Multiscale modeling of inelastic materials with Thermodynamics-based Artificial Neural Networks (TANN)

Abstract

The mechanical behavior of inelastic materials with microstructure is very complex and hard to grasp with heuristic, empirical constitutive models. For this purpose, multiscale, homogenization approaches are often used for performing reliable, accurate predictions of the macroscopic mechanical behavior of solids and structures. Nevertheless, the calculation cost of such approaches is extremely high and prohibitive for real-scale applications involving inelastic materials. Here, we propose the so-called Thermodynamics-based Artificial Neural Networks (TANN) for the constitutive modeling of materials with inelastic and complex microstructure. Our approach integrates thermodynamics-aware dimensionality reduction techniques and thermodynamics-based deep neural networks to identify, in an autonomous way, the constitutive laws and discover the internal state variables of complex inelastic materials. The efficiency and accuracy of TANN in predicting the average and local stress-strain response, the free-energy and the dissipation rate is demonstrated for both regular and perturbed two- and three-dimensional lattice microstructures in inelasticity. TANN manage to identify the internal state variables that characterize the inelastic deformation of the complex microstructural fields. These internal state variables are then used to reconstruct the microdeformation fields of the microstructure at a given state. Finally, a double-scale homogenization scheme (FEMxTANN) is used to solve a large scale boundary value problem. The high performance of the homogenized model using TANN is illustrated through detailed comparisons with microstructural calculations at large scale. An excellent agreement is shown for a variety of monotonous and cyclic stress-strain paths.

References in corpus (6)

• A Physics-Guided Neural Network Framework for Elastic Plates: Comparison of Governing Equations-Based and Energy-Based Approaches
• Interfacing Finite Elements with Deep Neural Operators for Fast Multiscale Modeling of Mechanics Problems
• Thermodynamics-informed graph neural networks
• Learning nonlocal constitutive models with neural networks
• A robust solution of a statistical inverse problem in multiscale computational mechanics using an artificial neural network
• Physics-informed cluster analysis and a priori efficiency criterion for the construction of local reduced-order bases

Cited by in corpus (20)

• A new family of Constitutive Artificial Neural Networks towards automated model discovery
• Neural networks meet hyperelasticity: A guide to enforcing physics
• Deep Learning in Deterministic Computational Mechanics
• FE${}^{\text{ANN}}$ $-$ An efficient data-driven multiscale approach based on physics-constrained neural networks and automated data mining
• Theory and implementation of inelastic Constitutive Artificial Neural Networks
• Physically recurrent neural networks for path-dependent heterogeneous materials: embedding constitutive models in a data-driven surrogate
• Integrated Finite Element Neural Network (I-FENN) for non-local continuum damage mechanics
• A comparative study on different neural network architectures to model inelasticity
• Evolution TANN and the identification of internal variables and evolution equations in solid mechanics
• Two-stage 2D-to-3D reconstruction of realistic microstructures: Implementation and numerical validation by effective properties
• Neural integration for constitutive equations using small data
• A generalized dual potential for inelastic Constitutive Artificial Neural Networks: A JAX implementation at finite strains
• Physics-Aware Neural Implicit Solvers for multiscale, parametric PDEs with applications in heterogeneous media
• A Complement to Neural Networks for Anisotropic Inelasticity at Finite Strains
• Experimental Learning of a Hyperelastic Behavior with a Physics-Augmented Neural Network
• Mesh d-refinement: a data-based computational framework to account for complex material response
• A physics-augmented neural network framework for finite strain incompressible viscoelasticity
• Learning inelastic constitutive models from stress-strain data under hard thermodynamic constraints
• Reversible and irreversible bracket-based dynamics for deep graph neural networks
• Hetero-EUCLID: Interpretable model discovery for heterogeneous hyperelastic materials using stress-unsupervised learning