Abstract
In the present paper, the shear band localization is studied for the case of large elasticplastic deformation. In the first part, Rice's formula for the plastic hardening modulus is unfolded to cover five constitutive relations. The first four are based on the general nonassociative flow rule and on different objective stress rates, and the last one is the simple J2 corner theory with the von Mises yield function. Moreover, some useful expressions for the acoustic tensor of these models are presented. In the second part, the explicit expressions for the shear band orientation and the plastic hardening modulus are given for the Jaumann rate formulation of the Cauchy stress tensor. These expressions are valid for a deviatoric associative flow rule, and it assumed that the stress tensor and the unit outward to the plastic and yield surface are coaxial. In addition, it has been proved that in the case of the Jaumann-Cauchy formulation the vector normal to the critical plane of localization is perpendicular to the direction of the second component of the unit deviatoric stress tensor.
Published Version
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