Superposition of small shear deformations on large uniaxial extensions for viscoelastic materials

Abstract

The equation for small amplitude torsional response superposed on a finite axial stretch history is derived for a material modelled by the BKZ constitutive equation. For the case of a uniaxial step stretch history, this equation contains a term generalizing the well known Rivlin result for nonlinear elasticity plus two additional terms. The equation is used to analyse a recent experiment which studies the relation between the period of free torsional oscillations, axial stretch and axial force in a material undergoing stress relaxation. It is shown that a 10% discrepancy which arises when the data is related by Rivlin's formula can be accounted for by the two additional terms associated with the BKZ formulation. Finally, an expression for the complex modulus for forced torsional oscillations is derived.