Two-scale simulations are often employed to analyze the effect of the microstructure on a component’s macroscopic properties. Understanding these structure–property relations is essential in the optimal design of materials, or to enable (for example) estimation of microstructure parameters through macroscale measurements. However, these two-scale simulations are typically computationally expensive and infeasible in multi-query contexts such as optimization and inverse problems. To make such analyses amenable, the microscopic simulations can be replaced by inexpensive, parametric surrogate models. In this talk, we (1) present some recent work on a non-intrusive reduced basis method to construct inexpensive surrogates for parametrized microscale problems, and (2) highlight difficulties for model order reduction presented by highly nonlinear constitutive relations in multi-scale problems in mechanics.

Acknowledgments: This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program (Grant agreement No. 818473).