Ultimate criteria for materials with different properties in biaxial tension and compression: a micromechanical approach

In a previous communication to this journal, the authors introduced a micromechanical method for developing ultimate-state, plane stress criteria, which was in turn based on the doublet-mechanical theory of solids. In this article, doublet mechanics is employed to derive microstructurally based yield and failure criteria containing four dimensionless parameters. This permits the exact representation of five independent ultimate plane stress states: uniaxial tension and compression, pure shear, and equibiaxial (hydrostatic) tension and compression. The novel criteria are shown to be successfully applicable to a variety of macroscopically continuous solids, including cast iron and several alloys, as well as to discontinua such as plain and short-steel-fiber reinforced concrete.