Fung’s theory of quasilinear viscoelasticity (QLV) was recently reappraised by the authors
[Proc. R. Soc. A 479 (2014), 20140058] 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.
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