General Failure Criterion for Isotropic Media

A general failure criterion dependent on three stress tensor invariants is proposed. It is applicable to a rather large class of materials including, metals, rocks, concrete and soils. The classical failure criteria and some recently proposed criteria are particular cases of this general criterion. The condition presented permits the uniform description of different groups of materials for which quite different forms of the failure criteria have been applied to date. A general form is applied to formulate failure criteria for plain concrete and sand. These criteria, to which smooth (conical for sand or paraboloidal for concrete) surfaces correspond, provide good agreement between predicted values of failure stresses and experimental results. This was possible due to the introduction of a new two‐parameter function describing the deviatoric cross section of the failure surface. Two cross sectional shape characteristic ratios, λ and θ, defined in this paper, make possible the systematic analysis of different criteria and allow prediction of the failure surface features, which can be helpful in interpretation of the experimental results.