Acceleration waves in incompressible elastic solids

A ray-theory approach is used to derive in a concise form general equations for the propagation and growth of acceleration waves in incompressible elastic solids. They are qualitatively similar to those for the compressible solid and the arbitrary pressure does not appear. The specialization to the hyperelastic, isotropic case is made, and it is seen that many of the results known in the compressible case carry straight over. More explicit solutions are possible for an incompressible solid because the waves are necessarily transverse, and some of these solutions are presented for certain plane and cylindrical waves. In certain examples it is shown that, for an isotropic solid, the requirement of ‘physically reasonable response’ implies the convexity of the slowness surface.