Growth and decay of acceleration waves in incompresible elastic solids

The growth equation for acceleration waves propagating in an incompressible elastic solid is derived, emphasis being placed on the role of certain tensors of elastic moduli. Particular attention is then paid to isotropic elastic solids, and conditions which determine whether transverse plane waves grow or decay are expressed in terms of elastic constants for a certain class of isotropic elastic materials. We examine how the growth/decay condition depends on the strain, the direction of propagation and the signs of these constants. The Mooney-Rivlin solid is one member of the class; for this material it is shown that transverse plane waves propagate with con-stant amplitude for any direction of propagation and arbitrary homogeneous pre-strain. The results obtained are compared with those of the exact theory for a third-order incompressible isotropic elastic solid. 1