My research interests lie in the study of mechanics of materials, ranging from inert solids such as metals, alloys, ceramics, rocks, concrete, polymers and hydro-gels to living material such as cellular systems, biological tissues, organs etc., Broadly my research tries to understand how synthetic and living materials grow, deform and break using analytical and computational tools. This pursuit underpins transformative applications across engineering and science — from the safety and reliability of aircraft, ships, and buildings, to the performance of medical, electronic, robotic, and energy-storage devices, to our understanding of disease progression, morphogenesis, and treatment.
My research work so far can be broadly organized into four interconnected research areas - Fracture and Failure Mechanics, Growth Mechanics and Morphogenesis, Material Characterization of Soft Materials and Shockwave Physics and Extreme Dynamics. My work in each area is described below.
Understanding fracture in synthetic systems is critical to safety and performance across industries — transportation, infrastructure, defense, energy generation and storage. In living systems, damage and fracture processes govern the breaking of bones, the tearing of muscles and ligaments, traumatic brain injury, and cardiovascular disease, where the rupture of blood clots can trigger heart attacks and strokes. While the specific constitutive physics and microscopic processes driving fracture in these systems are remarkably different, the macroscopic process of fracture happens in the same broad stages — the nucleation of cracks followed by their propagation and eventual complete failure. My research addresses the following question: "How can we develop a broad, unified theoretical and computational framework for fracture nucleation and propagation that can model such diverse systems?" I employ a two-pronged approach designed for cross-talk: (a) develop macroscopic continuum descriptions of fracture that accommodate diverse constitutive physics, and (b) probe the micromechanics of failure to ground and refine the macroscopic models. Below I describe my research so far towards this question.
In elastic brittle solids, propagation of large pre-existing cracks is governed by Griffith's theory and the fracture toughness; nucleation in pristine material is governed by the strength surface (critical set of stresses that nucleate cracks and fracture when material undergoes spatially uniform loading). Bridging these two regimes in a single, robust, physics-based framework has remained an open challenge. Existing approaches — cohesive zone models, gradient damage, peridynamics, multiscale micromechanics — each face limitations: ad hoc unphysical elements, prohibitive computational cost, or difficulty calibrating to experimental data. A recent promising direction, pioneered by Professors Aditya Kumar and Oscar Lopez-Pamies, introduces a crack nucleation driving force into the phase-field formulation that marries strength surface and fracture toughness. In my recent work, I have advanced this framework in several directions described below.
I derived a closed form expression for this nucleation driving force for a general brittle material described by any strength function. The solution allows the strength surface of any brittle material to be exactly captured in the limit of vanishing phase field regularization length and exactly at chosen calibration strength locations at all regularization lengths.
Publication [Paper] [Preprint] - Chockalingam, S., 2025. On the construction of explicit analytical driving forces for crack nucleation in the phase field approach to brittle fracture with application to Mohr-Coulomb and Drucker-Prager strength surfaces. Journal of Applied Mechanics, 92(4), p.041002.
Implementation of the above general driving force in the open source FEA framework FEniCS demonstrates successful crack nucleation and propagation under multimodal loading for diverse (mathematically and physically) strength surfaces — Mohr-Coulomb, 3D Hoek-Brown, and Mogi-Coulomb — with the 3D Hoek-Brown representing the first consistent implementation of a nonlinear (non-homogeneous) strength function in the phase-field formulation.
Publication [Paper] [Preprint] - Chockalingam, S., Buganza Tepole, A., and Kumar, A., 2026. The phase-field model of fracture incorporating Mohr-Coulomb, Mogi-Coulomb, and Hoek-Brown strength surfaces. Engineering Fracture Mechanics, 340, p. 112108.
We show that strength surfaces machine-learned through neural networks can be integrated into the unified phase-field approach using my explicit driving force solution. This offers (i) a single network architecture that captures all experimental data via weight selection rather than ad hoc choice of analytical functions, (ii) the ability to capture strength behaviors not easily represented by conventional functions — such as those of rubbery materials, and (iii) accurate capture of strength surfaces at high regularization lengths (due to high parametrization of the neural network strength function which allows exact capture of the strength surface at large number of locations at all regularization lengths), well beyond current state-of-the-art — a major advantage for fracture modeling of large structures. We show successful application of nucleation and propagation and under multimodal loadings to a wide range of experimental data (graphite, natural rubber, synthetic rubber) and synthetically generated data using popular analytic strength functions (Mohr-Coulomb, Mogi-Coulomb, Drucker-Prager, 3D Hoek-Brown).
Publication [Preprint] - Forthcoming
Neural network strength function
The primary damage process in metals undergoing ductile fracture is the nucleation, growth, and coalescence of microvoids. Voids nucleate from multiple sources, grow in isolation under plastic loading, and ultimately coalesce through plastic strain localization in the inter-void ligament — a critical event in ductile fracture nucleation. Predicting the onset of coalescence is therefore central to predictive ductile fracture modeling. Below are my key research contributions in this area.
Working with Prof. Shyam Keralavarma at IIT Madras, I developed a micromechanics-based analytical criterion for void coalescence in anisotropic porous ductile solids. Two possible modes of coalescence were considered - necking instability and shear strain localization in the transverse inter-void ligament. The final form of the coalescence criterion has an interesting symmetry with Gurson-type yield criteria for porous materials and was shown to be an improvement over existing models for the special case of isotropic matrix behavior. The criterion was validated by comparison to quasi-exact numerical coalescence loci computed using a FEA based limit analysis method for the special case of transversely isotropic materials. The criterion has since been widely employed in ductile fracture research.
Publication [Paper] - Keralavarma, S.M. and Chockalingam, S., 2016. A criterion for void coalescence in anisotropic ductile materials. International Journal of Plasticity, 82, pp.159-176.
I implemented the Keralavarma–Benzerga anisotropic void growth model (and the isotropic Gurson model) as Abaqus User Material Subroutines (UMATs), with the coalescence criterion above evaluated at each load step using the current microstructure state to detect coalescence onset. Predictions of the strain to coalescence under constant-triaxiality axisymmetric loading were validated against unit-cell finite element simulations across triaxiality, initial void aspect ratio, initial porosity, and anisotropy ratios.
Publication (thesis attached below) - Chockalingam, S., 2016. Void coalescence in anisotropic ductile materials. Honors Thesis. Indian Institute of Technology Madras.
Cavitation — the unstable expansion of a void or defect upon reaching a critical load — has long been recognized as a fundamental precursor to ultimate failure in materials ranging from ductile metals to soft and biological solids. Classical theory treats the critical pressure for cavity expansion as a length-scale-independent material property and has predicted it for many constitutive models. My work has extended cavitation theory in several directions that are essential for real-world materials, where defects often sit near interfaces, interact with each other, or are subjected to coupled physics.
While classical cavitation theory assumes defects in the bulk of a homogeneous medium, defects often sit at interfaces between distinct media — in filled rubbers, multi-material composites, and layer-by-layer additive manufacturing. We establish, for the first time, a length-scale-independent limit for interfacial cavitation in neo-Hookean solids, through asymptotic analysis of computational results. We also show favorable comparison to experimental results while additionally accounting for interfacial delamination. My role in this collaborative project was in carrying out numerical simulations and establishing the cavitation limit. Subsequently we also established the influence of surface tension on the interfacial cavitation limit - which increases the cavitation pressure.
Publications
a. [Paper] [Preprint] - Henzel, T.*, Nijjer, J.*, Chockalingam, S.*, Wahdat, H., Crosby, A.J., Yan, J. and Cohen, T., 2022. Interfacial Cavitation. PNAS Nexus, 1(4), p.pgac217. (* equal contribution)
b. [Paper] [Preprint] - Li, X., Unikewicz, B., Chockalingam, S., da Rocha, H.B. and Cohen, T., 2026. Interfacial Cavitation with Surface Tension: New Insights into Failure of Particle Reinforced Polymers. Journal of the Mechanics and Physics of Solids, 206, p.106379.
Real materials often contain defects near interfaces and in close proximity to one another, where interaction effects can significantly alter the onset of cavitation instability. Using large-deformation finite element simulations with asymptotic extrapolation, we quantify how interactions modify the cavitation threshold: proximity to a rigid interface produces a monotonic increase toward the interfacial limit, while cavity–cavity interactions produce a non-monotonic response with peak enhancement at intermediate spacing. The work provides a systematic framework for understanding interaction-driven cavitation in porous, biological, and multi-material systems.
Publication [Preprint] - Saeedi, A. *, Chockalingam, S. *, and Kothari, M. 2026. The effect of interactions on elastic cavitation. arXiv preprint arXiv:2603.19603. (* equal contribution)
Effect of a nearby rigid interface on the cavitation pressure
Effect of a nearby cavity on the cavitation pressure
Long term, my goal is to extend the phase-field approach to synthetic and living materials such as metallic alloys and blood clots where fracture nucleation is governed by more complex physics involving plasticity, viscoelasticity, poro-elasticity, and mass transfer (diffusion, growth, etc.). Key prongs include: (i) integrating micromechanically derived fracture nucleation criteria (such as from my ductile fracture work above) into the phase-field approach; (ii) investigating when and how cavitation drives macroscopic fracture nucleation, building on my cavitation work above; (iii) confronting the open question of what energetic competition drives fracture in the presence of significant bulk dissipation; and (iv) further developing machine learning–based approaches for inferring nucleation criteria directly from experimental data across diverse materials, building on my neural-network strength function work above.
Growth is ubiquitous in essential biological and synthetic material systems. In living systems, mechanics governs growth processes that determine both function and failure: pathological growth drives disease progression in solid tumors (85% of cancer mortality) and bacterial biofilms (responsible for a significant fraction of all human microbial infections); mechanical cues guide remodeling in muscle, bone, and vessels; and fundamental developmental processes — from brain lobe formation to embryogenesis — rely on growth coupled to mechanical forces. In synthetic systems, mechanics likewise governs growth and degradation outcomes: chemically driven secondary-phase growth generates stresses, interfacial mismatch, and cracking; surface films and dendrites in batteries limit safety and lifetime; oxide layers in high-temperature alloys degrade power-plant and aerospace components; tin whiskers threaten semiconductor reliability; and rebar corrosion compromises civil infrastructure.
My research in this area is motivated by the following question: "How do internal biological/chemical/thermal processes and external environmental loads drive and shape growth processes?" Most existing growth models are top-down and phenomenological — they reproduce observed behavior by fitting empirical rules. My approach is bottom-up: develop large-deformation theories that encode underlying mechanisms and thermodynamic principles, so that the emergent physics can both model and explain growth phenomena. Below I describe my research so far towards this question.
Growing biological systems are a mixture of fluid and solid components and increase their mass by intake of diffusing species such as fluids and nutrients (swelling) and subsequent conversion of some of the diffusing species into solid material (growth). Experiments indicate that these systems swell by large amounts and that the swelling and growth are intrinsically coupled, with the swelling being an important driver of growth. However, most existing theories for swelling coupled growth employ linear poroelasticity, which is limited to small swelling deformations, and employ phenomenological prescriptions for the dependence of growth rate on concentration of diffusing species and the stress-state in the system. In particular, the termination of growth is enforced through the prescription of a critical concentration of diffusing species and a homeostatic stress.
We develop a fully coupled swelling–growth theory accounting for large swelling through nonlinear poroelasticity. The emergent thermodynamic driving stress for growth automatically captures all the above phenomena without ad hoc prescriptions — the homeostatic stress, the dependence of growth rate on concentration of diffusing species (increasing with concentration, saturating at high values, unfavorable below a critical value), and the simultaneous effect of applied stresses and diffusion-consumption constraints. The theory is used to successfully model experimental growth behavior of solid tumors (Alessandri et al., 2013) and bacterial biofilms (Zhang et al., 2021) in response to mechanical and diffusion-limitation stimuli.
Publication [Paper] - Chockalingam, S. and Cohen, T., 2024. A large deformation theory for coupled swelling and growth with application to growing tumors and bacterial biofilms. Journal of the Mechanics and Physics of Solids, 187, p.105627.
The theory also demonstrates how mechanical confinement influences morphogenesis (shape change during growth) by suppressing and redirecting growth, without needing ad hoc empirical rules. It further shows that dynamically growing inclusions evolve in shape similarly to fluid-filled void expansion when remodeling processes (cellular rearrangement, microstructural evolution) are much faster than volumetric growth processes (cell division, ECM production) — a result previously also predicted by our work on nonlinear inclusion theory described below.
Publications
a. [PhD dissertation] - Senthilnathan, C., 2024. Understanding the mechanics of growth: A large deformation theory for coupled swelling-growth and morphogenesis of soft biological systems (Doctoral dissertation, Massachusetts Institute of Technology).
b. [Preprint (In prep)] - Chockalingam, S., Bonavia, J.E., Tepole, A.B. and Cohen, T. (in prep.). Explaining morphogenesis under mechanical confinement using a kinetic coupled swelling growth theory.
The work of J.D. Eshelby in the late 50's revolutionized our understanding of the elastic stress and strain fields due to an ellipsoidal inclusion/inhomogeneity that undergoes a transformation of shape and size inside a confining medium. However Eshelby's solutions are limited to the linear elastic regime. My work develops nonlinear extensions of the inclusion theory, with applications to confined growth in biological systems and beyond.
We developed an approximate theory for the growth of inclusions embedded in a solid medium for large deformations. Furthermore, instead of an inert inclusion undergoing a prescribed transformation strain, we allow for active re-modelling of the inclusion with the goal of modelling growth of active biological systems embedded in a soft matrix. Our experimental model system involves growth and morphogenesis of Vibrio cholerae biofilms embedded in hydrogels. While growth models typically prescribe a constitutive evolution law that ties together the volumetric growth rate and evolution of stress-free shape, the biofilm system re-organizes at a much faster rate than it grows and the volumetric growth rate is constant. Thus we kinematically prescribe the volumetric growth and propose a free energy minimization based path for evolution of the growth shape of the inclusion. While confined growth and morphogenesis is important in several systems such as tumors and bacterial biofilms, an interesting practical example where mechanical confinement affects the growth shape is in confined growth of vegetables and fruits such as the tomatoes shown previously. This work was covered by MIT News.
Publication [Paper] [Preprint] - Li, J., Kothari, M., Chockalingam, S., Henzel, T., Zhang, Q., Li, X., Yan, J. and Cohen, T., 2022. Nonlinear inclusion theory with application to the growth and morphogenesis of a confined body. Journal of the Mechanics and Physics of Solids, 159, p.104709.
In this manuscript published in a special issue edition of the Mathematics and Mechanics of Solids commemorating Professor Rohan Abeyaratne's 70th birthday, we present the most accurate extension to date of the Eshelby inclusion solution to the nonlinear regime, building on the earlier work described above. We also analytically demonstrate the existence of an asymptotic limit for the pressure applied by the matrix on the growing inclusion (which we call isomorphic pressure) as well as the deforming aspect ratio of the ellipsoidal inclusion (which we call isomorphic aspect ratio) which shows excellent agreement with numerical simulation results.
Publication [Paper] [Preprint] - Bonavia, J.E., Chockalingam, S. and Cohen, T., 2025. On the nonlinear Eshelby inclusion problem and its isomorphic growth limit. Mathematics and Mechanics of Solids, p.10812865251319798.
In the future, in addition to exploring other fundamental questions in growth mechanics such as size control and anisotropic growth, I am interested in exploring the intersection of fracture and growth mechanics: (i) how growing inclusions generate stresses and fracture the confining medium — critical to modeling failure in batteries, semiconductors, and high-temperature alloys in aerospace and power plant components; and (ii) how damaged tissues and wounds regenerate and heal.
Characterizing local mechanical properties of soft and biological materials is essential for understanding fundamental biological processes and for medical and engineering applications. For example, malignant thyroid nodules are significantly stiffer than benign nodules; among patients whose biopsies return indeterminate results, up to 80% currently undergo diagnostic surgery only to be found benign, and reliable local stiffness measurement could spare many of them unnecessary surgery. Similar pathology-linked changes in local mechanical response appear across tumors, fibrotic tissues, atherosclerotic plaques, and bacterial biofilms. Classical testing methods face significant limitations on very soft and biological materials: sample preparation in specific shapes is difficult, boundary effects and inhomogeneous deformation distort measurements, and bulk methods cannot resolve spatial heterogeneity. Biological tissues are often heterogeneous and behave very differently in-vivo versus ex-vivo, making minimally invasive, local, in-vivo characterization techniques essential. Needle-based methods such as Cavitation Rheology and Volume-Controlled Cavity Expansion (VCCE) address this need, but had been limited to elastic, quasi-static, rate-independent characterization. My work has extended VCCE to nonlinear viscoelasticity and refined the technique through controlled cavity geometries.
We propose several enhancements to VCCE that adapt it for characterization of rate-dependent material response at low-to-medium stretch rates. Critically, we demonstrate that these enhancements become essential even for accurate quasi-static property measurement: the loading protocols used in earlier studies can produce viscoelastic stiffening and saturation that masquerade as quasi-static response. This technique has now been successfully used to characterize mechanical properties of biological materials such as blood clots and thyroid nodules.
Publication [Paper] [Preprint] - Chockalingam, S., Roth, C., Henzel, T. and Cohen, T., 2021. Probing local nonlinear viscoelastic properties in soft materials. Journal of the Mechanics and Physics of Solids, 146, p.104172.
A variant of VCCE using carefully fabricated cylindrical cavities — trading slightly increased invasiveness for substantially higher accuracy through precise control of the initial configuration.
Publication [Paper] [Preprint] - Li, J., Xie, Z., Varner, H., Chockalingam, S., and Cohen, T., 2025. Cylindrical cavity expansion for characterizing mechanical properties of soft materials. Extreme Mechanics Letters, 77, p.102343.
In the future, I aim to (i) extend VCCE into new regimes by incorporating poro-viscoelastic coupling, enabling quantitative characterization of soft, fluid-saturated biological tissues where diffusive fluid loss obscures intrinsic mechanical response; and (ii) leverage machine learning on VCCE pressure-volume signatures to distinguish healthy from diseased tissues. Together, these directions will transform VCCE into a broadly applicable diagnostic tool for soft tissues.
Extreme loading produces dynamic phenomena—from wave propagation and shock formation to crack branching and shattering—that lie outside quasi-static theories yet are central to predicting behavior across disciplines: earthquake-resistant design and blasting in civil engineering; crash testing and protective structures in automotive; impact mechanics in aerospace (bird strikes, spacecraft landings, meteorite impacts); and helmet and protective-gear design in biomedical engineering. My research in this area is motivated by the following question: “How can we connect the physics of shockwave evolution, dynamic fracture, and rate-dependent material response to model material behavior under extreme dynamic loading?” Below I describe my research so far towards this question.
A material whose shear stress-strain response is linear would relay a shear wave loading waveform imparted on its surface unchanged (ignoring dissipation) at the constant linear elastic shear wavespeed. On the other hand, in materials with a nonlinear shear response, the shape of the velocity or shear strain profile of the shear wave can evolve as the wave is relayed through the material. For a shear stiffening material, this nonlinear effect would steepen the loading waveform as it is being relayed eventually resulting in a shock. A quick visualization of this phenomenon is shown below in shear loading.
Steepening of loading wave into a shear shock (shock location indicated by red cross)
Spreading of loading wave in shear softening material
A recent study demonstrates that such shear shocks could be a primary damage mechanism in Traumatic brain injuries (TBIs) due to high local accelerations and gradients at the shock. Therefore understanding how these shocks form and how far they take to evolve based on the loading/impact on the material and the mechanical properties of the material itself, is of paramount importance in beginning to design protective structures or studying the phenomenon in laboratory settings.
Most prior analyses relied on reduced acoustic wave equations under weak-nonlinearity or small-deformation assumptions that break down for realistic loading. My work develops fully nonlinear elastodynamic frameworks for shock evolution in soft solids and demonstrates analogous shock physics in tunable discrete lattices.
We present the first closed-form solutions for the distance taken for shear-shock formation while exactly solving the fully nonlinear elastodynamics equations — without the weak-nonlinearity assumptions of classical acoustics. Results are encapsulated in non-dimensional phase plots that identify regimes where shocks form. Applied to a simplified model of shear impact of the human brain, the predictions agree with experimental studies of TBI. The non-dimensional maps can guide protective-structure design by identifying combinations of loading, geometry, and material properties that prevent shock formation.
Publication [Paper] [Preprint] - Chockalingam, S. and Cohen, T., 2020. Shear shock evolution in incompressible soft solids. Journal of the Mechanics and Physics of Solids, 134, p.103746.
Working with Harold Berjamin, I extended the analysis to viscoelastic solids, again showing that small-deformation acoustic approximations yield inaccurate predictions and emphasizing the need for large-deformation frameworks in real-world shear-shock applications.
Publication [Paper] [Preprint] - Berjamin, H. and Chockalingam, S., 2022. Shear shock formation in incompressible viscoelastic solids. Wave Motion, 110, p.102899.
Confined thermo-chemical processes inside solids drive a range of extreme-dynamics phenomena — hotspot formation and micro-explosions in energetic materials, and laser-induced cavitation used for energy focusing and material characterization. Capturing the dynamics requires coupling solid mechanics with the thermodynamics and chemical kinetics of the cavity interior.
We study the motion of a cavity under thermo-chemical loading by coupling solid mechanics with internal thermodynamics and chemical kinetics. The model captures experimentally observed multi-phase energy bursts. More generally, we numerically map the dimensionless response of the system for arbitrary heat-power supply loadings and derive analytical expressions for the mechanical response limits.
In the future, I aim to (i) establish a fundamental framework for nonlinear shockwave mechanics that unifies diverse deformation modes, incorporates thermomechanical coupling with rate-dependent viscoplasticity, and elucidates post-shock evolution leading to damage and fracture; (ii) integrate my shockwave and extreme dynamics research with my fracture modeling to study dynamic fracture and failure, including dynamic instabilities such as crack branching.