The paper introduces a Gaussian‑process state‑space model (GP‑SSM) for constitutive modeling of quasi‑brittle materials, replacing traditional internal variables with latent states learned from stress‑strain data. The GP‑SSM provides uncertainty quantification, enforces physical constraints, and maps latent states and strain tensors to stress responses via a sparse multi‑output GP. The trained model is implemented in Abaqus/Explicit and validated through four cases, demonstrating accurate reproduction of RVE‑scale histories, confinement effects, unloading behavior, and structural responses comparable to the KCC model.
arXiv:2609.07294v1 Announce Type: new Abstract: Data-driven constitutive models for path-dependent plasticity are commonly formulated using nonlinear recurrent neural networks, whose sequential state...
The paper introduces a data‑driven constitutive modeling framework that treats a material as a functional mapping from its entire strain history to stress response. It uses neural operators with causal attention and spectral convolutions to predict full stress trajectories in a single parallel forward pass, enforcing temporal path dependence without relying on internal state variables. The method is validated on multidimensional, rate‑independent plasticity and ductile damage models, achieving accurate, resolution‑invariant predictions with excellent parallel efficiency.
The paper introduces a data‑driven constitutive modeling framework that treats a deforming material as a functional mapping from its entire strain history to the corresponding stress response. By training on full loading paths as function‑to‑function mappings, the model predicts complete stress trajectories in a single parallel forward pass, using causal attention to enforce temporal path dependence and spectral convolutions for discretization‑invariant representations. The approach is validated on multidimensional, rate‑independent material models, accurately capturing nonlinear plasticity and ductile damage while achieving resolution invariance and excellent parallel efficiency.
The paper introduces the Constitutive Parameterized Deep Energy Method (CPDEM), a physics‑driven neural network that embeds stochastic material parameters directly into the strain energy density functional. By training via expected energy minimization over the parameter domain, CPDEM learns a continuous solution manifold, enabling zero‑shot, real‑time inference of displacement fields for any material parameters without retraining or dataset generation. The method is validated on linear elasticity, finite‑strain hyperelasticity, and highly nonlinear contact mechanics, marking the first purely physics‑driven deep learning approach that efficiently handles continuous multi‑parameter variations in solid mechanics.
arXiv:2606. 08238v1 Announce Type: new Abstract: Constitutive modeling of the relationship between process-imposed material states and fundamental material properties is critical to control of material microstructure in manufacturing processes.
The paper introduces ADE‑FEMU, an end‑to‑end differentiable framework that embeds a constitutive neural network within a JAX‑based finite element solver and learns its parameters by minimizing a measurement‑mismatch loss using automatic differentiation. It demonstrates two neural network architectures—a flexible grey‑box CANN and an interpretable white‑box CANN—for incompressible isotropic hyperelastic materials, and validates the approach on three experimental datasets, including full‑field DIC, reduced‑data stretch profiles, and a heterogeneous matrix‑inclusion system.
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.
The paper introduces Thermodynamically Consistent Latent Dynamics Identification (tLaSDI) using parametric GENERIC Formalism-Informed Neural Networks (pGFINNs) to predict fracture patterns and evolution in heterogeneous materials. By embedding thermodynamic principles—such as total energy conservation and entropy generation—directly into the neural network architecture, the model operates in a lower‑dimensional latent space and maintains thermodynamic consistency on unseen data. A Geometry‑Conditioned Autoencoder further enhances geometry‑guided learning, and results show that tLaSDI‑pGFINNs outperform a purely data‑driven AE‑LSTM model in accurately capturing fracture behavior.
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.
GaussianBench is a physics‑fidelity evaluation suite designed for physics‑integrated Gaussian scene representations. It tests key physical properties—such as conservation, continuum response, material coupling, covariance transport, rendering, thermal phase change, and counterfactual response—using frozen scenes, simulator‑independent scorers, and analytical or measured references. The benchmark distinguishes physical failures from unsupported capabilities and invalid comparisons, and the authors also present GaussianFlesh, a thermomechanical reference system that couples rendering primitives with continuum material points via an MPM solver.
arXiv:2606. 04000v1 Announce Type: cross Abstract: We present a probabilistic modeling framework for incorporating small-scale spatial heterogeneity into macroscopic descriptions of material behavior for polycrystalline metallic materials.
The paper introduces a data‑driven framework for modeling the hyperelastic and viscoelastic behavior of digital materials made by multi‑material 3D printing. It extends a classical constitutive formulation by Bergström and Boyce, preserving multiplicative kinematics and invariant‑based strain‑energy functions while learning equilibrium and nonequilibrium parameters from multi‑rate uniaxial compression data across different compositions. The approach can either predict closed‑form model parameters as functions of composition or construct polyconvex strain‑energy functions using neural ordinary differential equations, ensuring thermodynamic consistency and capturing rate‑dependent stiffness and hysteresis.