Deduction of a porosity-dependent yield criterion and its geometrical description for porous materials

A yield criterion for porous materials, referred to as porosity-dependent (PD) yield criterion, is proposed in this paper. In order to reflect the change law between Poisson׳s ratio and material porosity, the relationship between them is established using a logarithm-fraction compound function. Then the criterion firstly weighted by Poisson׳s ratio and ultimately incorporated with material porosity is then obtained. Its physical meaning is that when the total elastic energy reaches its limit value, then the porous material yields. Its loci in the principal stress space and on the π-plane are mathematically proved to be an ellipsoid and a circle respectively. Validation with available experimental data and traditional theoretical results shows that the present results have the same change trend as those of traditional theoretical results, and are in good agreement with experimental ones.