A reduced order model for geometrically parameterized two-scale simulations of elasto-plastic microstructures under large deformations

Theron Guo (Corresponding author), Ondřej Rokoš, Karen Veroy

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In recent years, there has been a growing interest in understanding complex microstructures and their effect on macroscopic properties. In general, it is difficult to derive an effective constitutive law for such microstructures with reasonable accuracy and meaningful parameters. One numerical approach to bridge the scales is computational homogenization, in which a microscopic problem is solved at every macroscopic point, essentially replacing the effective constitutive model. Such approaches are, however, computationally expensive and typically infeasible in multi-query contexts such as optimization and material design. To render these analyses tractable, surrogate models that can accurately approximate and accelerate the microscopic problem over a large design space of shapes, material and loading parameters are required. In this work, we develop a reduced order model based on Proper Orthogonal Decomposition (POD), Empirical Cubature Method (ECM) and a geometrical transformation method with the following key features: (i) large shape variations of the microstructure are captured, (ii) only relatively small amounts of training data are necessary, and (iii) highly non-linear history-dependent behaviors are treated. The proposed framework is tested and examined in two numerical examples, involving two scales and large geometrical variations. In both cases, high speed-ups and accuracies are achieved while observing good extrapolation behavior.

Originele taal-2Engels
Aantal pagina's18
TijdschriftComputer Methods in Applied Mechanics and Engineering
Nummer van het tijdschriftPart A.
StatusGepubliceerd - 1 jan. 2024


This result is part of a project that has received funding from the European Research Council (ERC) under the European Union's Horizon 2020 Research and Innovation Programme (Grant Agreement No. 818473). The authors would in addition like to thank Martin Horák from Czech Technical University in Prague for his help with the implementation of the large-strain J2-plasticity model.

European Union’s Horizon Europe research and innovation programme
European Research Council
Horizon 2020818473


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