Multiphysics Mechanics of Materials Group
Overview of Research Projects
The effect of interactions on elastic cavitation
We characterize how proximity to interfaces and neighboring defects alters the critical pressure required for unstable cavity expansion in soft materials. While the classical cavitation threshold for an isolated defect in a neo-Hookean solid is well-established, we demonstrate that a nearby rigid interface monotonically increases this threshold by up to 40% as the spacing decreases. Conversely, we find that interactions between two identical neighboring cavities result in a non-monotonic relationship, where the cavitation pressure reaches a distinct maximum at a specific intermediate separation distance. By providing these first quantitative estimates for multi-defect and boundary interactions, our work offers new insights relevant for predicting failure nucleation in porous elastomers, biological tissues, and additively manufactured soft structures.
[MAR 2026] Checkout our preprint: arXiv
A visual depiction of two-cavity expansion under remote hydrostatic tension.
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 the FEniCS finite element package. This paper details the theoretical framework and showcases 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.
In our paper, A thermo-mechanically coupled finite-deformation model for freezing-induced damage in soft materials, we present a fully coupled, thermodynamically consistent framework designed to predict the structural failure of fluid-saturated soft tissues during cryopreservation. By integrating two phase-field models—one for the freezing process and another for mechanical damage—into a finite-deformation nonlinear elastic formulation, we are able to capture the complex interplay between heat transfer, solid-liquid phase transitions, and large-scale mechanical deformation. Our simulations demonstrate how differential thermal expansion and phase-change-induced volumetric shifts generate severe internal stresses that lead to irreversible tissue injury and fracture. This work serves as a predictive tool to help bridge the mechanistic gaps in organ banking, providing a foundation for designing optimized cooling and thawing protocols that minimize mechanical damage and improve the viability of preserved biological systems.
[FEB 2026] Checkout our Journal of the Mechanics and Physics of Solids paper here: Saeedi, A., Devireddy, R. and Kothari, M., 2026. A thermo-mechanically coupled finite-deformation model for freezing-induced damage in soft materials. Journal of the Mechanics and Physics of Solids, p.106545.
Catastrophic effects of freezing tissues.
A kidney-like geometry undergoing freezing. Damage tends to accumulate faster at the most curved region. T = 1 is the melting point. Phi is the freezing phase field with 0 being ice and 1 being water. d is the damage phase field.
A square annulus geometry undergoing freezing and thawing. T = 1 is the melting point. Phi is the freezing phase field with 0 being ice and 1 being water. d is the damage phase field.
Push and Pull: Elastic Interaction Between Pressurized Spherical Cavities in Nonlinear Elastic Media
We carried out a computational analysis of the elastic interaction between two pressurized spherical cavities within a nonlinear hyperelastic medium, using neo-Hookean, Mooney–Rivlin, and Arruda–Boyce material models. While classical linear elasticity suggests these cavities always attract one another, we found that nonlinear material behavior introduces a "push and pull" phenomenon at higher positive pressures (P >= shear modulus). In this regime, the system exhibits a nonmonotonic energy landscape where cavities attract at close range but repel once they exceed a critical separation distance. We further concluded that this transition is highly sensitive to the material’s strain-stiffening parameters and that the repulsive behavior is unique to positive (expansive) pressures, as negative (contractile) pressures result in purely attractive interactions. These insights are essential for understanding defect interactions and driving forces in soft solids, such as biological tissues and elastic networks.
[DEC 2025] Checkout our Journal of Applied Mechanics paper here: Saeedi, A. and Kothari, M., 2025. Push and Pull: Elastic Interaction Between Pressurized Spherical Cavities in Nonlinear Elastic Media. Journal of Applied Mechanics, 92(12), p.121010.
Center-to-center distance between cavities is 2.2 times the radius of the undeformed cavity
Elastic Interaction of Pressurized Cavities in Hyperelastic Media: Attraction and Repulsion
We investigated the elastic interactions between two pressurized cylindrical cavities embedded in a 2D hyperelastic medium using computational analysis. We found that unlike the consistent attraction observed in linear elastic materials, nonlinear material behaviors modeled through neo-Hookean, Mooney-Rivlin, and Arruda-Boyce constitutive laws reveal both attractive and repulsive interactions, governed by a critical pressure-to-shear modulus ratio. At low ratios, interactions remain attractive; at higher ratios, the interaction shows both attractive and repulsive regimes depending on separation between the cavities. Strain stiffening, particularly pronounced in the Arruda-Boyce model, influences these transitions. These findings are especially relevant for soft materials, with potential applications in poroelasticity, cavitation, and phase separation.
Checkout our Journal of Applied Mechanics paper here:
Saeedi, A. and Kothari, M., 2025. Elastic Interaction of Pressurized Cavities in Hyperelastic Media: Attraction and Repulsion. Journal of Applied Mechanics, 92(5), p.051008.
Center-to-center distance between cavities is 2.2 times the radius of the undeformed cavity
Center-to-center distance between cavities is 6 times the radius of the undeformed cavity
Elastic Effects in Liquid-Liquid Phase Separation
Physical systems consisting of an elastic matrix permeated by fluid mixture are ubiquitous, with examples ranging from morphogenesis of a single biological cell to the migration of greenhouse gases in sediments. Recent experimental studies show that the presence of the elastic networks in these systems significantly alters their phase-separation response by imposing an energetic cost to the growth of droplets. However, a quantitative understanding of the role played by elasticity is lacking. Our paper bridges this gap by building a comprehensive theoretical framework to analyze the effect of elasticity on the phase separation of a binary mixture in soft, nonlinear solids.
We employ an energy-based approach that captures both the short-time quasi-equilibrium and the long-time evolution of the phase separation, in elastically homogeneous as well as heterogeneous materials, to determine the constitutive sensitivities. At the short timescale, we find that elasticity arrests phase separation and leads to droplets of characteristic size (determined by the stiffness).
Short Timescale : elasticity arrests phase separation leading to mono-disperse droplets
At the longer timescale, our theory predicts a droplet dissolution front in heterogeneous materials. Crucially, we also find a nonlinear effect of elasticity on the dynamics, which challenges the current understanding in the literature. We quantify the thermodynamic driving forces to identify diffusion-limited and dissolution-limited regimes of front propagation. Our findings are applicable to a variety of material systems including food, metals, and aquatic sediments, and further substantiate the hypothesis that biological systems exploit such mechanisms to regulate their function.
Long Timescale : elastic heterogeneity can lead to droplet-dissolution front
We also created a video to communicate our research in a quick and fun manner to the wider audience.
From cells to ice-creams: how does elasticity affect phase separation?
Growth and Mechanics
Growth of one body inside another is ubiquitous in both nature as well as the engineering world — growing roots of a plant in the soil, growth of an embryo in the womb, formation of precipitates in metallic alloys are all examples of this common phenomenon. However, when a body grows inside another, it experiences resistance from the surrounding environment. How does this resistance affects the form of the growing body is a challenging question and has been poorly understood till date. To tackle this challenge, we analyzed a system of bacterial biofilms that grow inside another medium, to elucidate the intimate connection between the form of the growing body and the properties of the body-medium pair. The mathematical modeling of the growth process, which required us to develop an approximate non-linear inclusion theory, revealed that the confining medium exerts a strong influence on the fate of the growing body. This framework can help us understand a broad range of other phenomenon germane to both engineering and biology, such as, tumor growth, design of novel composites, and antibiotic resistance, to name a few.
Peeling of Soft Adhesive Layers
We study a representative setting — peeling of an adhesive layer by pushing on it — that underlies many complex processes ranging from Schallamach waves to evolution of geological formations to movement of cells.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. More details here.
Controlled peeling of a soft, adhesive layer that eventually leads to jamming
Flexoelectricity-based Nanostructures In Multilayer Graphene
Graphene develops electrical polarization when it is bent. This property of graphene is called as 'quantum flexoelectricity' since it arises due to distortion of electron cloud upon bending. Flexoelectricity has profound implications in the buckling response of graphene, especially multilayer graphene (MLG). MLG when gently compressed, instead of buckling into a sinusoidal shape, buckles into kink-shaped crinkles. The dipole-dipole interactions, both intralayer and interlayer, provide the energy reduction through a localized and oscillatory curvature distribution.
Typical curvature distribution in an MLG crinkle
AFM image of MLG crinkle
A very subtle but critical finding is that flexoelectricity in graphene switches the bifurcation from typically supercritical to subcritical. If the flexoelectricity effect is turned off, a much smoother curvature distribution is observed. The boundary layer of the localized curvature is approximately 2 nm wide. The dipole magnitude is directly proportional to the curvature. Such a narrow boundary layer focuses the flexoelectric charges into nearly a line charge along the crinkle ridge/valley which is controllable by external strain. This opens up exciting possibilities including manipulating charged and polarizable molecules through crinkles.
This is a brief overview - for more exciting findings and details take a look at our paper.
Dielectricity-Flexoelectricity Coupling in Graphene
We recently discovered that graphene, especially multilayer graphene, upon buckling forms kink-shaped elastic crinkles. We examine the coupling of flexoelectricity and dielectricity in multilayer graphene (MLG) in detail. A thermodynamically motivated, non-local constitutive law for modeling the coupling is proposed. The flexoelectric-dielectric coupling is critical for the existence of crinkle buckling mode and a uniform bending model cannot be directly applied to a general non-uniform case. The non-local model can be simplified in adequate situations to a lumped model - either uniform curvature or e-local model (discussed in 1). In addition to this, the mathematical details of the thermodynamic formalism and its further reduction under different scenarios are treated.
Buckyball adsorption on HOPG
Positively (P-type)/ Negatively (N-type) charged crinkles
The non-local formalism allows an accurate prediction of the induced flexoelectric charges on graphene crinkles. These charges can be either positive or negative depending on the curvature. We demonstrate the existence of these charges experimentally by adsorption study of buckyballs on HOPG. The inter-buckyball spacing predicted by the model is in agreement with experiments, indicating that flexoelectricity of graphene is the mechanism behind the aligned adsorption. Check out the paper for more.
Thermo-Mechanically Coupled Finite Strain Model for Phase-Transitioning Steels at Cryogenic Temperature
Austenitic steels are widely used for cryogenic temperature applications, for instance in LNG transportation pipes. Metastable austenitic steels show significant changes in constitutive response due to plastic-strain driven phase transition to martensite and this transition is accelerated at cryogenic temperatures. This leads to a second strain hardening, modeling which is critical to predict the accurate response of complex structures (like corrugated pipes). We developed a model and the simulation capability to account for the phase transitions and complex thermo-mechanical history for austenitic steels and validated it against full-scale C-pipe experiments conducted at cryogenic temperatures. Take a look at the paper for details.
Martensite volume fraction in the C-pipe undergoing tension test
Martensite volume fraction in a notched plate sample
Creasing in Soft Materials
Soft materials are susceptible to a variety of instabilities that lead to an array of surface patterns including wrinkles, folds and creases. Crease is a cusp shaped surface pattern and one situation where creasing is observed is on the surface of a homogenous half-space, of say neo-hookean material, under lateral compression. The critical compressive strain for this case is found by many to be 35.6 %. We are focused on analytically modeling the crease to pinpoint this critical compressive strain.
Checkout the Journal of Mechanics and Physics of Solids publication here:
Song, S., Kothari, M. and Kim, K.S., 2024. On Inherent Hyperelastic Crease. Journal of the Mechanics and Physics of Solids, p.105716.