arXiv subjects

Mohit Pundir

Publications and source records attributed to Mohit Pundir.

15 recordsLinked to original sources

arXiv2026

Crack-Tip Opening as a Probe for Length-Scale Separation in Geometrically Nonlinear Solids

Soft elastic solids are highly deformable materials where fracture is driven by the complex coupling of geometric and material nonlinearities. While geometric nonlinearity (GNL) arises kinematically from the intrinsic capacity of solids to undergo large deformations, material nonlinearity stems from the constitutive behavior unique to each class of materials. Because GNL is a universal feature of all highly deformable solids, establishing its standalone impact is a prerequisite for understanding nonlinear fracture. Here, we focus on brittle soft solids to study the role of GNL alone on the near-tip fields of a static crack under mode I plane-strain conditions, providing a canonical baseline for integrating material nonlinearities in future investigations. By utilizing a compressible St. Venant-Kirchhoff material model, we analyze crack behavior under large deformations in the absence of material nonlinearity. We propose a robust postprocessing methodology based on the crack-tip opening displacement (CTOD) profile and derive asymptotic analytical solutions. Our results reveal a distinct near-tip region where the CTOD departs from classical linear elastic predictions, transitioning into a nonlinear regime dictated by Poisson's ratio. Using a matched-asymptotics approach, we define a physical nonlinear length scale $\lambda_\mathrm{nl}$ that bounds this region and scales quadratically with the far-field stress intensity factor $K_I$. We show that GNL acts as an intrinsic strain-stiffening mechanism sufficient to trigger energy partitioning, effectively shielding the crack tip and imparting an apparent toughening. Ultimately, we conclude that the geometrically nonlinear material model serves as a foundational framework for the broader study of nonlinear elastic fracture mechanics.

cond-mat.soft↗

arXiv2026

A versatile FEM framework with native GPU scalability via globally-applied AD

Energy-based finite-element formulations provide a unified framework for describing complex physical systems in computational mechanics. In these energy-based methods, the governing equations can be obtained directly by considering the derivatives of a single global energy functional. While Automatic Differentiation (AD) can be used to automate the generation of these derivatives, current frameworks face a clear trade-off based primarily on the scale upon which the AD method is applied. Globally applied AD offers high expressivity but cannot currently be scaled to large problems. Locally applied AD scales well through traditional assembly methods, but the variety of physics and couplings that the framework can easily represent is more limited than the global approach. Here, we introduce an energy-centric framework tatva (https://github.com/smec-ethz/tatva) that defines the physics of a problem as a single global functional and applies AD globally to generate residual and tangent operators. By leveraging Jacobian-vector products for matrix-free solvers and coloring-based sparse differentiation for materializing sparse tangent stiffness matrices when needed, our flexible design scales linearly with the problem size on GPUs. We demonstrate that our framework can handle large problems (with millions of degrees of freedom) without memory exhaustion. Additionally, it offers a unified, fully differentiable methodology that can address a wide range of problems, including multi-point constraints, mixed-dimensional coupling, and the incorporation of neural networks, while maintaining high performance and scalability on modern GPU architectures.

math.NA↗

arXiv2025

Disordered origins, deterministic outcomes: How the architecture of elastic networks imprints relaxed structure and mechanics

This work targets the influence of disorder on the relaxed structure and macroscopic mechanical properties of elastic networks. We construct network classes of different types of disorder (length, topology and stiffness), which are subsequently equilibrated in a finite kinematics setting. Relaxed network structures are distinct among network classes, which opens the path towards exploiting easily accessible experimental measures as a way of inferring further microstructural details.

cond-mat.soft↗

arXiv2025

Learning Physics-Consistent Material Behavior from Dynamic Displacements

Accurately modeling the mechanical behavior of materials is crucial for numerous engineering applications. The quality of these models depends directly on the accuracy of the constitutive law that defines the stress-strain relation. However, discovering these constitutive material laws remains a significant challenge, in particular when only material deformation data is available. To address this challenge, unsupervised machine learning methods have been proposed to learn the constitutive law from deformation data. Nonetheless, existing approaches have several limitations: they either fail to ensure that the learned constitutive relations are consistent with physical principles, or they rely on boundary force data for training which are unavailable in many in-situ scenarios. Here, we introduce a machine learning approach to learn physics-consistent constitutive relations solely from material deformation without boundary force information. This is achieved by considering a dynamic formulation rather than static equilibrium data and applying an input convex neural network (ICNN). We validate the effectiveness of the proposed method on a diverse range of hyperelastic material laws. We demonstrate that it is robust to a significant level of noise and that it converges to the ground truth with increasing data resolution. We also show that the model can be effectively trained using a displacement field from a subdomain of the test specimen and that the learned constitutive relation from one material sample is transferable to other samples with different geometries. The developed methodology provides an effective tool for discovering constitutive relations. It is, due to its design based on dynamics, particularly suited for applications to strain-rate-dependent materials and situations where constitutive laws need to be inferred from in-situ measurements without access to global force data.

cond-mat.mtrl-sci↗

arXiv2025

Navigating the Complexities of Multiple Redox State Interactions in Aqueous Systems

Numerous aqueous systems host elements in multiple redox states, with wide ranging implications such as their influence on the formation/dissolution of minerals, water toxicity, and nutrient cycling. To uncover governing mechanisms and complex chemical interactions in aqueous systems, reactive-transport models have increasingly gained importance. However, their predictive capabilities remain limited because existing approaches struggle to accurately account for the full complexities of redox reactions. Here, we develop a reactive-transport framework that leverages recent advancements in thermodynamic modelling, speciation chemistry, and redox kinetics. Distinct from traditional models, we uniquely treat redox kinetics along with transport as transient phenomena, decoupled from Gibbs free energy minimisation. Ensuring ion concentrations are governed by non-equilibrium rate laws, this approach allows predicting the tempo-spatial distribution of speciation and precipitation of species across oxidation states. We illustrate the versatility of our framework through two case studies: manganese speciation in natural waters and the fate of dissolved iron in aqueous/porous media. Our framework significantly enhances the modelling of a diverse range of redox-sensitive environments.

cond-mat.mtrl-sci↗

arXiv2024

Frictional contact between solids: A fully Eulerian phase-field approach

Recent advancements have demonstrated that fully Eulerian methods can effectively model frictionless contact between deformable solids. Unlike traditional Lagrangian approaches, which require contact detection and resolution algorithms, the Eulerian framework utilizes a single, fixed spatial mesh combined with a diffuse interface phase-field approach, simplifying contact resolution significantly. Moreover, the Eulerian method is well-suited for developing a unified framework to handle multiphysical systems involving growing bodies that interact with a constraining medium. In this work, we extend our previous methodology to incorporate frictional contact. By leveraging the intersection of the phase fields of multiple bodies, we define normal and tangential penalty force fields, which are incorporated into the linear momentum equations to capture frictional interactions. This formulation allows independent motion of each body using distinct velocity fields, coupled solely through interfacial forces arising from contact and friction. We thoroughly validate the proposed approach through several numerical examples. The method is shown to handle large sliding effortlessly, accurately capture the stick-slip transition, and preserve history-dependent energy dissipation, offering a solution for modeling frictional contact in Eulerian models.

cond-mat.soft↗

arXiv2024

Simplifying FFT-based methods for solid mechanics with automatic differentiation

Fast-Fourier Transform (FFT) methods have been widely used in solid mechanics to address complex homogenization problems. However, current FFT-based methods face challenges that limit their applicability to intricate material models or complex mechanical problems. These challenges include the manual implementation of constitutive laws and the use of computationally expensive and complex algorithms to couple microscale mechanisms to macroscale material behavior. Here, we incorporate automatic differentiation (AD) within the FFT framework to mitigate these challenges. We demonstrate that AD-enhanced FFT-based methods can derive stress and tangent stiffness directly from energy density functionals, facilitating the extension of FFT-based methods to more intricate material models. Additionally, automatic differentiation simplifies the calculation of homogenized tangent stiffness for microstructures with complex architectures and constitutive properties. This enhancement renders current FFT-based methods more modular, enabling them to tackle homogenization in complex multiscale systems, especially those involving multiphysics processes. Furthermore, we illustrate the use of the AD-enhanced FFT method for problems that extend beyond homogenization, such as uncertainty quantification and topology optimization where automatic differentiation simplifies the computation of sensitivities. Our work will simplify the numerical implementation of FFT-based methods for complex solid mechanics problems.

cond-mat.mtrl-sci↗

arXiv2024

Precipitation of corrosion products in macroscopic voids at the steel-concrete interface -- observations, mechanisms and research needs

Macroscopic voids at the steel-concrete interface and their degree of saturation with an aqueous electrolyte are known to play an important role in the corrosion of steel in reinforced concrete. Irrespective of the exposure conditions and testing parameters, corrosion products have been reported to consistently precipitate in a unique pattern within these macroscopic voids, preferentially along the void walls and growing inward. The underlying mechanisms governing corrosion product precipitation in macroscopic voids and their effects on long-term durability remain unclear. Through in-situ X-ray computed tomography observations, thermodynamic and kinetic considerations, and numerical modelling of water transport within macroscopic voids, here, we provide plausible hypotheses of the processes responsible for the precipitation of corrosion products along the walls of the voids. Understanding the mechanisms of corrosion product precipitation can offer insights into the development of stresses in and around the macroscopic interfacial void and the durability of reinforced concrete structures. This contribution also discusses opportunities for different avenues for research to elucidate several multiscale processes that influence the durability of reinforced concrete.

cond-mat.mtrl-sci↗

arXiv2024

A thermo-hygro computational model to determine the factors dictating cold joint formation in 3D printed concrete

Cold joints in extruded concrete structures form once the exposed surface of a deposited filament dries prematurely and gets sequentially covered by a layer of fresh concrete. This creates a material heterogeneity which lowers the structural durability and shortens the designed service life. Many factors concurrently affect cold joint formation, yet a suitable tool for their categorization is missing. Here, we present a computational model that simulates the drying kinetics at the exposed structural surface, accounting for cement hydration and the resulting microstructural development. The model provides a time estimate for cold joint formation as a result. It allows us to assess the drying severity for a given structure's geometry, its interaction with the environment, and ambient conditions. We evaluate the assessed factors and provide generalized recommendations for cold joint mitigation.

cond-mat.soft↗

arXiv2024

Transonic and supershear crack propagation driven by geometric nonlinearities

Linear elastic fracture mechanics theory predicts that the speed of crack growth is limited by the Rayleigh wave speed. Although many experimental observations and numerical simulations have supported this prediction, some exceptions have raised questions about its validity. The underlying reasons for these discrepancies and the precise limiting speed of dynamic cracks remain unknown. Here, we demonstrate that tensile (mode~I) cracks can exceed the Rayleigh wave speed and propagate at supershear speeds. We show that taking into account geometric non-linearities, inherent in most materials, is sufficient to enable such propagation modes. These geometric non-linearities modify the crack-tip singularity, resulting in different crack-tip opening displacements, cohesive zone behavior, and energy flows towards the crack tip.

cond-mat.soft↗

arXiv2023

The key to the enhanced performance of slab-like topologically interlocked structures with non-planar blocks

Topologically interlocked structures are assemblies of interlocking blocks that hold together solely through contact. Such structures have been shown to exhibit high strength, energy dissipation, and crack arrest properties. Recent studies on topologically interlocked structures have shown that both the peak strength and work-to-failure saturate with increasing friction coefficient. However, this saturated structural response is only achievable with nonphysically high values of the friction coefficient. For beam-like topologically interlocked structures, non-planar blocks provide an alternate approach to reach similar structural response with friction properties of commonly used materials. It remains unknown whether non-planar blocks have similar effects for slab-like assemblies, and what the achievable structural properties are. Here, we consider slab-like topologically interlocked structures and show, using numerical simulations, that non-planar blocks with wave-like surfaces allow for saturated response capacity of the structure with a realistic friction coefficient. We further demonstrate that non-planar morphologies cause a non-linear scaling of the work-to-failure with peak strength and result in significant improvements of the work-to-failure and ultimate deflection - values that cannot be attained with planar-faced blocks. Finally, we show that the key morphology parameter responsible for the enhanced performance of non-planar blocks with wave-like surfaces is the local angle of inclination at the hinging points of the loaded block. These findings shed new light on topologically interlocked structures with non-planar blocks, allowing for a better understanding of their strengths and energy absorption.

math.NA↗

arXiv2023

Eulerian framework for contact between solids represented as phase fields

Mechanical contact between solids is almost exclusively modeled in Lagrangian frameworks. While these frameworks have been developed extensively and applied successfully to numerous contact problems, they generally require complex algorithms for contact detection and resolution. These challenges become particularly important when contact appears between solids with evolving boundaries, such as in systems where crystals grow in a constrained space. In this work, we introduce a fully Eulerian finite element framework for modeling contact between elastic solids tailored towards problems including evolving and intricate surfaces. The proposed approach uses a phase-field method that involves a diffuse representation of geometries on a fixed mesh, simplifying the modeling of evolving surfaces. Our methodology introduces a novel volumetric contact constraint based on penalty body forces, efficiently resolving the interpenetration of solids. We showcase the validity and versatility of our method through numerical examples, highlighting its ability to accurately capture complex solid-solid interactions. The Eulerian phase-field formulation greatly simplifies contact detection and its resolution. Furthermore, the framework can be straightforwardly coupled with other physical phenomena through the inclusion of multiple energy terms in the evolution of the phase-field. This enables multiphysics modeling, potentially providing a valuable tool for a wide range of applications involving chemically or physically evolving deformable solids in contact, as they commonly occur in deterioration processes of porous media.

cond-mat.soft↗

arXiv2023

An FFT-based framework for predicting corrosion-driven damage in fractal porous media

Understanding fracture in cementitious materials caused by the deposition and growth of corrosion products requires scale-bridging approaches due to the large length-scale difference between the micro-pores, where deposition occurs, and the structure, where deterioration manifests. Cementitious materials bear a highly heterogeneous micro-structure owing to the fractal nature of micro-pores. Simultaneously, a corrosion-driven fracture is a multi-physics problem involving ionic diffusion, chemical reactions, and stress development. This multi-scale and multi-physical character makes scale-bridging studies computationally costly, often leading to the use of simplified fractal porous media, which has important consequences for the quantitative interpretation of the results. Recent advances in homogenization approaches using Fast-Fourier-Transform (FFT) based methods have raised interest due to their ease of implementation and low computational cost. This paper presents an FFT-based framework for solving corrosion-driven fractures within fractal porous media. We demonstrate the effectiveness of the Fourier-based spectral method in resolving the multiple corrosion-driven mechanisms such as ionic diffusion, stress development, and damage within a fractal porous microstructure. Based on the presented methodology, we analyze the impact of simplifying fractal porous media with simple Euclidean geometry on corrosion-driven fracture. Our results demonstrate the importance of preserving both the porosity and fractal nature of pores for precise and reliable modeling of corrosion-driven failure mechanisms.

cond-mat.soft↗

arXiv2023

Beam-like topologically interlocked structures with hierarchical interlocking

Topologically interlocked materials and structures, which are assemblies of unbonded interlocking building blocks, are promising concepts for versatile structural applications. They have been shown to exhibit exceptional mechanical properties, including outstanding combinations of stiffness, strength, and toughness, beyond those achievable with common engineering materials. Recent work has established a theoretical upper limit for the strength and toughness of beam-like topologically interlocked structures. However, this theoretical limit is only achievable for structures with unrealistically high friction coefficients; therefore, it remains unknown whether it is achievable in actual structures. Here, we demonstrate that a hierarchical approach for topological interlocking, inspired by biological systems, overcomes these limitations and provides a path toward optimized mechanical performance. We consider beam-like topologically interlocked structures that present a sinusoidal surface morphology with controllable amplitude and wavelength and examine the properties of the structures using numerical simulations. The results show that the presence of surface morphologies increases the effective frictional strength of the interfaces and, if well-designed, enables us to reach the theoretical limit of the structural carrying capacity with realistic friction coefficients. Furthermore, we observe that the contribution of the surface morphology to the effective friction coefficient of the interface is well described by a criterion combining the surface curvature and surface gradient. Our study demonstrates the ability to architecture the surface morphology in beam-like topological interlocked structures to significantly enhance its structural performance.

math.NA↗

arXiv2022

On the failure of beam-like topologically interlocked structures

Topologically interlocked structures are architectured by fitting together blocks that are constrained geometrically through contact and friction by their neighboring blocks. As long as the frictional strength is nowhere exceeded, the blocks stick against each other, allowing for large rotations. Once the interfacial stresses exceed the frictional strength, relative sliding between the blocks alters the structure's mechanical response. Improving the structural performance, precisely the strength and the toughness, has been one of the main focal points in the literature. However, many fundamental questions regarding the role and effect of the interface mechanisms (stick and slip) and rotation of the blocks have not been addressed yet. Here, we carry out a parametric analysis to understand the effect of Young's modulus, friction coefficient and geometry of the blocks on the dominance of the stick or slip governed mechanism. We combine analytical and computational tools to analyze the failure mechanisms and the response capacities of beam-like topologically interlocked structures. This is achieved using a finite element method coupled with a penalty-based approach for enforcing contact constraints along interfaces. We show that the combination of the structure's height and the friction coefficient controls whether the failure mechanism is slip-governed or stick-governed. Furthermore, we demonstrate that the sticking mechanism across all interfaces along with the rotation of the blocks dictates a saturation level to the mechanical performance of a given structure irrespective of geometric and material properties. This provides a theoretical upper bound for the structural response of topologically interlocked structures and establishes a theoretical benchmark of achievable performance.

math.NA↗