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.
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...
By Rui Barreira, Taylan Soydan, Francesco Scipione, Miguel A. Bessa, Dirk Mohr
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.
By Josu\'e Garc\'ia-\'Avila (Department of Mechanical Engineering, Columbia University, New York City, USA), Beijun Shen (Department of Mechanical Engineering, Columbia University, New York City, USA), Manuel K. Rausch (Department of Aerospace Engineering and Engineering Mechanics, University of Texas at Austin, Austin, USA, Department of Biomedical Engineering, University of Texas at Austin, Austin, USA, Department of Mechanical Engineering, University of Texas at Austin, Austin, USA), Mary C. Boyce (Department of Mechanical Engineering, Columbia University, New York City, USA), Adri\'an Buganza-Tepole (Department of Mechanical Engineering, Columbia University, New York City, USA)
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. 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: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.
By Chenyi Ji, Kian P. Abdolazizi, Hagen Holthusen, Christian J. Cyron, Kevin Linka
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.
By Hagen Holthusen, Paul Steinmann, Ellen Kuhl
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: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.
By Hyeonbin Moon, Donghyuk Cho, Jecheon Yu, Jeong Whan Yoon, Seunghwa Ryu
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
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.
By Pouria Behnoudfar, Deekshith Naidu Ponnana, Noah J. Schmelzer, Janith Wanni, George T. Gray III, Dan J. Thoma, Curt A. Bronkhorst, Nan Chen, Wenxiao Pan
arXiv:2607. 19060v1 Announce Type: cross Abstract: Fast prediction of the response of adhesive soft viscoelastic contacts represents a current challenge in soft robotics and for gripping and manipulation tasks.
By Ali Maghami, Merten Stender, Michele Ciavarella, Antonio Papangelo