Application of Objective Rates in Mechanical Modeling of Solids

Abstract

A unified formulation is developed for deformation-related spins, and for objective rates based on them. The approach generalizes the underlying concepts, and allows new rates to be constructed. Mathematical and 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 emerge very clearly. Consequences of the proposed formalism are explored in hypoelastic and in rigid-plastic constitutive relations, the latter involving purely isotropic and purely kinematic hardening. The application of the resulting models to the simple shear deformation is shown.