Adaptive MOR techniques for non‐linear FE simulations of unit cells

Abstract This work shows an adaptive Model Order Reduction (MOR) scheme for the computation of unit cells with non‐linear material behavior. A reduction of dimensionality and computational cost is achieved by projecting the high‐fidelity system of equations (SOE) from the full vector space to a lower dimensional subspace. An adaptive algorithm updates the projection operator, which is initially gained from a Proper Orthogonal Decomposition (POD), to ensure convergence and optimal size control of the reduced problem. Numerical examples show a comparison between the discretization of full displacements and fluctuations of a hexagonal unit cell, which show the independence of the MOR basis from the macroscopic displacements.