On the computation of the exact overall consistent algorithmic tangent moduli for non-linear finite strain homogenization problems using six finite perturbations

This work is concerned with the development of a numerically robust two-scale computational approach for the prediction of the local and overall mechanical behavior of heterogeneous materials with non-linear constitutive behavior at finite strains. Assuming scale separation, the macroscopic constitutive behavior is determined by the mean response of the underlying microstructure which is attached to each macroscopic integration point in the form of a periodic unit cell. The algorithmic formulation and numerical solution of the two locally-coupled boundary value problems is based on the FE-FFT method (e.g. [14, 17]). In particular, a numerically robust algorithmic formulation for the computation of the overall consistent algorithmic tangent moduli is presented. The underlying concept is a perturbation method. In contrast to existing numerical tangent computation algorithms the proposed method yields the exact tangent using only six (instead of nine) perturbations (3 in 2d). As an example, the micromechanical fields and effective material behavior of elasto-viscoplastic polycrystals are predicted for representative simulation examples. copyright © Crown copyright (2018).All right reserved