  In order to model nonlinear viscous dissipative motions in solids, acoustical
physicists usually add terms linear in dot{E}, the material time derivative of
the Lagrangian strain tensor E, to the elastic stress tensor sigma derived from
the expansion to the third- (sometimes fourth-) order of the strain energy
density e=e(trace(E), trace(E^2), trace(E^3)). Here, it is shown that this
practice, which has been widely used in the past three decades or so, is
physically wrong for at least two reasons, and that it should be corrected. One
reason is that the elastic stress tensor sigma is not symmetric while dot{E) is
symmetric, so that motions for which sigma + sigma^T <> 0 will give rise to
elastic stresses which have no viscous pendant. Another reason is that dot{E}
is frame-invariant, while sigma is not, so that an observer transformation
would alter the elastic part of the total stress differently than it would
alter the dissipative part, thereby violating the fundamental principle of
material frame-indifference. These problems can have serious consequences for
nonlinear shear wave propagation in soft solids, as seen here with an example
of a kink in almost incompressible soft solids.
