Analytical criterion for porous solids containing cylindrical voids in an incompressible matrix exhibiting tension–compression asymmetry

Abstract

A new analytic plastic potential is developed using a rigorous limit analysis approach. Conditions of homogeneous boundary strain rate are imposed on every cylinder concentric with the cavity. It is shown that, due to the tension–compression asymmetry of the incompressible matrix, the third invariant of the stress deviator has a strong influence on the yielding of the porous solid. New and intriguing results are obtained; namely, for axisymmetric loadings and plane strain conditions, the stress state at yielding is not hydrostatic. In the case when the matrix has the same yield in tension as in compression, the new criterion reduces to Gurson’s criterion for cylindrical voids.

Keywords:

• voids shape
• third-invariant effects
• deformation twinning
• porous media