Objective corotational rates and shear oscillation

Abstract

Influence of objective corotational rates to shear oscillation is discussed here under the framework of finite deformation, J 2 -flow theory. Under an elastic-plastic, mixed hardening constitutive law, the active stress s , as defined in eqn (8) of the text, and back stress b are shown to be governed by two sets of equations formally uncoupled to each otther. Formal solutions of complex stresses are obtained for plane strain, isochoric deformation, with the conclusion that the shear oscillation behavior for an elastic-plastic solid can be asymptotically reduced to a rigid-plastic solution and a higher order correction, provided the initial shear strain is small. Consequently, the active stress s appears to be nonoscillatory under a realistic but arbitrary corotational rate, whereas the oscillatory behavior of back stress b is solely determined by the maximum corotation angle, defined in eqns (18) and (41), as well as the variation of material hardening with respect to the corotation angle. A spectrum of back stress responses could be predicted by the incorporation of different objective corotational rates.