COROTATIONAL INTEGRALS IN CONSTITUTIVE FORMULATIONS.

Instead of, or in addition to, rate equations, a constitutive theory may involve integrals, as a particular case of what is called a functional formulation. Under large deformations and rotations, the physical meaning of such integrals necessitates that the integration process is initially perceived and defined in reference to the rotating system. Similarly to the case with corotational derivatives, the transition of the equations from the rotating to the fixed system introduces the concept of corotational integrals. Although such integrals have been informally used, the purpose of this note is to introduce formally the definition of a corotational integral, relate it to corotational derivatives, and discuss its significance to different aspects of existing functional constitutive formulations.