to study the classical problem of simple
shear by employing the authors’ new approach to QLV; this is therefore the aim of the present paper. We will carry out
the full analysis of the simple shear problem for both incompressible and compressible viscoelastic materials of quasilinear
type. Importantly, and unlike the case of simple shear of purely hyperelastic materials, even for isochoric deformations the
effects of compressibility can have an influence on the deformation due to the memory effect of the relaxation term
associated with hydrostatic compression