A model order reduction method for computational homogenization at finite strains on regular grids using hyperelastic laminates to approximate interfaces

Abstract

FFT-based homogenization methods operate on regular voxel grids and cannot resolve interfaces exactly in general. In this article we study hyperelastic laminates and associate their effective properties to voxels containing interfaces, extending previous ideas, successfully applied in the framework of linear elasticity. More precisely, we show that for strictly rank-one convex energy densities of the constituents there is precisely one phase-wise affine minimizer of the laminate problem, a result of independent interest. We demonstrate that furnishing interface voxels with appropriately rotated effective hyperelastic properties of a two-phase laminate significantly enhances both the local solution quality and the accuracy of the computed effective elastic properties, with only a small computational overhead compared to using classical FFT-based homogenization. In particular, for equal accuracy, problems with a lower number of degrees of freedom suffice.