On two-scale adaptive FE analysis of micro-heterogeneous media with seamless scale-bridging

In principle, two approaches are possible for resolving strong material micro-heterogeneity: one approach is to adopt homogenization with the underlying assumption of scale separation, whereas the other approach is to completely resolve the fine scale(s) in a single-scale computation. The point of departure for this paper is a recently proposed algorithm for scale-transition such that the two extreme approaches are bridged in a “seamless” fashion. Numerical homogenization is carried out locally, where needed, based on the relation of the macro-scale mesh diameter to the typical length scale of the subscale structure. Moreover, the macroscale mesh adaptivity is driven by an estimation of discretization errors. In the present paper, we generalize this procedure by introducing two-scale adaptivity, whereby subscale discretization errors are viewed as model errors from the macroscale perspective. Numerical examples, adopting elastic–plastic subscale material properties, illustrate the principle and the effectiveness of the adaptive procedure.