On a Lamb-type problem for a bi-axially pre-stressed incompressible elastic plate

The far-field response of a bi-axially pre-stressed incompressible elastic plate, subjected to an instantaneous edge impulse loading, is studied using a refined long-wave low-frequency theory. The second order correction introduced by the refined theory is demonstrated to smooth the discontinuity associated with one of the wave fronts predicted by the leading order hyperbolic theory. The character of so-called quasi-front is shown to depend greatly both on the material parameters and pre-stress and may be either classical receding or advancing. Additionally, and in contrast to the analogous problem in linear isotropic elasticity, in a pre-stressed plate the dilatational quasi-front may propagate slower than the shear wave front. This situation is demonstrated to lead to the formation of a head-wave quasi-front.