ON SHEAR-BAND FORMATION .1. CONSTITUTIVE RELATIONSHIP FOR A DUAL YIELD MODEL

A phenomenological constitutive relation, for capturing the shear band formation in a rate-independent elastic-plastic material, is establis hed. The model takes into account both the J2-isotropic flow and a thr eshold shear stress-based flow. The elastic-plastic constitutive tenso r is expressed explicitly in terms of elastic constants, the deviatori c 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 har dening conditions and does not demand an a priori knowledge of the ori entation of the shear band. This is incorporated in an FEM, and the pl ane strain tensile test of ANAND and SPITZIG [1980] is numerically sim ulated. The computed results compare favorably with the experimental d ata. The shear band emerges more naturally as a solution to the bounda ry value problem, unlike the situations in solutions based on classica l bifurcation methods. Nevertheless, the usefulness of the local insta bility condition (ORTIZ et al. [1987]) is also demonstrated.