Abstract: We propose a novel approach for the accurate and efficient modeling of complex mechanical structures througha new class of surrogate models, termed Ersatz Models (EMs). Our method results in substantial computationalspeedups due to a drastic reduction in the number of degrees of freedom. In contrast to surrogate models relying onartificial neural networks, our approach is purely mechanistic, as EMs are abstract mechanical devices. To accuratelyreproduce the features of the modeled mechanical systems, EMs contain generalized external and internal degreesof freedom. Moreover, EMs feature inherent non-affine kinematics and leverage exact knowledge of the materiallaws governing the constituents of the analyzed structure. Importantly, EMs naturally accommodate geometricand material nonlinearities, while explicitly adhering to fundamental mechanical principles such as power balanceand internal equilibrium. Within the framework of computational homogenization, the numerical analysis ofrepresentative volume elements (RVEs) results in refined microstructure-based constitutive relations. For increasedcomputational efficiency, we suggest using EMs instead of direct FEM simulations of RVEs. EM-based constitutiveequations 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 numericalalgorithms and demonstrates the performance of EMs through academic examples. Examples show that EMsaccelerate the simulation of visco-elastic composites by several orders of magnitude, while still retaining acceptableaccuracy. In a special example, EMs approximate the stress response of a geometrically and physically nonlinearmodel, showcasing their suitability for full-scale FEM simulations

Cite: Shutov A.V. , Ufimzev K.P.
Computationally Efficient Ersatz Models for Mechanical Structures and Refined Material Modeling
ZAMM Zeitschrift fur Angewandte Mathematik und Mechanik. 2026. V.106. N8. 106:e70531 :1-35. DOI: 10.1002/zamm.70531 WOS Scopus OpenAlex

Dates:

Submitted:	Jan 22, 2026
Accepted:	Jul 11, 2026

Identifiers:

≡ Web of science:	WOS:001836836200001
≡ Scopus:	2-s2.0-105046244265
≡ OpenAlex:	W4396851049

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