Perturbation of Constitutive Relations in Tensor Non-Linear Materials

Abstract

Isotropic both vector and tensor functions in the most general case of scalar and tensor nonlinearity are investigated from a position of stability with respect to perturbations of material functions. These vector and tensor functions mean constitutive relations connecting stress tensor and strain rate tensor in continuum with complex rheology (advanced materials). The constitutive relations involve scalar material functions of invariants. Perturbations proportional to some low physical parameter α may be imposed on these material functions. They provoke as a consequence, a perturbation of tensor function itself. Both linear and quadratic in α components of such perturbations are obtained. In each approximation the closed system consisting of the motion equations and incompressibility condition is recorded.