Mohr-Coulomb criterion with circular failure envelope, extended to materials with strength-differential effect

Abstract

The linear Mohr–Coulomb (M-C) failure criterion is widely used to describe the behaviour of materials with compression/tension asymmetry, such as geological materials. Difference in compressive and tensile fracture/yielding stress is so-called strength difference or SD effect. A modified M-C criterion was proposed previously to describe the failure of ductile materials and to better fit the experimental data [1]. A circular failure envelope, tangent to the Mohr's circles corresponding to the limit state of stress for uniaxial tension, compression and pure shear, was considered. In this paper, the above circular M-C criterion is extended to brittle materials (with SD effect). The new criterion has been compared with fundamental criteria in plasticity theory and experimental results taken from literature. In the space σ1-σ3 it is represented by two segments of hyperbola and allows a smooth transition from linear M-C to Rankine criteria. It proves to be adaptable to a wide range of materials and this is a major advantage. Moreover, the paper demonstrates also that all yield criteria for standard plastic materials, without SD effect, under biaxial state of stress, are insensitive to hydrostatic pressure.