Hybrid Physically Recurrent Neural Network Surrogate for Multiscale Analysis of Metal Matrix Composites
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Particle‑reinforced metal matrix composites (MMCs) exhibit complex mechanical responses governed by the interaction between an elasto‑plastic metallic matrix and stiff elastic inclusions at the microscale. Accurately capturing this behavior at the structural scale typically requires multiscale finite element formulations, such as computational homogenization or FE². In this approach, a representative volume element (RVE) boundary value problem is nested to each integration point at the macroscale [1]. Although highly predictive, these simulations rapidly become prohibitively expensive for nonlinear problems and large structures. This contribution expands the applicability of Physically Recurrent Neural Networks (PRNNs), a recently proposed hybrid surrogate model for accelerating FE² simulations, from fiber reinforced laminates to particle reinforced MMCs [2]. The key idea is to replace the full RVE boundary value problem with a new neural architecture in which classical elasto plastic constitutive relations are explicitly embedded, thus preserving path and history dependence while substantially reducing the computational cost of the microscopic problem. The training data are generated from virtual RVEs with random particulate distributions, where the metallic matrix obeys a J2 elasto‑plastic model and the inclusions remain linear elastic. The proposed surrogate is assessed in terms of accuracy and computational speed‑up with respect to full FE² simulations and to macroscopic homogenized models such as incremental Mori–Tanaka or Tamura–Tomota–Ozawa‑type schemes. Numerical examples investigate monotonic and non‑proportional loading paths, highlighting the ability of the PRNN to reproduce path dependent nonlinear behavior, including arbitrary unloading and reloading. The results demonstrate that the hybrid architecture can achieve substantial reductions in computational cost while retaining the physical interpretability of classical constitutive modeling, making it a promising tool for nonlinear structural analysis of MMC components.
