Interaction-based material networks for efficiently estimating the homogenized behavior of microstructured materials

peer reviewedA material network, as pioneered by [1] and consisting of discrete material nodes and their interactions, is a data-driven reduced order model that can represent complex microstructure responses. The predictive capability of the material networks can be achieved thanks to its ability to learn the topology representation of the material microstructure. We investigate in this work the concept of material networks under the viewpoint of the network interactions, leading to so-called interaction-based material networks. Instead of relying on the micromechanics of multiple-phase laminates as considered in the other existing works, an 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. As a result, the interaction-based material network can be viewed as a trainable system involving fitting parameters, including not only the weights of the material nodes, which characterize their contribution into the network, but also the parameters characterizing their interactions. To make this material network being a surrogate of a full-field microscopic model, we propose two different training procedures in order to infer its fitting parameters. On the one hand, a nonlinear training procedure is proposed considering sequential data collected from finite element simulations on the full-field model subjected to proportional loading paths. On the other hand, a linear elastic training procedure considers only the elastic response of the heterogeneous material. The accuracy and efficiency of the proposed framework are demonstrated for multiplephases composites [2] and for porous materials [3] by comparing the predictions of the trained material networks with the ones of the direct numerical simulations in both contexts of virtual testing and multiscale simulations. [1] Z. Liu, C.T. Wu and M. Koishi, Computer Methods in Applied Mechanics and Engineering, 345:1138–1168, 2019. [2] V.-D. Nguyen and L. Noels, European Journal of Mechanics - A/Solids, 91, 2022. [3] V.-D. Nguyen and L. Noels, Interaction-based material network: a general framework for (porous) microstructured materials, submitted