Characterization of micro- to macroscopic response of polymers containing voids under macroscopically uniform deformation

For the characterization of mechanical characteristics of polymers containing voids (cavitated rubbery particles), a homogenization method has been developed, which can handle large deformation problems including the onset and propagation of instability and can reproduce the micro- to macroscopic deformation behavior of polymers with periodically distributed voids under macroscopically inhomogeneous loading conditions. A parametric study has clarified the characteristic features of polymers containing periodically distributed heterogeneous cylindrical voids of different volume fractions subjected to macroscopically homogeneous stress in different directions. Different types of shear bands are observed, depending on the tensile direction with respect to the unit cell. The shear band connecting the voids that appear in the early stages of deformation is responsible for the macroscopic yielding. Increasing the volume fraction of the voids results in a decrease in the macroscopic yield stress and in the directional dependence of the macroscopic stress–strain relationship. The moderate heterogeneity of voids causes complicated and different types of shear bands; however, due to the high stress concentration caused by the presence of small voids, the onset and propagation of the shear bands are promoted, and the macroscopic stress–strain relationships become essentially isotropic. Nevertheless, the volumetric strain of unit cell changes with volume fraction and heterogeneity of the voids and tension directions