Micromorphic FE2 simulation of plastic deformations of foam structures

Capturing and predicting the effective mechanical properties of highly porous cellular media still represents a significant challenge for the research community, due to their complex structural interdependencies and known size effects. Micromorphic theories are often applied in this context to model the inelastic deformation behavior of foam-like structures, in particular to incorporate such size effect into the investigation of structure–property correlations. This raises the problems of formulating appropriate constitutive relations for the numerous non-classical stress measures and determining the corresponding material parameters, which are usually difficult to assess experimentally. The present contribution therefore alternatively employs a hierarchical micromorphic multi-scale approach within the direct FE2 framework to simulate the complex irreversible behavior of foam-like porous solids. The predictions of Cosserat (micropolar) and a fully-micromorphic theory are compared with conventional FE2 results and direct numerical simulations (DNS) for complex loading scenarios with elastic, elastic–plastic, and creep deformations. Therein, non-classical deformation modes of the microstructure resulting from the introduced micromorphic kinematics are visualized, as are the macroscopic hyperstresses and deformations.