Let us now consider the shear deformation, or stress, that results from the imposition of a specified shear profile. We
begin in Section 5.1 by considering the influence of compressibility in the simple shear problem, where we increase and then
decrease the deformation, or stress, linearly in time. In contrast to the perfectly elastic case, here we note that the memory
effect of compressibility plays a role even for this isochoric deformation. In Section 5.2 we then determine the dissipation of
energy associated with an imposed linear deformation, and with the more complicated field that results when oscillations
are superposed on an initial linear shear. In the latter case we determine the energy dissipated over one cycle, after significant
time, so that a steady state has been reached.
To specify matters, let us consider a material with moduli ratios (in the compressible case)