Ambiguities in Characterizing Stress States Involving Simple Shear

For many applications, such as forming, crash, and cutting simulations, it is necessary to describe material behavior for large plastic strains or even until fracture occurs. For these types of finite element analysis, damage models are required to adequately describe changes in the stress-strain relationship. Many phenomenological damage models rely on the Lode parameter and stress triaxiality to characterize the stress state of a material element. However, these parameters alone are not sufficient to distinguish between coaxial and non-coaxial deformations. Non-coaxial deformations occur when the principal strain and principal stress axes do not remain aligned. The cause of this misalignment is the presence of simple shear during the deformation. This study utilizes Mohr’s circle of strain to describe non-coaxial deformations and derives equations for various superpositions of biaxial stretch and simple shear. The equations to achieve specific Lode parameter and stress triaxiality pairs for variations of super-position are presented. Finite element simulations of single elements serve to validate these equations. These single-element simulations also demonstrate that, in non-coaxial deformations, the Lode parameter calculated from principal stress values differs from the Lode parameter calculated from principal strain values. The misalignment between principal stress and strain axes is a key to identifying simple shear. The findings of this study can contribute to improving damage models of ductile materials.