On the concept of relative and plastic spins and its implications to large deformation theories. Part I: Hypoelasticity and vertex-type plasticity

The concept of relative spin WD/S is introduced to facilitate the formulation of large deformation stress-rate models of inelasticity. Roughly speaking, it is a measure of non-coaxiality between stress and deformation rate of the form WD/S=W-WS with WS and W signifying the angular velocities or spins of the two material frames corresponding to the stress and strain rate respectively. It is suggested that an objective stress rate be defined with respect to WS for use in the constitutive equations and this requires explicit representations for WD/S reflecting the aforementioned non-coaxiality. It is shown that this practice leads conveniently to an elegant generalization of previous proposals resorting to either use of a variety of different spins or considerably complex constitutive equations, in order to dispense with undesirable oscillatory solutions of simple shear problems