Analytic plastic potential for porous aggregates with matrix exhibiting tension–compression asymmetry

This paper is devoted to modeling the effects of the tension–compression asymmetry of the matrix on yielding of the void–matrix aggregate. The matrix plastic behavior is described by the Cazacu et al. [2006. Orthotropic yield criterion for hexagonal closed packed metals. Int. J. Plasticity 22, 1171–1194] isotropic yield criterion, which captures strength differential effects. Using an upper-bound approach, a new analytic isotropic plastic potential for a random distribution of spherical voids is obtained. The derived analytic potential is sensitive to the third invariant of the stress deviator and displays tension–compression asymmetry. In the case when the matrix material has the same yield in tension and compression, it reduces to Gurson's [1977. Continuum theory of ductile rupture by void nucleation and growth: Part I: Yield criteria and flow rules for porous ductile media. J. Eng. Mater. Technol. Trans. ASME Ser. H 99, 2–15.] criterion. Furthermore, the proposed criterion predicts the exact solution of a hollow sphere loaded in hydrostatic tension or compression. The accuracy of the proposed analytical criterion is assessed through comparisons with finite-element cell calculations.