A new analytical model about the relationship between nominal failure stresses and porosity for foamed metals under biaxial tension

Foamed metals have been widely used as various engineering materials, and their mechanical properties have also been drawing extensive attention. In the present paper, a new mechanical and analytical model is established for these materials with isotropic three-dimensional reticulated structure under biaxial tension, and the mathematical equation about biaxial nominal stresses is deduced for the biaxial tension at the beginning of failure of the porous body. With the relevant experiment, the relation formula is proved to be very effective. Different from the relevant theoretical system of Gibson and Ashby, the present mathematical relationship can be conveniently achieved from directly using the “beam theory” on this mechanical and analytical model. In addition, this relationship can be further expressed as the mathematical relationship among the nominal failure “deviatoric stress”, the nominal failure “average stress” and porosity, but the concepts of both the “deviatoric stress” and the “average stress” can appear just from the mathematical treatment.