A review on data-driven constitutive laws for solids

JN Fuhg, G Anantha Padmanabha, N Bouklas… - … Methods in Engineering, 2024 - Springer
This review article highlights state-of-the-art data-driven techniques to discover, encode,
surrogate, or emulate constitutive laws that describe the path-independent and path …

Thermodynamics-based artificial neural networks for constitutive modeling

F Masi, I Stefanou, P Vannucci… - Journal of the Mechanics …, 2021 - Elsevier
Abstract Machine Learning methods and, in particular, Artificial Neural Networks (ANNs)
have demonstrated promising capabilities in material constitutive modeling. One of the main …

Sobolev training of thermodynamic-informed neural networks for interpretable elasto-plasticity models with level set hardening

NN Vlassis, WC Sun - Computer Methods in Applied Mechanics and …, 2021 - Elsevier
We introduce a deep learning framework designed to train smoothed elastoplasticity models
with interpretable components, such as the stored elastic energy function, yield surface, and …

Polyconvex anisotropic hyperelasticity with neural networks

DK Klein, M Fernández, RJ Martin, P Neff… - Journal of the Mechanics …, 2022 - Elsevier
In the present work, two machine learning based constitutive models for finite deformations
are proposed. Using input convex neural networks, the models are hyperelastic, anisotropic …

Neural networks for constitutive modeling: From universal function approximators to advanced models and the integration of physics

J Dornheim, L Morand, HJ Nallani, D Helm - Archives of Computational …, 2024 - Springer
Analyzing and modeling the constitutive behavior of materials is a core area in materials
sciences and a prerequisite for conducting numerical simulations in which the material …

Learning deep implicit Fourier neural operators (IFNOs) with applications to heterogeneous material modeling

H You, Q Zhang, CJ Ross, CH Lee, Y Yu - Computer Methods in Applied …, 2022 - Elsevier
Constitutive modeling based on continuum mechanics theory has been a classical approach
for modeling the mechanical responses of materials. However, when constitutive laws are …

Geometric deep learning for computational mechanics part i: Anisotropic hyperelasticity

NN Vlassis, R Ma, WC Sun - Computer Methods in Applied Mechanics and …, 2020 - Elsevier
We present a machine learning approach that integrates geometric deep learning and
Sobolev training to generate a family of finite strain anisotropic hyperelastic models that …

On physics-informed data-driven isotropic and anisotropic constitutive models through probabilistic machine learning and space-filling sampling

JN Fuhg, N Bouklas - Computer Methods in Applied Mechanics and …, 2022 - Elsevier
Data-driven constitutive modeling is an emerging field in computational solid mechanics
with the prospect of significantly relieving the computational costs of hierarchical …

Learning constitutive relations using symmetric positive definite neural networks

K Xu, DZ Huang, E Darve - Journal of Computational Physics, 2021 - Elsevier
We present a new neural-network architecture, called the Cholesky-factored symmetric
positive definite neural network (SPD-NN), for modeling constitutive relations in …

[HTML][HTML] Deep active learning for constitutive modelling of granular materials: From representative volume elements to implicit finite element modelling

T Qu, S Guan, YT Feng, G Ma, W Zhou… - International Journal of …, 2023 - Elsevier
Constitutive relation remains one of the most important, yet fundamental challenges in the
study of granular materials. Instead of using closed-form phenomenological models or …