arXiv:2603. 28707v3 Announce Type: replace-cross Abstract: We present a physics-based neural network framework for the discovery of constitutive models in fully coupled thermomechanics.
arXiv:2602. 17750v2 Announce Type: replace-cross Abstract: A key problem of solid mechanics is the identification of the constitutive law of a material, that is, the relation between strain history and stress.
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.
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 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.
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 presents a novel multi‑agent approach to generating physics‑constrained constitutive models using large language models (LLMs). A Creator agent proposes a model tailored to the data, while an Inspector agent audits each proposal against nine physical constraints and requests refinement if violations occur. Experiments with constitutive artificial neural networks on brain tissue, rubber, and porcine skin show that adding the Inspector increases the proportion of models passing all checks from 90 % to 95 % for Claude Opus 4.7 and from 47 % to 60 % for Kimi K2.5, while the resulting models match or exceed expert‑designed models in accuracy and generalization.
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.
Nonlinear GENERIC-Embedded Neural Networks (N-GENNs) are a deep learning framework designed to discover evolution equations for systems governed by the nonlinear GENERIC formalism. The method incorporates generalized gradient flows through convex dissipation potentials, allowing it to capture a wider range of thermodynamically consistent dynamics, including those with non‑quadratic dissipation potentials. Thermodynamic structure is enforced by construction, ensuring compliance with the first and second laws, and the approach is validated on a harmonic oscillator with a heat bath, an idealized chemical motor, and a one‑dimensional viscoplastic Perzyna model.
arXiv:2606. 01179v1 Announce Type: cross Abstract: Entropy production governs irreversibility and uncertainty in both physical and information-theoretic systems.
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...
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.
arXiv:2606. 19375v1 Announce Type: new Abstract: Identifying anisotropic yield functions remains challenging since yielding is not directly observed in full-field mechanical measurements, directional calibration can require many loading directions, and selecting an appropriate analytical form is nontrivial.