Redefinition of the interactions in Deep-Material-Networks

A material network consists of discrete material nodes whose interactions are defined by data-driven approaches. The material networks can represent complex non-linear microstructure responses at a reduced computational cost, while ensuring thermodynamic consistency and extrapolation capabilities in terms of the loading and phase behaviors. Instead of relying on the micromechanics of multiple-phase laminates as considered in the literature to define the nodes interactions, in this work we investigate two alternatives. In the first one, we reformulate the concept of material networks under the viewpoint of the network interactions, leading to the so-called interaction-based material networks. This interaction-based material network relies on constraining all requirements of a truly microscopic boundary value problem including the stress and strain averaging principles and the Hill-Mandel energetically consistent condition. This approach is shown to be accurate and efficient for multiple-phase non-linear composites and for non-linear porous materials. In the second approach, Mean-Field Homogenization and laminate theories are considered to define the interactions in order to represent the behavior of woven composite materials. Because of the added physics at the interaction level, the number of nodes defining the material network can be drastically reduced.