Validity of Finite Element Unit Cell Model for Studying Yield Condition of Isotropic Porous Materials

Assuming a spherical void in an infinite rigid plastic material, Gurson proposed a yield function for isotropic porous solids. It is, however, well known that the Gurson model gives harder response than those predicted by experimentation on actual porous solids. In numerical studies to check the validity of Gurson's model, most of the past researchers have introduced a cubic unit cell model, in which a spherical void is placed at the center of the cube. The cubic model can be a good approximation of a porous solid, if the void volume fraction is very small. The cubic model, however, may be not appropriate for the study of porous solids with high ratio of void volume fraction since the model automatically introduces an orthotropy effect due to the geometrically repetitive distribution of voids in three orthogonal axis directions. This research will propose a new unit cell model which is appropriate for the study of the yield functions for isotropic porous materials. The model is also favorable for the study of the anisotropic effect due to the void shape because the unit cell includes less of the anisotropy based on the distribution than the cubic model does