Corotational Integrals in Constitutive Formulations

Abstract

The definition of a corotational integral is formally introduced. Such definition is the counterpart of the definition of a corotational derivative and requires the introduction of an orthogonal tensor which corresponds to the spin entering the corotational derivative. The corotational derivatives are used to generalize the rate-form of constitutive equations from small to large deformations and rotations. Likewise, the corotational integrals substitute for the classical integrals in constitutive theories expressed in integral form, in order to extend their applicability to large deformations and rotations within an Eulerian framework. A number of existing theories such as viscoelasticity, endochronic plasticity, and functional plasticity are thus generalized by use of prope corotational integrals.