A physics-augmented neural network framework for finite strain incompressible viscoelasticity

Abstract

We propose a physics-augmented neural network (PANN) framework for finite strain incompressible viscoelasticity within the generalized standard materials theory. The formulation is based on the multiplicative decomposition of the deformation gradient and enforces unimodularity of the inelastic deformation part throughout the evolution. Invariant-based representations of the free energy and the dual dissipation potential by monotonic and fully input-convex neural networks ensure thermodynamic consistency, objectivity, and material symmetry by construction. The evolution of the internal variables during training is handled by solving the evolution equations using an implicit exponential time integrator. In addition, a trainable gate layer combined with lp regularization automatically identifies the required number of internal variables during training. The PANN is calibrated with synthetic and experimental data, showing excellent agreement for a wide range of deformation rates and different load paths. We also show that the proposed model achieves excellent interpolation as well as plausible and accurate extrapolation behaviors. In addition, we demonstrate consistency of the PANN with linear viscoelasticity by linearization of the full model.

References in corpus (27)

• Thermodynamics-based Artificial Neural Networks for constitutive modeling
• Unsupervised discovery of interpretable hyperelastic constitutive laws
• Physics informed neural networks for continuum micromechanics
• Geometric deep learning for computational mechanics Part I: Anisotropic Hyperelasticity
• Multiscale modeling of inelastic materials with Thermodynamics-based Artificial Neural Networks (TANN)
• NN-EUCLID: deep-learning hyperelasticity without stress data
• Neural networks meet hyperelasticity: A guide to enforcing physics
• Automated discovery of generalized standard material models with EUCLID
• FE${}^{\text{ANN}}$ $-$ An efficient data-driven multiscale approach based on physics-constrained neural networks and automated data mining
• Data-driven Tissue Mechanics with Polyconvex Neural Ordinary Differential Equations
• Physics-Informed Neural Networks for Shell Structures
• Theory and implementation of inelastic Constitutive Artificial Neural Networks
• Variational Onsager Neural Networks (VONNs): A thermodynamics-based variational learning strategy for non-equilibrium PDEs
• A comparative study on different neural network architectures to model inelasticity
• Modular machine learning-based elastoplasticity: generalization in the context of limited data
• Automated identification of linear viscoelastic constitutive laws with EUCLID
• Data-driven anisotropic finite viscoelasticity using neural ordinary differential equations
• Consistent machine learning for topology optimization with microstructure-dependent neural network material models
• Neural integration for constitutive equations using small data
• When invariants matter: The role of I1 and I2 in neural network models of incompressible hyperelasticity
• A generalized dual potential for inelastic Constitutive Artificial Neural Networks: A JAX implementation at finite strains
• A Complement to Neural Networks for Anisotropic Inelasticity at Finite Strains
• Input convex neural networks: universal approximation theorem and implementation for isotropic polyconvex hyperelastic energies
• Rate- and temperature-dependent ductile-to-brittle fracture transition: Experimental investigation and phase-field analysis for toffee
• In search of constitutive conditions in isotropic hyperelasticity: polyconvexity versus true-stress-true-strain monotonicity
• Precise, efficient and flexible modeling of crystallizing elastomers based on physics-augmented neural networks
• A Direct-adjoint Approach for Material Point Model Calibration with Application to Plasticity