Analytical Yield Criterion for an Anisotropic Material Containing Spherical Voids and Exhibiting Tension-Compression Asymmetry

摘要

This paper is devoted to the development of a macroscopic anisotropic yield criterion for a porous material when the matrix material is incompressible, anisotropic and displays tension - compression asymmetry. The analytical yield criterion is obtained based on micromechanical considerations and non-linear homogenization. The matrix plastic behavior is described by the Cazacu et al. (2006) anisotropic yield criterion that is pressure-insensitive and accounts for strength-differential effects. Comparison between finite element cell calculations and theory show the predictive capabilities of the developed anisotropic model in terms of modeling the combined effects of anisotropy, tension- compression asymmetry of the matrix and voids on the overall yielding of the porous aggregate. It is shown that if the matrix material does not display tension-compression asymmetry, the developed criterion reduces to that of Benzerga and Besson (2001). If the matrix is isotropic, it reduces to the isotropic criterion developed in Cazacu and Stewart (2009).