The paper introduces a mesh‑free multiresolution deep energy method for phase‑field modeling of brittle fracture. A single neural network represents displacement and phase fields, trained by minimizing incremental energy with multiresolution B‑spline feature encoding and stratified Monte Carlo integration. Across six benchmark problems, the method reproduces load‑displacement curves and crack patterns with high accuracy, outperforming a deep Ritz baseline on a random multi‑crack dataset.
By Han Zhang, Mehrisadat Makki Alamdari, Babak Shahbodagh, Mohammad Vahab, Cosmin Anitescu, Timon Rabczuk, Elena Atroshchenko
Phase-field modeling of brittle fracture removes the need to track cracks explicitly by recasting their evolution as the minimization of an energy functional. In return it requires a discretization de...
arXiv:2606. 10909v1 Announce Type: cross Abstract: Reconstructing local stress fields in heterogeneous microstructures under non-linear, history-dependent loading remains a major computational bottleneck in multi-scale simulations.
By Manuel Ricardo Guevara Garban, Yves Chemisky, \'Etienne Pruli\`ere, Micha\"el Cl\'ement, Martin Abendroth, Bj\"orn Kiefer
arXiv:2607. 06479v1 Announce Type: new Abstract: Physics-informed neural networks (PINNs) provide a promising framework for solving partial differential equations while embedding the underlying physical laws directly into the learning process.
By Sonal Ankush Chibire, Jenn-Terng Gau, Bo Zhang
Physics-informed neural networks (PINNs) provide a promising framework for solving partial differential equations while embedding the underlying physical laws directly into the learning process. This study presents a PINN-based framework for modeling transient elastodynamic wave propagation in bimaterial systems governed by the axisymmetric equations of linear elasticity.
arXiv:2606. 08287v1 Announce Type: new Abstract: Finite element analysis (FEA) is essential for structural design but remains computationally expensive, particularly when evaluating multiple design iterations or load scenarios.
By Josiah D. Kunz, Kamal Choudhary
arXiv:2607. 09382v1 Announce Type: new Abstract: This work aims to develop a fast and physically consistent surrogate model for real-time structural health monitoring of fractured elastic domains.
By Rodolphe Barlogis, Ferhat Tamssaouet, Quentin Falcoz, St\'ephane Grieu
The paper introduces a variational, label‑free physics‑informed graph neural network (PI‑GNN) that models heterogeneous solid mechanics by embedding material heterogeneity into the discretization rather than the neural network’s trial field. The PI‑GNN operates on a conforming adaptive mesh graph, assigns constitutive behavior per element, and minimizes the discrete total potential energy without penalty terms or interface weights, yielding a discrete energy equivalent to the finite element Ritz functional. Across small‑strain elasticity and finite‑strain Neo‑Hookean hyperelasticity in 2D and 3D, the method achieves von Mises errors below 3.58 % over a wide stiffness‑contrast range, outperforming strong‑form PINNs and reducing displacement errors significantly.
By Aashay Rajan Yadav, Amiya Prakash Das, Ratna Kumar Annabattula
arXiv:2606. 05199v1 Announce Type: cross Abstract: The identification of constitutive neural network models from heterogeneous full-field deformation data provides a robust alternative to traditional calibration methods based on homogeneous stress-strain experiments, particularly given the high dimensionality of trainable parameters.
By Matthias Knipper, Chenyi Ji, Malte Brand, Kevin Linka
arXiv:2609.26426v1 Announce Type: new
Abstract: Finite Element Analysis (FEA) is widely used for transient mechanical simulations, but its high computational cost limits real-time and high-resolution...
By Georgios Triantafyllou, Panagiotis G. Kalozoumis, Dimitris K. Iakovidis
The paper introduces a differentiable finite element framework that discovers hyperelastic constitutive laws from limited experimental data, such as boundary-only displacement measurements and global reaction forces. By embedding the nonlinear finite element equilibrium problem into the learning loop, the method evaluates candidate strain‑energy densities through the deformation fields they produce, enforcing mechanical equilibrium as a constraint. The constitutive response is modeled with Hyperelastic Neural Networks, a structure‑preserving class that guarantees physical admissibility, including residual energy and stress‑free conditions, frame indifference, isotropic symmetry, polyconvexity, coercivity, and controlled volumetric growth. Numerical experiments in two and three dimensions show accurate recovery of hyperelastic isotropic responses, robustness to noise, and generalization across geometries, loading, and boundary conditions.
By Francesco Regazzoni
arXiv:2606. 28996v1 Announce Type: new Abstract: Short-fiber thermoplastic (SFT) composites are increasingly employed in lightweight aerospace and automotive structures owing to their favorable strength-to-weight ratio, high production rates, and recyclability.
By Pharindra Pathak (Auburn University, Oakridge National Lab, NASA Glenn Research Center, Auburn University, Auburn University), Vipin Kumar (Auburn University, Oakridge National Lab, NASA Glenn Research Center, Auburn University, Auburn University), Trenton M. Ricks (Auburn University, Oakridge National Lab, NASA Glenn Research Center, Auburn University, Auburn University), Suhasini Gururaja (Auburn University, Oakridge National Lab, NASA Glenn Research Center, Auburn University, Auburn University), Siddhartha Srivastava (Auburn University, Oakridge National Lab, NASA Glenn Research Center, Auburn University, Auburn University)