Can Coulomb criterion be generalized in case of ductile materials? An application to Bridgman experiments

The failure behavior of isotropic non-linear elastic materials is macroscopically studied in terms of elastic strain energy density generalizing the Coulomb criterion. This generalization is based on a rigorous mathematical substrate developed on the principle of conservation of the total elastic strain energy. In the general case of loading the behavior of a material is described with regard to the secant elastic moduli depending on both first strain and second deviatoric strain invariants. This dependence enlightens, in physical terms, the different reaction of materials in normal and shear stresses. Besides, these two moduli establish two constitutive equations for the complete description of any material, instead of the usual one. A theoretical application is given and the failure surfaces which are obtained in stress space are being commented. Predictions obtained in tension of steel under pressure from Bridgman's experiments and some of his observations for the failure behavior of steels are explained on the existence of a universal criterion with the present approach.

► A two equations failure criterion for non-linear elastic materials is presented.
► It generalizes Coulomb–Mohr criterion in terms of elastic strain energy density terms.
► Plastic strains are not necessary in forming a failure criterion.
► The necessity of two constitutive equations for the description of any material is emphasized.
► Bridgman's experiments of metals under high pressure are predicted satisfactorily.