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.
By Rishabh Arora, Lisa Scheunemann, Tim Brepols, Shahed Rezaei
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)
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
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: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: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: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: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
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:2608. 13826v1 Announce Type: cross Abstract: Machine learning is increasingly used to learn structure property relationships from spectroscopic and diffraction data, yet its adoption in materials discovery is often limited by poor interpretability of model predictions.
By Aditya Raghavan, Utkarsh Pratiush, Dalton A. Pearl, Jade Holliman Jr, Katharine Page, Philip D Rack, Sergei V Kalinin