Abstract :
[en] A 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.
