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

• Published in: International journal of mechanical sciences 2014-12, Vol.89, p.58-64
• Main Authors: Zhang, Shunhu, Chen, Xiaodong
• Format: Article
• Language: English
• Subjects: Criteria; Elastic limit; Ellipsoids; Functions (mathematics); Loci; Mathematical analysis; PD yield criterion; Poisson׳s ratio; Porosity; Porous material; Porous materials; Principal stress space; Yield locus
• ISSN: 0020-7403; 1879-2162
• DOI: 10.1016/j.ijmecsci.2014.08.018

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. •Using a logarithm-fraction compound function, the relationship between Poisson׳s ratio and relative density is established.•A yield criterion incorporated with material porosity is proposed.•The yield locus in the principal stress space is proved to be an ellipsoid.•The yield stress and shear yield stress decrease as the material porosity increases.