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N.P. Andrianopoulos, V.M. Manolopoulos
International Journal of Mechanical Sciences, Volume 54, Issue 1, January 2012
Abstract
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.
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