on the compressive strain, raising crease resistance. The new findings in crease mechanisms will help study ruga mechanics of self-organization and design soft-material structures for high crease resistance.

physics.app-ph↗

arXiv2022

The crucial role of elasticity in regulating liquid-liquid phase separation in cells

Liquid-liquid phase separation has emerged as a fundamental mechanism underlying intracellular organization, with evidence for it being reported in numerous different systems. However, there is a growing concern regarding the lack of quantitative rigor in the techniques employed to study phase separation, and their ability to account for the complex nature of the cellular milieu, which affects key experimentally observable measures, such as the shape, size and transport dynamics of liquid droplets. Here we bridge this gap by combining recent experimental data with theoretical predictions that capture the subtleties of nonlinear elasticity and fluid transport. We show that within a biologically accessible range of material parameters, phase separation is highly sensitive to elastic properties and can thus be used as a mechanical switch to rapidly transition between different states in cellular systems. Furthermore, we show that this active mechanically mediated mechanism can drive transport across cells at biologically relevant timescales and could play a crucial role in promoting spatial localization of condensates; whether cells exploit such mechanisms for transport of their constituents, remains an open question.

cond-mat.soft↗

arXiv2022

Biofilms as self-shaping growing nematics

Active nematics are the nonequilibrium analog of passive liquid crystals in which anisotropic units consume free energy to drive emergent behavior. Similar to liquid crystal (LC) molecules in displays, ordering and dynamics in active nematics are sensitive to boundary conditions; however, unlike passive liquid crystals, active nematics, such as those composed of living matter, have the potential to regulate their boundaries through self-generated stresses. Here, using bacterial biofilms confined by a hydrogel as a model system, we show how a three-dimensional, living nematic can actively shape itself and its boundary in order to regulate its internal architecture through growth-induced stresses. We show that biofilms exhibit a sharp transition in shape from domes to lenses upon changing environmental stiffness or cell-substrate friction, which is explained by a theoretical model considering the competition between confinement and interfacial forces. The growth mode defines the progression of the boundary, which in turn determines the trajectories and spatial distribution of cell lineages. We further demonstrate that the evolving boundary defines the orientational ordering of cells and the emergence of topological defects in the interior of the biofilm. Our findings reveal novel self-organization phenomena in confined active matter and provide strategies for guiding the development of programmed microbial consortia with emergent material properties.

q-bio.QM↗

arXiv2021

Nonlinear Inclusion Theory with Application to the Growth and Morphogenesis of a Confined Body

One of the most celebrated contributions to the study of the mechanical behavior of materials is due to J.D. Eshelby, who in the late 50s revolutionized our understanding of the elastic stress and strain fields due to an ellipsoidal inclusion/inhomogeneity that undergoes a transformation of shape and size. While Eshelby's work laid the foundation for significant advancements in various fields, including fracture mechanics, theory of phase transitions, and homogenization methods, its extension into the range of large deformations, and to situations in which the material can actively reorganize in response to the finite transformation strain, is in a nascent state. Beyond the theoretical difficulties imposed by highly nonlinear material response, a major hindrance has been the absence of experimental observations that can elucidate the intricacies that arise in this regime. To address this limitation, our experimental observations reveal the key morphogenesis steps of Vibrio cholerae biofilms embedded in hydrogels, as they grow by four orders of magnitude from their initial size. Using the biofilm growth as a case study, our theoretical model considers various growth scenarios and employs two different and complimentary methods -- a minimal analytical model and finite element computations -- to obtain approximate equilibrium solutions. A particular emphasis is put on determining the natural growth path of an inclusion that optimizes its shape in response to the confinement, and the onset of damage in the matrix, which together explain the observed behavior of biofilms. Beyond bacterial biofilms, this work sheds light on the role of mechanics in determining the morphogenesis pathways of confined growing bodies and thus applies to a broad range of phenomena that are ubiquitous in both natural and engineered material systems.

cond-mat.soft↗

arXiv2020

Controlled Propagation and Jamming of a Delamination Front

We study the birth and propagation of a delamination front in the peeling of a soft, weakly adhesive layer. In a controlled-displacement setting, the layer partially detaches via a subcritical instability and the motion continues until arrested, by jamming of the two lobes. Using numerical solutions and scaling analysis, we quantitatively describe the equilibrium shapes and obtain constitutive sensitivities of jamming process to material and interface properties. We conclude with a way to delay or avoid jamming altogether by tunable interface properties.

cond-mat.soft↗

arXiv2020

Effect of Elasticity on Phase Separation in Heterogeneous Systems

A recent study has demonstrated that phase separation in binary liquid mixtures is arrested in the presence of elastic networks and can lead to a nearly uniformly-sized distribution of the dilute-phase droplets. At longer timescales, these droplets exhibit a directional preference to migrate along elastic property gradients to form a front of dissolving droplets [K. A. Rosowski, T. Sai, E. Vidal-Henriquez, D. Zwicker, R. W. Style, E. R. Dufresne, Elastic ripening and inhibition of liquid-liquid phase separation, Nature Physics (2020) 1-4]. In this work, we develop a complete theoretical understanding of this phenomenon in nonlinear elastic solids by employing an energy-based approach that captures the process at both short and long timescales to determine the constitutive sensitivities and the dynamics of the resulting front propagation. We quantify the thermodynamic driving forces to identify diffusion-limited and dissolution-limited regimes in front propagation. We show that changes in elastic properties have a nonlinear effect on the process. This strong influence can have implications in a variety of material systems including food, metals, and aquatic sediments, and further substantiates the hypothesis that biological systems exploit such mechanisms to regulate important function.

cond-mat.soft↗