Nonlinear model order reduction using local basis methods on RVEs: A parameter study and comparison of different variants

Abstract

All possible solutions to a static representative volume element (RVE) problem lie on a solution manifold, which is often quite low‐dimensional. Solutions of a hyperelastic 3D RVE problem, for example, are determined by the macroscopic deformation gradient, meaning that its solution manifold is only six‐dimensional. Established projection‐based model order reduction (MOR) methods such as the Proper Orthogonal Decomposition (POD), however, often require much higher‐dimensional approximation spaces to successfully capture such a nonlinear solution manifold on account of their linearity. One approach to modelling the solution manifold more closely is the local basis method by Amsallem et al.. It utilises a locally, rather than globally, linear approximation of the solution manifold. In this work, we investigate several variants of this algorithm with respect to their performance on an example RVE problem.