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In this paper, a new data-driven multiscale material modeling method, whichwe refer to as deep material network, is developed based on mechanistichomogenization theory of representative volume element (RVE) and advancedmachine learning techniques. We propose to use a collection of connectedmechanistic building blocks with analytical homogenization solutions whichavoids the loss of essential physics in generic neural networks, and thisconcept is demonstrated for 2-dimensional RVE problems and network depth up to7. Based on linear elastic RVE data from offline direct numerical simulations,the material network can be effectively trained using stochastic gradientdescent with backpropagation algorithm, enhanced by model compression methods.Importantly, the trained network is valid for any local material laws withoutthe need for additional calibration or micromechanics assumption. Itsextrapolations to unknown material and loading spaces for a wide range ofproblems are validated through numerical experiments, including linearelasticity with high contrast of phase properties, nonlinear history-dependentplasticity and finite-strain hyperelasticity under large deformations.  By discovering a proper topological representation of RVE with fewer degreesof freedom, this intelligent material model is believed to open newpossibilities of high-fidelity efficient concurrent simulations for alarge-scale heterogeneous structure. It also provides a mechanisticunderstanding of structure-property relations across material length scales andenables the development of parameterized microstructural database for materialdesign and manufacturing.

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