172 citations · 463 across the 11 of their papers we have counts for
11 papers
Construction of minimal integrity basis for anisotropic hyperelasticity via structural tensors
Brain M. Riemer, Jörg Brummund, Karl A. Kalina +3
We present minimal integrity bases for all common anisotropies in hyperelasticity via the structural tensor concept, which can be used to formulate any algebraic invariant function…
A physics-augmented neural network framework for finite strain incompressible viscoelasticity
Karl A. Kalina, Jörg Brummund, Markus Kästner
We propose a physics-augmented neural network (PANN) framework for finite strain incompressible viscoelasticity within the generalized standard materials theory. The formulation is…
A dual-stage constitutive modeling framework based on finite strain data-driven identification and physics-augmented neural networks
Lennart Linden, Karl A. Kalina, Jörg Brummund +2
In this contribution, we present a novel consistent dual-stage approach for the automated generation of hyperelastic constitutive models which only requires experimentally measurab…
Neural networks meet anisotropic hyperelasticity: A framework based on generalized structure tensors and isotropic tensor functions
Karl A. Kalina, Jörg Brummund, WaiChing Sun +1
We present a data-driven framework for the multiscale modeling of anisotropic finite strain elasticity based on physics-augmented neural networks (PANNs). Our approach allows the e…
Viscoelasticty with physics-augmented neural networks: Model formulation and training methods without prescribed internal variables
Max Rosenkranz, Karl A. Kalina, Jörg Brummund +2
We present an approach for the data-driven modeling of nonlinear viscoelastic materials at small strains which is based on physics-augmented neural networks (NNs) and requires only…
Neural network-based multiscale modeling of finite strain magneto-elasticity with relaxed convexity criteria
Karl A. Kalina, Philipp Gebhart, Jörg Brummund +3
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 invarian…
A comparative study on different neural network architectures to model inelasticity
Max Rosenkranz, Karl A. Kalina, Jörg Brummund +1
The mathematical formulation of constitutive models to describe the path-dependent, i.e., inelastic, behavior of materials is a challenging task and has been a focus in mechanics r…
Neural networks meet hyperelasticity: A guide to enforcing physics
Lennart Linden, Dominik K. Klein, Karl A. Kalina +3
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…
Overview of phase-field models for fatigue fracture in a unified framework
Martha Kalina, Tom Schneider, Jörg Brummund +1
In the last ten years, the phase-field method has gained much attention as a novel method to simulate fracture due to its straightforward way allowing to cover crack initiation and…
FE An efficient data-driven multiscale approach based on physics-constrained neural networks and automated data mining
Karl A. Kalina, Lennart Linden, Jörg Brummund +1
Herein, we present a new data-driven multiscale framework called FE which is based on two main keystones: the usage of physics-constrained artificial neural networks…
Phase-field modeling of fracture in heterogeneous materials -- jump conditions, convergence and crack propagation
Arne Claus Hansen-Dörr, Jörg Brummund, Markus Kästner
In this contribution, a variational diffuse modeling framework for cracks in heterogeneous media is presented. A static order parameter smoothly bridges the discontinuity at materi…