APPLICATION OF OBJECTIVE RATES IN MECHANICAL MODELING OF SOLIDS

A unified formulation is developed for deformation-related spins, and for objective rates based on them. The approach generalizes the underl ying concepts, and allows new rates to be constructed. Mathematical an d thermodynamical restrictions on these are shown. As a result, it can be demonstrated that the Eulerian strain rate is an objective rate of logarithmic strain, based on a spin easily derivable from the general form. Interrelations between other known spins and objective rates em erge very clearly. Consequences of the proposed formalism are explored in hypoelastic and in rigid-plastic constitutive relations, the latte r involving purely isotropic and purely kinematic hardening. The appli cation of the resulting models to the simple shear deformation is show n.