Efficient surrogate models for microstructured materials based on interaction-based material networks

A material network consists of discrete material nodes whose interactions are defined by datadriven approaches. In this work, we investigate the concept of material networks from the viewpoint of network interactions, leading to interaction-based material networks [1,2]. The developed material networks can represent complex non-linear microstructure responses at a reduced computational cost while ensuring thermodynamic consistency and extrapolation capabilities in terms of loading and phase behaviours. Instead of relying on the micromechanical of multiple-phase laminates as considered in the literature to define the interactions of the material nodes, we formulate the concept of material networks relying 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. [1] Nguyen, V. D., & Noels, L. (2022). Micromechanics-based material networks revisited from
the interaction viewpoint; robust and efficient implementation for multi-phase
composites. European Journal of Mechanics - A/Solids, 91, 104384.
[2] Nguyen, V. D., & Noels, L. (2022). Interaction-based material network: A general
framework for (porous) microstructured materials. Computer Methods in Applied Mechanics and Engineering, 389, 114300.