Proper formulation of viscous dissipation for nonlinear waves in solids

To model nonlinear viscous dissipative motions in solids, acoustical physicists usually add terms the material time derivative of the Lagrangian strain tensor E, to the elastic stress tensor; derived from the expansion to the third (sometimes fourth) order of the strain energy density . 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.peer-reviewe