A reduced order model for geometrically parameterized two-scale simulations of elasto-plastic microstructures under large deformations
arXiv:2307.16894 · doi:10.1016/j.cma.2023.116467
Abstract
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.
References in corpus (10)
- A numerical method for computing the overall response of nonlinear composites with complex microstructure
- Data-driven computational mechanics
- Micromorphic Computational Homogenization for Mechanical Metamaterials with Patterning Fluctuation Fields
- Randomized Local Model Order Reduction
- A comparative study on low-memory iterative solvers for FFT-based homogenization of periodic media
- High performance reduction technique for multiscale finite element modeling (HPR-FE2): towards industrial multiscale FE software
- Size effects in nonlinear periodic materials exhibiting reversible pattern transformations
- Learning constitutive models from microstructural simulations via a non-intrusive reduced basis method
- Computational frameworks for homogenization and multiscale stability analyses of nonlinear periodic metamaterials
- Learning constitutive models from microstructural simulations via a non-intrusive reduced basis method: Extension to geometrical parameterizations