  This paper extends the deep material network (DMN) proposed by Liu et al.
(2019) to tackle general 3-dimensional (3D) problems with arbitrary material
and geometric nonlinearities. It discovers a new way of describing multiscale
heterogeneous materials by a multi-layer network structure and mechanistic
building blocks. The data-driven framework of DMN is discussed in detail about
the offline training and online extrapolation stages. Analytical solutions of
the 3D building block with a two-layer structure in both small- and
finite-strain formulations are derived based on interfacial equilibrium
conditions and kinematic constraints. With linear elastic data generated by
direct numerical simulations on a representative volume element (RVE), the
network can be effectively trained in the offline stage using stochastic
gradient descent and advanced model compression algorithms. Efficiency and
accuracy of DMN on addressing the long-standing 3D RVE challenges with complex
morphologies and material laws are validated through numerical experiments,
including 1) hyperelastic particle-reinforced rubber composite with Mullins
effect; 2) polycrystalline materials with rate-dependent crystal plasticity; 3)
carbon fiber reinforced polymer (CFRP) composites with fiber anisotropic
elasticity and matrix plasticity. In particular, we demonstrate a three-scale
homogenization procedure of CFRP system by concatenating the microscale and
mesoscale material networks. The complete learning and extrapolation procedures
of DMN establish a reliable data-driven framework for multiscale material
modeling and design.
