A deep material network for multiscale topology learning and accelerated nonlinear modeling of heterogeneous materials

Abstract

Abstract In this paper, a new data-driven multiscale material modeling method, which we refer to as deep material network, is developed based on mechanistic homogenization theory of representative volume element (RVE) and advanced machine learning techniques . We propose to use a collection of connected mechanistic building blocks with analytical homogenization solutions to describe complex overall material responses which avoids the loss of essential physics in generic neural network . This concept is demonstrated for 2-dimensional RVE problems and network depth up to 7. Based on linear elastic RVE data from offline direct numerical simulations , the material network can be effectively trained using stochastic gradient descent with backpropagation algorithm , further enhanced by model compression methods . Importantly, the trained network is valid for any local material laws without the need for additional calibration or micromechanics assumption. Its extrapolations to unknown material and loading spaces for a wide range of problems are validated through numerical experiments, including linear elasticity with high contrast of phase properties, nonlinear history-dependent plasticity and finite-strain hyperelasticity under large deformations . By discovering a proper topological representation of RVE with fewer degrees of freedom , this intelligent material model is believed to open new possibilities of high-fidelity efficient concurrent simulations for a large-scale heterogeneous structure. It also provides a mechanistic understanding of structure–property relations across material length scales and enables the development of parameterized microstructural database for material design and manufacturing.