Computational homogenization analysis in finite elasticity: material and structural instabilities on the micro- and macro-scales of periodic composites and their interaction

摘要

The paper investigates instability phenomena in the context of homogenization-based micro-to-macro transitions of heterogeneous materials at finite strains. This covers structural instability effects (buckling) and material instability effects (localization) which can occur on both the macro- as well as the micro-scale and may influence each other. We develop a general framework for the theoretical and computational treatment of these instability problems for elastic composites with given periodic fine-scale micro-structures.