Operator Learning for Inelastic Homogenization
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Homogenization enables the modeling and simulation of multiscale material behaviors directly at the application scale. However, evaluating a homogenized constitutive model often requires repeated, computationally expensive micromechanical simulations. To address this bottleneck, we propose an operator learning framework that learns homogenized constitutive models from micromechanical simulations to accelerate macroscopic analysis. A key attribute of our approach is the use of Markovian recurrent Fourier neural operators, designed to capture both history- and microstructure-dependence in the macroscopic behavior of inelastic materials. We provide theoretical and numerical results supporting this framework. In particular, we prove a universal approximation theorem demonstrating that the proposed model has the capacity to homogenize two-scale Kelvin-Voigt viscoelasticity with arbitrary accuracy.
