A review on data-driven constitutive laws for solids
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 …
surrogate, or emulate constitutive laws that describe the path-independent and path …
Neural networks meet hyperelasticity: A guide to enforcing physics
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 …
which fulfills all common constitutive conditions by construction, and in particular, is …
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 …
mechanics, has resulted in an extensive and diverse body of literature. To help researchers …
Efficient multiscale modeling of heterogeneous materials using deep neural networks
Material modeling using modern numerical methods accelerates the design process and
reduces the costs of developing new products. However, for multiscale modeling of …
reduces the costs of developing new products. However, for multiscale modeling of …
[HTML][HTML] Neural network-based multiscale modeling of finite strain magneto-elasticity with relaxed convexity criteria
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 …
on physics-augmented neural networks (NNs). By using a set of problem specific invariants …
Two-stage 2D-to-3D reconstruction of realistic microstructures: Implementation and numerical validation by effective properties
Realistic microscale domains are an essential step towards making modern multiscale
simulations more applicable to computational materials engineering. For this purpose, 3D …
simulations more applicable to computational materials engineering. For this purpose, 3D …
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 …
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
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 …
(FLV) or quasi-linear viscoelastic (QLV) models. These popular models are simplifications …
Physics‐constrained symbolic model discovery for polyconvex incompressible hyperelastic materials
We present a machine learning framework capable of consistently inferring mathematical
expressions of hyperelastic energy functionals for incompressible materials from sparse …
expressions of hyperelastic energy functionals for incompressible materials from sparse …
Deep homogenization networks for elastic heterogeneous materials with two-and three-dimensional periodicity
We present a deep learning framework that leverages computational homogenization
expertise to predict the local stress field and homogenized moduli of heterogeneous …
expertise to predict the local stress field and homogenized moduli of heterogeneous …