On the Computation of the Macroscopic Tangent for Multiscale Volumetric Homogenization Problems

For the computation of the macroscopic tangent that is required in multiscale volumetric homogenization techniques, two methods are summarized. First, a condensation approach is followed where the linearity of variational terms associated with the penalty enforcement of boundary conditions is explored in order to extract a macroscopic tangent at any stage of the Newton–Raphson iterations of a microstructural testing procedure. As an alternative approach, a second method is explored that requires only the knowledge of infinitesimally close macroscopic deformation states. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)