THE APPROPRIATE COROTATIONAL RATE, EXACT FORMULA FOR THE PLASTIC SPINAND CONSTITUTIVE MODEL FOR FINITE ELASTOPLASTICITY

the exact formulae for the plastic and the elastic spin referred to th e deformed configuration are derived, where the plastic spin is a func tion of the plastic strain rate and the elastic spin a function of the elastic strain rate. With these exact formulae we determine the macro scopic substructure spin that allows us to define the appropriate coro tational rate for finite elastoplasticity. Plastic, elastic and substr ucture spin are considered and simplified for various sub-classes of r estricted elastic-plastic strains. It is shown that for the special ca ses of rigid-plasticity and hypo-elasticity the proposed corotational rate is identical with the Green-Naghdi rate, while the Zaremba-Jauman n rate yields a good approximation for moderately large strains. To co mpare our exact plastic spin formula with the constitutive assumption for the plastic spin introduced by Dafalias and others, we simplify ou r result for small elastic-moderate plastic strains and introduce a si mplest evolution law for kinematic hardening leading to the Dafalias f ormula and to an exact determination of its unknown coefficient. It is also shown that contrary to statements in the literature the plastic spin is not zero for vanishing kinematic hardening. For isotropic-elas tic material with induced plastic how undergoing isotropic and kinemat ic hardening constitutive and evolution laws are proposed. Elastic and plastic Lagrangean and Eulerian logarithmic strain measures are intro duced and their material time derivatives and corotational rates, resp ectively, are considered. Finally, the elastic-plastic tangent operato r is derived. The presented theory is implemented in a solution algori thm and numerically applied to the simple shear problem for finite ela stic-finite plastic strains as well as for sub-classes of restricted s trains. The results are compared with those of the literature and with those obtained by using other corotational rates.