Yield criteria for voided materials with anisotropic matrix behavior

This paper presents a theoretical and micromechanical procedure for determining the macroscopic behavior of voided materials with anisotropic matrix constitutive behavior. Within the Gurson approach (Gurson, 1977), it combines the IPE (Isotropy Plasticity Equivalent) concept proposed by Karafillis and Boyce (1993) to the procedure proposed by Benallal (2017) to build macroscopic behavior of voided materials with general isotropic matrix behavior. For sake of clarity, the simple Gurson kinematically admissible velocity field is used and can be replaced by any more suitable trial field. The matrix may have any anisotropic behavior represented by the linear transformation of the IPE setting, which is traceless. A general parametric constitutive relation is obtained for the six-dimensional yield surface of the porous solid. A numerical algorithm is then proposed to evaluate and visualize arbitrary sections of this full six-dimensional macroscopic yield surface and various illustrations are provided for different matrix plastic constitutive behavior including Lode angle effects and materials symmetries. Some qualitative aspects of the macroscopic yield locus are summarized and discussed.