Computationally Efficient Ersatz Models for Mechanical Structures and Refined Material Modeling

ABSTRACT We propose a novel approach for the accurate and efficient modeling of complex mechanical structures through a new class of surrogate models, termed Ersatz Models (EMs). Our method results in substantial computational speedups due to a drastic reduction in the number of degrees of freedom. In contrast to surrogate models relying on artificial neural networks, our approach is purely mechanistic, as EMs are abstract mechanical devices. To accurately reproduce the features of the modeled mechanical systems, EMs contain generalized external and internal degrees of freedom. Moreover, EMs feature inherent non‐affine kinematics and leverage exact knowledge of the material laws governing the constituents of the analyzed structure. Importantly, EMs naturally accommodate geometric and material nonlinearities, while explicitly adhering to fundamental mechanical principles such as power balance and internal equilibrium. Within the framework of computational homogenization, the numerical analysis of representative volume elements (RVEs) results in refined microstructure‐based constitutive relations. For increased computational efficiency, we suggest using EMs instead of direct FEM simulations of RVEs. EM‐based constitutive equations are objective and thermodynamically consistent. Since EMs contain a small number of tunable parameters, the data‐driven calibration and refinement of EMs is straightforward. This study outlines the underlying numerical algorithms and demonstrates the performance of EMs through academic examples. Examples show that EMs accelerate the simulation of visco‐elastic composites by several orders of magnitude, while still retaining acceptable accuracy. In a special example, EMs approximate the stress response of a geometrically and physically nonlinear model, showcasing their suitability for full‐scale FEM simulations.