New analytical criterion for porous solids with Tresca matrix under axisymmetric loadings

• New criterion for porous solids with Tresca matrix derived using rigorous limit-analysis theorems.
• New criterion reveals a very specific coupling between the mean stress and third invariant.
• Due to this coupling, confirmed by FE cell calculations, void growth depends on the third-invariant.

In this paper, a new analytic criterion for porous solids with matrix obeying Tresca yield criterion is derived. The criterion is micromechanically motivated and relies on rigorous upscaling theorems. Analysis is conducted for both tensile and compressive axisymmetric loading scenarios and spherical void geometry. Finite element cell calculations are also performed for various triaxialities. Both the new model and the numerical calculations reveal a very specific coupling between the mean stress and the third invariant of the stress deviator that results in the yield surface being centro-symmetric and void growth being dependent on the third-invariant of the stress deviator. Furthermore, it is verified that the classical Gurson’s criterion is an upper bound of the new criterion with Tresca matrix.