Deep learning in computational mechanics: a review

L Herrmann, S Kollmannsberger - Computational Mechanics, 2024 - Springer
The rapid growth of deep learning research, including within the field of computational
mechanics, has resulted in an extensive and diverse body of literature. To help researchers …

Neural networks meet hyperelasticity: A guide to enforcing physics

L Linden, DK Klein, KA Kalina, J Brummund… - Journal of the …, 2023 - Elsevier
In the present work, a hyperelastic constitutive model based on neural networks is proposed
which fulfills all common constitutive conditions by construction, and in particular, is …

[HTML][HTML] Automated discovery of generalized standard material models with EUCLID

M Flaschel, S Kumar, L De Lorenzis - Computer Methods in Applied …, 2023 - Elsevier
We extend the scope of our recently developed approach for unsupervised automated
discovery of material laws (denoted as EUCLID) to the general case of a material belonging …

FE: an efficient data-driven multiscale approach based on physics-constrained neural networks and automated data mining

KA Kalina, L Linden, J Brummund, M Kästner - Computational Mechanics, 2023 - Springer
Herein, we present a new data-driven multiscale framework called FE ANN which is based
on two main keystones: the usage of physics-constrained artificial neural networks (ANNs) …

[HTML][HTML] Neural network-based multiscale modeling of finite strain magneto-elasticity with relaxed convexity criteria

KA Kalina, P Gebhart, J Brummund, L Linden… - Computer Methods in …, 2024 - Elsevier
We present a framework for the multiscale modeling of finite strain magneto-elasticity based
on physics-augmented neural networks (NNs). By using a set of problem specific invariants …

Extreme sparsification of physics-augmented neural networks for interpretable model discovery in mechanics

JN Fuhg, RE Jones, N Bouklas - Computer Methods in Applied Mechanics …, 2024 - Elsevier
Data-driven constitutive modeling with neural networks has received increased interest in
recent years due to its ability to easily incorporate physical and mechanistic constraints and …

A comparative study on different neural network architectures to model inelasticity

M Rosenkranz, KA Kalina, J Brummund… - … Journal for Numerical …, 2023 - Wiley Online Library
The mathematical formulation of constitutive models to describe the path‐dependent, that is,
inelastic, behavior of materials is a challenging task and has been a focus in mechanics …

[HTML][HTML] Viscoelastic constitutive artificial neural networks (vCANNs)–A framework for data-driven anisotropic nonlinear finite viscoelasticity

KP Abdolazizi, K Linka, CJ Cyron - Journal of Computational Physics, 2024 - Elsevier
The constitutive behavior of polymeric materials is often modeled by finite linear viscoelastic
(FLV) or quasi-linear viscoelastic (QLV) models. These popular models are simplifications …

[HTML][HTML] Physics-augmented neural networks for constitutive modeling of hyperelastic geometrically exact beams

JO Schommartz, DK Klein, JCA Cobo… - Computer Methods in …, 2025 - Elsevier
We present neural network-based constitutive models for hyperelastic geometrically exact
beams. The proposed models are physics-augmented, ie, formulated to fulfill important …

Multiscale modeling of functionally graded shell lattice metamaterials for additive manufacturing

M Shojaee, I Valizadeh, DK Klein, P Sharifi… - Engineering with …, 2024 - Springer
In this work, an experimentally validated multiscale modeling framework for additively
manufactured shell lattice structures with graded parameters is introduced. It is exemplified …