Computational homogenization of elasto-plastic porous metals

The effective material response of ductile metals containing spherical pores at volume fractions between 0.1% and 30% is investigated on a computational basis. Periodic hard core models of spherical voids are used in a Monte Carlo type finite element study. The objective of the study is the investigation of the pressure dependency of the deviatoric limit stress of the three-dimensional microstructures. In order to characterize the underlying morphology, the statistical properties of the unit cells are evaluated. The representativeness of the computational results is investigated. With respect to the local material response, the inelastic deformations within the unit cell are analyzed and compared for different types of boundary conditions. The computational results are related to existing analytical models and an extension of the Gurson–Tvergaard–Needleman model is proposed to overcome the observed discrepancies. The new model has only one additional parameter, and is found to efficiently predict the pressure dependency of the limit stress for all examined porosities.