A Deep Material Network for Multiscale Topology Learning and Accelerated Nonlinear Modeling of Heterogeneous Materials
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The discovery of efficient and accurate descriptions for the macroscopic constitutive behavior of heterogeneous materials with complex microstructure remains an outstanding challenge in mechanics. The difficulty of finding the macroscopic responses becomes apparent when material or geometric nonlinearities (e.g. irreversible plasticity, large deformations) are considered. 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. Inspired by the basic concept in artificial neural networks, we use a collection of connected simple building blocks with analytical homogenization solutions to describe complex overall material responses. With linear elastic RVE data from offline direct numerical simulations (DNS), the material network can be effectively trained using stochastic gradient descent with backpropagation algorithm, enhanced by various model compression methods. Furthermore, extrapolations of the trained network to a wide range of problems are also 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 parametrized microstructural database for material design and manufacturing.
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