SearcharxivSearch

arXiv subjects

Debdeep Bhattacharya

Publications and source records attributed to Debdeep Bhattacharya.

10 recordsLinked to original sources

Crushing, Comminution and Fracture: Extreme Particle Deformation in Three-Dimensional Granular Aggregates

We present a high-fidelity three dimensional computational framework for simulating the bulk mechanical behavior of granular aggregates composed of deformable brittle grains. Departing from classical discrete element methods (DEM), our approach captures both inter-particle and intra-particle deformation using a nonlocal continuum formulation based on peridynamics. Each grain is individually meshed from level-set representations, enabling accurate modeling of elastic response and autonomous fracture evolution without requiring explicit crack tracking or fragment reconstruction. We validate the method through benchmark simulations, including the Kalthoff-Winkler fracture test, crushing of hollow spheres, and compound impact-crushing scenarios. The framework is further applied to large aggregates of up to 1000 sand grains of irregular shapes reconstructed from three dimensional X-ray computed tomography. Simulations reveal convergence of bulk stress response under compression, suggesting the feasibility of constructing representative volume elements (RVEs) for multiscale modeling. Finally, we investigate the role of grain geometry and topology on the macroscopic strength of the aggregate, providing insight into microstructure-driven failure mechanisms. The framework exhibits excellent strong and weak scaling behavior, with simulations executed on up to 1600 cores, demonstrating its suitability for high-performance computing environments and large-scale modeling.

cond-mat.soft

Design of resilient structures by randomization and bistability

This paper examines various ways of improving the impact resilience of protective structures. Such structures' purpose is to dissipate an impact's energy while avoiding cracking and failure. We have tested the reaction of plane elastic-brittle lattices to an impulse. Four topologies are compared: periodic triangular, square, and hexagonal topologies, and aperiodic Penrose topology. Then, structures with random variations of the links' stiffness, node positions, and random holes are compared. Combinations of these random factors are also considered, as well as the resilience of bistable elastic-brittle lattices with sacrificial links. Several parameters are introduced to measure the structural resilience of the compared designs: (i) the amount of dissipated impact energy, (ii) the size of broken clusters of links, and (iii) the spread of damage. The results suggest new routes for rationally designing protective structures using nonperiodic topology, bistability, and structural randomness. In particular, we find that some quantities of interest can be maximized by tuning the randomized design appropriately -- for example, randomly removing 8\% of links maximizes energy dissipation. We also find that randomization of bistable lattices can offer superior energy dissipation while reducing the connectivity between broken clusters of links.

physics.comp-ph

Energy balance and damage for dynamic brittle fracture from a nonlocal formulation

A nonlocal model of peridynamic type for dynamic brittle damage is introduced consisting of two phases, one elastic and the other inelastic. Evolution from the elastic to the inelastic phase depends on material strength. Existence and uniqueness of the displacement-failure set pair follow from the initial value problem. The displacement-failure pair satisfies energy balance. The length of nonlocality $\epsilon$ is taken to be small relative to the domain in $\mathbb{R}^d$, $d=2,3$. The new nonlocal model delivers a two point strain evolution on a subset of $\mathbb{R}^d\times\mathbb{R}^d$. This evolution provides an energy that interpolates between volume energy corresponding to elastic behavior and surface energy corresponding to failure. In general the deformation energy resulting in material failure over a region $R$ is given by a $d-1$ dimensional integral that is uniformly bounded as $\epsilon\rightarrow 0$. For fixed $\epsilon$, the failure energy is nonzero for $d-1$ dimensional regions $R$ associated with flat crack surfaces. This failure energy is the Griffith fracture energy given by the energy release rate multiplied by area for $d=3$ (or length for $d=2$). The nonlocal field theory is shown to recover a solution of Naiver's equation outside a propagating flat traction free crack in the limit of vanishing spatial nonlocality. Simulations illustrate fracture evolution through generation of an internal traction free boundary as a wake left behind a moving strain concentration. Crack paths are seen to follow a maximal strain energy density criterion.

math.AP

Quasistatic fracture evolution

Nonlocal quasistatic fracture evolution for interacting cracks is developed and supporting numerical examples are presented. The approach is implicit and is based on local stationarity and fixed point methods. It is proved that the fracture evolution decreases stored elastic energy with each load step as the cracks advance; provided the load increments are chosen sufficiently small. This is also seen in the numerical examples. The numerical examples include evolution of a straight crack, a crack propagating inside an L-shaped domain, and two offset inward propagating cracks.

math.NA

Quasistatic Evolution with Unstable Forces

We consider load controlled quasistatic evolution. Well posedness results for the nonlocal continuum model related to peridynamics are established. We show local existence and uniqueness of quasistatic evolution for load paths originating at stable critical points. These points can be associated with local energy minima among the convex set of deformations belonging to the strength domain of the material. The evolution of the displacements however is not constrained to lie inside the strength domain of the material. The load-controlled evolution is shown to exhibit energy balance.

math.AP

Simulating grain shape effects and damage in granular media using PeriDEM

We provide a numerical platform for the analysis of particle shape and topology effect on the macroscopic behavior of granular media. We work within a Discrete Element Method (DEM) framework and apply a peridynamic model for deformable particles accounting for deformation and damage of individual particles. To accommodate arbitrary particle shapes including nonconvex ones as well as particle topology, an efficient method is developed to keep intra-particle peridynamic interaction within particle boundaries. Particle contact with the rigid boundary wall is computed analytically to improve accuracy. To speed up simulations with particles of different shapes and sizes the initial configuration is chosen using security disks containing different particle shapes that are placed in a jammed state using an optimization-based method. The effect of particle shape and topology on settling and compaction of the aggregate for deformable particles is analyzed.

cond-mat.soft

Peridynamics for Quasistatic Fracture Modeling

Fracture involves interaction across large and small length scales. With the application of enough stress or strain to a brittle material, atomistic scale bonds will break, leading to fracture of the macroscopic specimen. From the perspective of mechanics fracture should appear as an emergent phenomena generated by a continuum field theory eliminating the need for a supplemental kinetic relation describing crack growth. We develop a new fast method for modeling quasi-static fracture using peridynamics. We apply fixed point theory and model stable crack evolution for hard and soft loading. For soft loading we recover unstable fracture. For hard loading we recover stable crack growth. We show existence of quasistatic fracture solutions in the neighborhood of stable critical points for appropriately defined energies. The numerical method uses an analytic stiffness matrix for fast numerical implementation. A rigorous mathematical analysis shows that the method converges for load paths associated with soft and hard loading. For soft loading the crack becomes unstable shortly after the stress at the tip of the pre-crack reaches the material strength.

cond-mat.soft

Peridynamics-based discrete element method (PeriDEM) model of granular systems involving breakage of arbitrarily shaped particles

Usage, manipulation, transport, delivery, and mixing of granular or particulate media, comprised of spherical or polyhedral particles, is commonly encountered in industrial sectors of construction (cement and rock fragments), pharmaceutics (tablets), and transportation (ballast). Elucidating particulate media's behavior in concert with particle attrition (i.e., particle wear and subsequent particle fragmentation) is essential for predicting the performance and increasing the efficiency of engineering systems using such media. Discrete element method (DEM) based techniques can describe the interaction between particles but cannot model intra-particle deformation, especially intra-particle fracture. On the other hand, peridynamics provides the means to account for intra-particle deformation and fracture due to contact forces between particles. The present study proposes a hybrid model referred to as \textit{PeriDEM} that combines the advantages of peridynamics and DEM. The model parameters can be tuned to achieve desired DEM contact forces, damping effects, and intra-particle stiffness. Two particle impacts and compressive behavior of multi-particle systems are thoroughly investigated. The model can account for any arbitrarily shaped particle in general. Spherical, hexagonal, and non-convex particle shapes are simulated in the present study. The effect of mesh resolution on intra-particle peridynamics is explicitly studied. The proposed hybrid model opens a new avenue to explore the complicated interactions encountered in discrete particle dynamics that involve the formation of force chains, particle interlocking, particle attrition, wear, and the eventual breakage.

cs.CE

Mass-concentration of low-regularity blow-up solutions to the focusing 2D modified Zakharov-Kuznetsov equation

We consider the focusing modified Zakharov-Kuznetsov (mZK) equation in two space dimensions. We prove that solutions which blow up in finite time in the $H^1(\R^{2})$ norm have the property that they concentrate a non-trivial portion of their mass (more precisely, at least the amount equal to the mass of the ground state) at blow-up time. For finite-time blow-up solutions in the $H^s(\R^2)$ norm for $\frac{17}{18} < s < 1$, we prove a slightly weaker result. Moreover, we prove that the stronger concentration result can be extended to the range $ \frac{17}{18} < s \le 1$ under an additional assumption on the upper bound of the blow-up rate of the solution. The main tools used here are the $I$-method and a profile decomposition theorem for a bounded family of $H^1(\R^{2})$ functions.

math.AP

Global well-posedness for low regularity data in the 2d modified Zakharov-Kuznetsov equation

We consider the modified Zakharov-Kuznetsov (mZK) equation in two space dimensions in both focusing and defocusing cases. Using the $I$-method, we prove the global well-posedness of the $H^s$ solutions for $s>\frac{3}{4}$ for any data in the defocusing case and under the assumption that the mass of the initial data is less than the mass of the ground state solution of $\Delta \varphi - \varphi + \varphi^3 = 0$ in the focusing case. This improves the global well-posedness result of Linares and Pastor [20].

math.AP