A Non-Intrusive, Online Reduced Order Method for Non-Linear Micro-Heterogeneous Materials

Abstract

In this contribution we present an adaptive model order reduction technique for non-linear finite element computations of micro-heterogeneous materials. The presented projection-based method performs updates of the reduced basis during the iterative process and at the end of each load step. Convergence is achieved in all stages of the simulation and the best choice of basis vectors is assured. A novel technique for the choice of basis, the recursive Proper Orthogonal Decomposition, is introduced and compared to an existing technique, the comparative Proper Orthogonal Decomposition, in an academic two-dimensional unit cell example. Numerical examples of real two- and three-dimensional microstructures unveil the performance of the adaptive technique for industrial applications.