General failure criterion and stress-strain relation for granular materials to metals

Abstract

A general failure criterion and stress-strain relation for frictional and cohesive materials are presented on the basis of the Matsuoka-Nakai criterion for a frictional material and the Mises criterion for a cohesive material. In order to extend the Matsuoka-Nakai criterion and constitutive relation on the 'spatially mobilized plane (SMP)' for a frictional material to those for frictional and cohesive materials, a parameter of 'bonding stress σ0' is introduced. The proposed failure criterion and constitutive relation are reduced to the Matsuoka-Nakai criterion and stress-strain relation on the SMP in the case of σ0=0. They are also reduced to the Mises criterion and stress-strain relation on the octahedral plane in the case of σ0→∞.