arXiv subjects

Vinamra Agrawal

Publications and source records attributed to Vinamra Agrawal.

15 recordsLinked to original sources

arXiv2025

A Foundation Model for Material Fracture Prediction

Accurately predicting when and how materials fail is critical to designing safe, reliable structures, mechanical systems, and engineered components that operate under stress. Yet, fracture behavior remains difficult to model across the diversity of materials, geometries, and loading conditions in real-world applications. While machine learning (ML) methods show promise, most models are trained on narrow datasets, lack robustness, and struggle to generalize. Meanwhile, physics-based simulators offer high-fidelity predictions but are fragmented across specialized methods and require substantial high-performance computing resources to explore the input space. To address these limitations, we present a data-driven foundation model for fracture prediction, a transformer-based architecture that operates across simulators, a wide range of materials (including plastic-bonded explosives, steel, aluminum, shale, and tungsten), and diverse loading conditions. The model supports both structured and unstructured meshes, combining them with large language model embeddings of textual input decks specifying material properties, boundary conditions, and solver settings. This multimodal input design enables flexible adaptation across simulation scenarios without changes to the model architecture. The trained model can be fine-tuned with minimal data on diverse downstream tasks, including time-to-failure estimation, modeling fracture evolution, and adapting to combined finite-discrete element method simulations. It also generalizes to unseen materials such as titanium and concrete, requiring as few as a single sample, dramatically reducing data needs compared to standard ML. Our results show that fracture prediction can be unified under a single model architecture, offering a scalable, extensible alternative to simulator-specific workflows.

cs.LG↗

arXiv2025

The Alamo multiphysics solver for phase field simulations with strong-form mechanics and block structured adaptive mesh refinement

Alamo is a high-performance scientific code that uses block-structured adaptive mesh refinement to solve such problems as: the ignition and burn of solid rocket propellant, plasticity, damage and fracture in materials undergoing loading, and the interaction of compressible flow with eroding solid materials. Alamo is powered by AMReX, and provides a set of unique methods, models, and algorithms that enable it to solve solid-mechanics problems (coupled to other physical behavior such as fluid flow or thermal diffusion) using the power of block-structured adaptive mesh refinement.

physics.comp-ph↗

arXiv2024

Ductile fracture in functionally graded materials: Insight into crack behavior within the gradient interface

Despite advances in manufacturing making metal functionally graded materials (FGMs) more common, numerical methods for predicting fracture in ductile functionally graded materials remain limited. In this work we study the crack propagation in ductile FGMs, specifically focusing on crack propagation within the gradient region of an FGM. We investigate the direct effects of plasticity, and the exact correlations between accumulated plastic strain and crack growth patterns in an FGM. Through this, we determine key differences in crack growth patterns between well-studied brittle FGMs, and more recently developed ductile FGMs. We provide substantial insight on the influence of both the angle of incidence and the width of the gradient, and expose potential pathways for engineering crack-arresting behavior in ductile FGMs

cond-mat.mtrl-sci↗

arXiv2024

Multiscale graph neural networks with adaptive mesh refinement for accelerating mesh-based simulations

Mesh-based Graph Neural Networks (GNNs) have recently shown capabilities to simulate complex multiphysics problems with accelerated performance times. However, mesh-based GNNs require a large number of message-passing (MP) steps and suffer from over-smoothing for problems involving very fine mesh. In this work, we develop a multiscale mesh-based GNN framework mimicking a conventional iterative multigrid solver, coupled with adaptive mesh refinement (AMR), to mitigate challenges with conventional mesh-based GNNs. We use the framework to accelerate phase field (PF) fracture problems involving coupled partial differential equations with a near-singular operator due to near-zero modulus inside the crack. We define the initial graph representation using all mesh resolution levels. We perform a series of downsampling steps using Transformer MP GNNs to reach the coarsest graph followed by upsampling steps to reach the original graph. We use skip connectors from the generated embedding during coarsening to prevent over-smoothing. We use Transfer Learning (TL) to significantly reduce the size of training datasets needed to simulate different crack configurations and loading conditions. The trained framework showed accelerated simulation times, while maintaining high accuracy for all cases compared to physics-based PF fracture model. Finally, this work provides a new approach to accelerate a variety of mesh-based engineering multiphysics problems

cs.CE↗

arXiv2023

Dynamic and adaptive mesh-based graph neural network framework for simulating displacement and crack fields in phase field models

Fracture is one of the main causes of failure in engineering structures. Phase field methods coupled with adaptive mesh refinement (AMR) techniques have been widely used to model crack propagation due to their ease of implementation and scalability. However, phase field methods can still be computationally demanding making them unfeasible for high-throughput design applications. Machine learning (ML) models such as Graph Neural Networks (GNNs) have shown their ability to emulate complex dynamic problems with speed-ups orders of magnitude faster compared to high-fidelity simulators. In this work, we present a dynamic mesh-based GNN framework for emulating phase field simulations of crack propagation with AMR for different crack configurations. The developed framework - ADAPTive mesh-based graph neural network (ADAPT-GNN) - exploits the benefits of both ML methods and AMR by describing the graph representation at each time-step as the refined mesh itself. Using ADAPT-GNN, we predict the evolution of displacement fields and scalar damage field (or phase field) with high accuracy compared to conventional phase field fracture model. We also compute crack stress fields with high accuracy using the predicted displacements and phase field parameter. Finally, we observe speed up of 15-36x compared to serial execution of the phase field model.

cond-mat.mtrl-sci↗

arXiv2023

Robust, strong form mechanics on an adaptive structured grid: efficiently solving variable-geometry near-singular problems with diffuse interfaces

Many solid mechanics problems on complex geometries are conventionally solved using discrete boundary methods. However, such an approach can be cumbersome for problems involving evolving domain boundaries due to the need to track boundaries and constant remeshing. In this work, we employ a robust smooth boundary method (SBM) that represents complex geometry implicitly, in a larger and simpler computational domain, as the support of a smooth indicator function. We present the resulting equations for mechanical equilibrium, in which inhomogeneous boundary conditions are replaced by source terms. The resulting mechanical equilibrium problem is semidefinite, making it difficult to solve. In this work, we present a computational strategy for efficiently solving near-singular SBM elasticity problems. We use the block-structured adaptive mesh refinement (BSAMR) method for resolving evolving boundaries appropriately, coupled with a geometric multigrid solver for an efficient solution of mechanical equilibrium. We discuss some of the practical numerical strategies for implementing this method, notably including the importance of grid versus node-centered fields. We demonstrate the solver's accuracy and performance for three representative examples: a) plastic strain evolution around a void, b) crack nucleation and propagation in brittle materials, and c) structural topology optimization. In each case, we show that very good convergence of the solver is achieved, even with large near-singular areas, and that any convergence issues arise from other complexities, such as stress concentrations. We present this framework as a versatile tool for studying a wide variety of solid mechanics problems involving variable geometry.

math.NA↗

arXiv2022

A generalized machine learning framework for brittle crack problems using transfer learning and graph neural networks

Despite their recent success, machine learning (ML) models such as graph neural networks (GNNs), suffer from drawbacks such as the need for large training datasets and poor performance for unseen cases. In this work, we use transfer learning (TL) approaches to circumvent the need for retraining with large datasets. We apply TL to an existing ML framework, trained to predict multiple crack propagation and stress evolution in brittle materials under Mode-I loading. The new framework, ACCelerated Universal fRAcTure Emulator (ACCURATE), is generalized to a variety of crack problems by using a sequence of TL update steps including (i) arbitrary crack lengths, (ii) arbitrary crack orientations, (iii) square domains, (iv) horizontal domains, and (v) shear loadings. We show that using small training datasets of 20 simulations for each TL update step, ACCURATE achieved high prediction accuracy in Mode-I and Mode-II stress intensity factors, and crack paths for these problems. %case studies (i) - (iv). We demonstrate ACCURATE's ability to predict crack growth and stress evolution with high accuracy for unseen cases involving the combination of new boundary dimensions with arbitrary crack lengths and crack orientations in both tensile and shear loading. We also demonstrate significantly accelerated simulation times of up to 2 orders of magnitude faster (200x) compared to an XFEM-based fracture model. The ACCURATE framework provides a universal computational fracture mechanics model that can be easily modified or extended in future work.

cond-mat.mtrl-sci↗

arXiv2022

Investigating shock wave propagation, evolution, and anisotropy using a moving window concurrent atomistic-continuum framework

Despite their success in microscale modeling of materials, atomistic methods are still limited by short time scales, small domain sizes, and high strain rates. Multiscale formulations can capture the continuum-level response of solids over longer runtimes, but using such schemes to model highly dynamic, nonlinear phenomena is very challenging and an active area of research. In this work, we develop novel techniques within the concurrent atomistic-continuum multiscale framework to simulate shock wave propagation through a two-dimensional, single-crystal lattice. The technique is described in detail, and two moving window methods are incorporated to track the shock front through the domain and thus prevent spurious wave reflections at the atomistic-continuum interfaces. We compare our simulation results to analytical models as well as previous atomistic and CAC data and discuss the apparent effects of lattice orientation on the shock response of FCC crystals. We then use the moving window techniques to perform parametric studies which analyze the shock front's structure and planarity. Finally we compare the efficiency of our model to molecular dynamics simulations. This work showcases the power of using a moving window concurrent multiscale framework to simulate dynamic shock evolution over long runtimes and opens the door to more complex studies involving shock propagation through composites and high-entropy alloys.

cond-mat.mtrl-sci↗

arXiv2022

Transmitting multiple high-frequency waves across length scales using the concurrent atomistic-continuum method

Coupled atomistic-continuum methods can describe large domains and model dynamic material behavior for a much lower computational cost than traditional atomistic techniques. However, these multiscale frameworks suffer from wave reflections at the atomistic-continuum interfaces due to the numerical discrepancy between the fine-scaled and coarse-scaled models. Such reflections are non-physical and may lead to unfavorable outcomes such as artificial heating in the atomistic region. In this work, we develop a technique to allow the full spectrum of phonons to be incorporated into the coarse-scaled regions of a periodic concurrent atomistic-continuum (CAC) framework. This scheme tracks phonons generated at various time steps and thus allows multiple high-frequency wave packets to travel between the atomistic and continuum regions. Simulations performed with this method demonstrate the ability of the technique to preserve the coherency of waves with a range of wavevectors as they propagate through the domain. This work has applications for systems with defined boundary conditions and may be extended to more complex problems involving waves randomly nucleated from an impact within a multiscale framework.

cond-mat.mes-hall↗

arXiv2022

Graph neural networks for simulating crack coalescence and propagation in brittle materials

High-fidelity fracture mechanics simulations of multiple microcracks interaction via physics-based models quickly become computationally expensive as the number of microcracks increases. This work develops a Graph Neural Network (GNN) based framework to simulate fracture and stress evolution in brittle materials due to multiple microcracks' interaction. The GNN framework is trained on the dataset generated by XFEM-based fracture simulator. Our framework achieves high prediction accuracy on the test set (compared to an XFEM-based fracture simulator) by engineering a sequence of GNN-based predictions. The first prediction stage determines Mode-I and Mode-II stress intensity factors (which can be used to compute the stress evolution by LEFM), the second prediction stage determines which microcracks will propagate, and the final stage actually propagates crack-tip positions for the selected microcracks to the next time instant. The trained GNN framework is capable of simulating crack propagation, coalescence and corresponding stress distribution for a wide range of initial microcrack configurations (from 5 to 19 microcracks) without any additional modification. Lastly, the framework's simulation time shows speed-ups 6x-25x faster compared to an XFEM-based simulator. These characteristics, make our GNN framework an attractive approach for simulating microcrack propagation and stress evolution in brittle materials with multiple initial microcracks.

cond-mat.mtrl-sci↗

arXiv2021

Moving window techniques to model shock wave propagation using the concurrent atomistic-continuum method

Atomistic methods have successfully modeled different aspects of shock wave propagation in mate-rials over the past several decades, but they suffer from limitations which restrict the total runtime and system size. Multiscale methods have been able to increase the length and time scales that can be modeled but employing such schemes to simulate wave propagation and evolution through engineering-scale domains is an active area of research. In this work, we develop two distinct moving window approaches within a Concurrent Atomistic-Continuum (CAC) framework to model shock wave propagation through a one-dimensional monatomic chain. In the first method, the entire CAC system travels with the shock in a conveyor fashion and maintains the shock front in the middle of the overall domain. In the second method, the atomistic region follows the shock by the simultaneous coarsening and refinement of the continuum regions. The CAC and moving window frameworks are verified through dispersion relation studies and phonon wave packet tests. We achieve good agreement between the simulated shock velocities and the values obtained from theory with the conveyor technique, while the coarsen-refine technique allows us to follow the propagating wave front through a large-scale domain. This work showcases the ability of the CAC method to accurately simulate propagating shocks and also demonstrates how a moving window technique can be used in a multiscale framework to study highly nonlinear, transient phenomena.

cond-mat.mes-hall↗

arXiv2021

Block structured adaptive mesh refinement and strong form elasticity approach to phase field fracture with applications to delamination, crack branching and crack deflection

Fracture is a ubiquitous phenomenon in most composite engineering structures, and is often the responsible mechanism for catastrophic failure. Over the past several decades, many approaches have emerged to model and predict crack failure. The phase field method for fracture uses a surrogate damage field to model crack propagation, eliminating the arduous need for explicit crack meshing. In this work a novel numerical framework is proposed for implementing hybrid phase field fracture in heterogeneous materials. The proposed method is based on the "reflux-free" method for solving, in strong form, the equations of linear elasticity on a block-structured adaptive mesh refinement (BSAMR) mesh. The use of BSAMR enables highly efficient and scalable regridding, facilitates the use of temporal subcycling for explicit time integration, and allows for ultra-high refinement at crack boundaries with minimal computational cost. The method is applied to a variety of simple heterogeneous structures: laminates, wavy interfaces, and circular inclusions. In each case a non-dimensionalized parameter study is performed to identify regions of behavior, varying both the geometry of the problem and the relative fracture energy release rate. In the laminate and wavy interface cases, regions of delamination and fracture correspond to simple analytical predictions. For the circular inclusions, the modulus ratio of the inclusion is varied as well as the delamination energy release rate and the problem geometry. In this case, a wide variety of behaviors was observed, including deflection, splitting, delamination, and pure fracture.

cond-mat.mes-hall↗

arXiv2021

Optimized and autonomous machine learning framework for characterizing pores, particles, grains and grain boundaries in microstructural images

Additively manufactured metals exhibit heterogeneous microstructure which dictates their material and failure properties. Experimental microstructural characterization techniques generate a large amount of data that requires expensive computationally resources. In this work, an optimized machine learning (ML) framework is proposed to autonomously and efficiently characterize pores, particles, grains and grain boundaries (GBs) from a given microstructure image. First, using a classifier Convolutional Neural Network (CNN), defects such as pores, powder particles, or GBs were recognized from a given microstructure. Depending on the type of defect, two different processes were used. For powder particles or pores, binary segmentations were generated using an optimized Convolutional Encoder-Decoder Network (CEDN). The binary segmentations were used to used obtain particle and pore size and bounding boxes using an object detection ML network (YOLOv5). For GBs, another optimized CEDN was developed to generate RGB segmentation images, which were used to obtain grain size distribution using two regression CNNS. To optimize the RGB CEDN, the Deep Emulator Network SEarch (DENSE) method which employs the Covariance Matrix Adaptation - Evolution Strategy (CMA-ES) was implemented. The optimized RGB segmentation network showed a substantial reduction in training time and GPU usage compared to the unoptimized network, while maintaining high accuracy. Lastly, the proposed framework showed a significant improvement in analysis time when compared to conventional methods.

eess.IV↗

arXiv2020

Massively parallel finite difference elasticity using block-structured adaptive mesh refinement with a geometric multigrid solver

Computationally solving the equations of elasticity is a key component in many materials science and mechanics simulations. Phenomena such as deformation-induced microstructure evolution, microfracture, and microvoid nucleation are examples of applications for which accurate stress and strain fields are required. A characteristic feature of these simulations is that the problem domain is simple (typically a rectilinear representative volume element (RVE)), but the evolution of internal topological features is extremely complex. Traditionally, the finite element method (FEM) is used for elasticity calculations; FEM is nearly ubiquituous due to (1) its ability to handle meshes of complex geometry using isoparametric elements, and (2) the weak formulation which eschews the need for computation of second derivatives. However, variable topology problems (e.g. microstructure evolution) require either remeshing, or adaptive mesh refinement (AMR) - both of which can cause extensive overhead and limited scaling. Block-structured AMR (BSAMR) is a method for adaptive mesh refinement that exhibits good scaling and is well-suited for many problems in materials science. Here, it is shown that the equations of elasticity can be efficiently solved using BSAMR using the finite difference method. The boundary operator method is used to treat different types of boundary conditions, and the "reflux-free" method is introduced to efficiently and easily treat the coarse-fine boundaries that arise in BSAMR. Examples are presented that demonstrate the use of this method in a variety of cases relevant to materials science: Eshelby inclusions, fracture, and microstructure evolution. Reasonable scaling is demonstrated up to $\sim$4000 processors with tens of millions of grid points, and good AMR efficiency is observed.

cs.CE↗

arXiv2020

One-dimensional moving window atomistic framework to model long-time shock wave propagation

We develop a long-time moving window framework using Molecular Dynamics (MD) to model shock wave propagation through a one-dimensional chain of atoms. The domain is divided into a purely atomistic "window" region containing the shock wave flanked by boundary or "continuum" regions on either end. The dynamics of the window atoms are governed by classic MD equations of motion while continuum shock conditions are applied to the continuum atoms. Spurious wave reflections are removed by employing a damping band method using the Langevin thermostat applied locally to the continuum region. The moving window effect is achieved by adding/removing atoms to/from the window and boundary regions, and thus the shock wave front is focused at the center of the window region indefinitely. As a result, the required domain size is very small allowing us to model shock wave propagation for a long time. We simulate the shock through a one-dimensional chain of copper atoms using either the Lennard-Jones, modified Morse, or Embedded Atom Model (EAM) interatomic potential. We first perform verification studies to ensure proper implementation of the thermostat, potential functions, and damping band method, respectively. Next, we track the propagating shock and compare the actual shock velocity and average particle velocity to their corresponding analytical input values. From these comparisons, we optimize the linear shock Hugoniot relation for the given "lattice" orientation and compare these results to those in literature. When incorporated into the linear shock equation, these new Hugoniot parameters are shown to produce a stationary shock wave front. Finally, we perform one-dimensional moving window simulations of an unsteady, structured shock up to a few nanoseconds and characterize the increase in the shock front's width.

physics.comp-ph↗