Simple shear of a compressible quasilinear viscoelastic material

Fung's theory of quasilinear viscoelasticity (QLV) was recently reappraised by the authors [Proc. R Soc. A 479 (2014), 201400581 in light of discussions in the literature of its apparent deficiencies. Due to the utility of the deformation of simple shear in a variety of applications, especially in experiment to deduce material properties, here QLV is employed to solve the problem of the simple shear of a nonlinear compressible quasilinear viscoelastic material. The effects of compressibility on the subsequent deformation and stress fields that result in this isochoric deformation are highlighted, and calculations of the dissipated energy associated with both a 'ramp' simple shear profile and oscillatory shear are given.