Error Controlled Use of the Taylor Assumption in Adaptive Hierarchial Modeling of DSS

Journal article, 2015

A strategy for macroscale modeling adaptivity in fully nested two-scale computational (first-order) homogenization based on assumed scale separation is proposed. The representative volume element (RVE) for a substructure pertinent to duplex stainless steel is considered with its typical phase morphology, whereby crystal plasticity with hardening is adopted for the subscale material modeling. The quality of the macroscale constitutive response depends on, among the various assumptions regarding the modeling and discretization, the choice of a prolongation condition defining the deformation mapping from the macro- to the subscale This is the sole source of model error discussed in the present contribution. Two common choices are (in hierarchical order) (1) a "simplified" model based on homogeneous (macroscale) deformation within the RVE, that is the Taylor assumption, and (2) a "reference" model employing Dirichlet boundary conditions on the RVE, which is taken as the exact model in the present context. These errors are assessed via computation of the pertinent dual problem. The results show that both the location and the number of qudrature points where the reference model is employed depend on the chosen goal function.