Doublet-based micromechanical approaches to yield and failure criteria

The doublet-based micromechanical theory introduced by the authors is employed to investigate the multi-axial yield and failure properties of solids in terms of their ultimate properties in tension, compression and shear. Emphasis is placed on the special case of spatially uniform plane states imposed on a macroscopically isotropic material domain capable of axial doublet interactions only. In view of the invertibility of the microstress/macrostress relations for this special case, the derived microcriterion is equivalently re-expressed as a criterion that employs the conventional stresses and models different tensile and compressive properties. It is further shown that assuming the tensile and compressive limits to coincide recovers Von Mises criterion, while the criterion of Tresca is associated with a microscopically inconsistent procedure. Single-microstress yield and strength criteria are introduced for microstructured media with axial and shear doublet interactions. The relationships among the biaxial limit macrostresses in tension, compression and shear to their microscopic counterparts are established for the plane case with arbitrary structural angle φ. The ratio of the macroscopic limit in tension and shear is obtained in terms of its microscopic counterpart and φ. The proposed natural criteria are compared with the classical ones of Von Mises and Tresca. The analysis of the failure conditions in the Flamant problem for a microstructured medium is employed to establish the necessity for the single-microstress canonical criteria.