← Back to all news
arXiv AI 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)

Data-Driven Discovery of Composition-Dependent Constitutive Models for Hyperelasticity and Viscoelasticity of Digital Materials

Read the original on arXiv AI →

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.

Machine-generated by The Flow from the publisher's headline and feed description — not written or checked by a human. The full article lives at arXiv AI.

Related stories

arXiv Machine Learning
Sep 10

Hyperelastic constitutive model discovery with differentiable finite elements and structure-preserving neural networks

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
More like this →
arXiv Machine Learning
Sep 3

Learning the Constitutive Behavior of Materials via Neural Operators and Causal Attention: Case Studies in Plasticity and Damage

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
More like this →
Hugging Face Trending Papers
Sep 2

Learning the Constitutive Behavior of Materials via Neural Operators and Causal Attention: Case Studies in Plasticity and Damage

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.

More like this →