Physics informed neural networks for continuum micromechanics

Abstract

Recently, physics informed neural networks have successfully been applied to a broad variety of problems in applied mathematics and engineering. The principle idea is to use a neural network as a global ansatz function to partial differential equations. Due to the global approximation, physics informed neural networks have difficulties in displaying localized effects and strong non-linear solutions by optimization. In this work we consider material non-linearities invoked by material inhomogeneities with sharp phase interfaces. This constitutes a challenging problem for a method relying on a global ansatz. To overcome convergence issues, adaptive training strategies and domain decomposition are studied. It is shown, that the domain decomposition approach is able to accurately resolve nonlinear stress, displacement and energy fields in heterogeneous microstructures obtained from real-world $\mu$CT-scans.

https://www.sciencedirect.com/science/article/pii/S0045782522001268?via%3Dihub

References in corpus (4)

• Understanding and mitigating gradient pathologies in physics-informed neural networks
• On physics-informed data-driven isotropic and anisotropic constitutive models through probabilistic machine learning and space-filling sampling
• Physics-Informed Neural Networks for Nonhomogeneous Material Identification in Elasticity Imaging
• A deep learning driven pseudospectral PCE based FFT homogenization algorithm for complex microstructures

Cited by in corpus (32)

• Transfer learning based physics-informed neural networks for solving inverse problems in engineering structures under different loading scenarios
• Deep Learning in Deterministic Computational Mechanics
• Recent Advances and Applications of Machine Learning in Experimental Solid Mechanics: A Review
• Mixed formulation of physics-informed neural networks for thermo-mechanically coupled systems and heterogeneous domains
• Physics-informed radial basis network (PIRBN): A local approximating neural network for solving nonlinear PDEs
• Theory and implementation of inelastic Constitutive Artificial Neural Networks
• Enhanced physics-informed neural networks for hyperelasticity
• Integrated Finite Element Neural Network (I-FENN) for non-local continuum damage mechanics
• A comparative study on different neural network architectures to model inelasticity
• Three-dimensional microstructure generation using generative adversarial neural networks in the context of continuum micromechanics
• Deep energy method in topology optimization applications
• MAgNET: A Graph U-Net Architecture for Mesh-Based Simulations
• Reduced and All-at-Once Approaches for Model Calibration and Discovery in Computational Solid Mechanics
• Error convergence and engineering-guided hyperparameter search of PINNs: towards optimized I-FENN performance
• Physics-informed neural networks for understanding shear migration of particles in viscous flow
• I-FENN for thermoelasticity based on physics-informed temporal convolutional network (PI-TCN)
• Stochastic stiffness identification and response estimation of Timoshenko beams via physics-informed Gaussian processes
• Data-driven rheological characterization of stress buildup and relaxation in thermal greases
• Micromechanics-Informed Parametric Deep Material Network for Physics Behavior Prediction of Heterogeneous Materials with a Varying Morphology
• When invariants matter: The role of I1 and I2 in neural network models of incompressible hyperelasticity
• Physics-Informed Holomorphic Neural Networks (PIHNNs): Solving Linear Elasticity Problems
• Deep learning for full-field ultrasonic characterization
• A mixed formulation for physics-informed neural networks as a potential solver for engineering problems in heterogeneous domains: comparison with finite element method
• Input convex neural networks: universal approximation theorem and implementation for isotropic polyconvex hyperelastic energies
• Hybrid data-driven and physics-informed regularized learning of cyclic plasticity with Neural Networks
• Precise, efficient and flexible modeling of crystallizing elastomers based on physics-augmented neural networks
• Deterministic and statistical calibration of constitutive models from full-field data with parametric physics-informed neural networks
• Multiscale Analysis of Woven Composites Using Hierarchical Physically Recurrent Neural Networks
• Empirical Hyper Element Integration Method (EHEIM) with Unified Integration Criteria for Efficient Hyper Reduced FE${}^2$ Simulations
• Fast meta-solvers for 3D complex-shape scatterers using neural operators trained on a non-scattering problem
• A physics-augmented neural network framework for finite strain incompressible viscoelasticity
• Predicting Stress in Two-phase Random Materials and Super-Resolution Method for Stress Images by Embedding Physical Information