Rate type constitutive equations for fiber reinforced nonlinearly vicoelastic solids using spectral invariants

Abstract

tIn this paper we are interested in developing constitutive equations for fiber-reinforced nonlinearlyviscoelastic solids. It has been shown that constitutive equations for such bodies can be expressed in termsof a complete minimal set of 18 classical invariants associated with deformation and fiber orientation. Inthis paper, we give an alternative formulation using a set of spectral invariants. It is shown via the useof spectral invariants that only 11 of the 18 classical invariants are independent. We analyze the spectralinvariants for two illustrative deformation gradients: (i) simple tension, and (ii) simple shear