Micromechanics-based material networks revisited from the interaction viewpoint; robust and efficient implementation for multi-phase composites

Abstract A material network consists of discrete material nodes, which, when interacting, can represent complex microstructure responses. In this work, we investigate this concept of material networks under the viewpoint of the hierarchical network interactions. Within this viewpoint, the response of the material network is governed by a well-defined system of equations and an arbitrary number of phases can be considered, independently of the network architecture. The predictive capability is achieved by, on the one hand, sufficiently deep and rich network interactions to tie the discrete material nodes together, and, on the other hand, an efficient offline training procedure. For this purpose, a unified and efficient framework for an arbitrary network architecture is developed, not only for the offline training, but also for the online evaluation. The efficiency and prediction accuracy of the material network as a surrogate of a homogenization-based multiscale model in predicting the stress–strain response in both contexts of a virtual test and of FE 2 multiscale simulations are demonstrated through numerical examples with two-phase and three-phase fiber-reinforced composites.