TY - JOUR

T1 - Computationally Efficient Ersatz Models for Mechanical Structures and Refined Material Modeling

AU - Shutov, A. V.

AU - Ufimzev, K. P.

N1 - A. V. Shutov and K. P. Ufimzev, “ Computationally Efficient Ersatz Models for Mechanical Structures and Refined Material Modeling.” ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik 106, no. 8 (2026): e70531. https://doi.org/10.1002/zamm.70531

PY - 2026/7/31

Y1 - 2026/7/31

N2 - 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.

AB - 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.

KW - Ersatz Models

KW - composite materials

KW - data-driven approach

KW - large strain

KW - material nonlinearity

KW - multiscale finite element method

KW - surrogate models

KW - композиционные материалы

KW - подход, основанный на данных

KW - суррогатные модели

KW - большие деформации

KW - материальная нелинейность

KW - многомасштабный метод конечных элементов

UR - https://www.mendeley.com/catalogue/fbde33ff-c08b-3be5-b1a5-410a5ff96337/

UR - https://www.scopus.com/pages/publications/105046244265

U2 - 10.1002/zamm.70531

DO - 10.1002/zamm.70531

M3 - Article

VL - 106

JO - ZAMM Zeitschrift fur Angewandte Mathematik und Mechanik

JF - ZAMM Zeitschrift fur Angewandte Mathematik und Mechanik

SN - 0044-2267

IS - 8

M1 - e70531

ER -