On shear band formation. I: Constitutive relationship for a dual yield model (Q1341236)

A phenomenological constitutive relation, for capturing the shear band formation in a rate-independent elastic-plastic material, is established. The model takes into account both the \(J_ 2\)-isotropic flow and a threshold shear stress-based flow. The elastic-plastic constitutive tensor is expressed explicitly in terms of elastic constants, the deviatoric stress tensor, the direction of the principal shear velocity- strain, and other material constants. This model particularly facilitates the resolution of the formation of the shear band even under material hardening conditions and does not demand an a priori knowledge of the orientation of the shear band.