THE STABILITY OF A PLANE LONGITUDINAL SHOCK-WAVE IN AN ISOTROPIC ELASTIC MEDIUM

The problem of the linear stability of fast plane longitudinal shock w aves (SW) in an isotropic elastic body whose elastic potential is it g iven function of the deformation tensor invariants depending additivel y on entropy is considered. When the medium is in a state of uniaxial compression or extension, the resulting dispersion equation can be fac torized. Assuming that ahead of the SW the medium is in a state of uni axial compression (extension), sufficient conditions for the instabili ty of longitudinal SWs are obtained. When the medium is in a state of uniaxial extension ahead of the SW and the velocity of the SW is such that the deformations behind the SW are close to zero and much smaller than those ahead of the SW, the problem of linear stability is solved completely, i.e. the necessary and sufficient conditions for stable, unstable and neutrally stable SWs to exist are stated. All the results obtained remain valid in the case of a medium with transverse anisotr opy (the direction of the anisotropy axis coinciding with the directio n of SW propagation), and also for an isotropic medium in a state of c ompression (extension) in the direction of two mutually perpendicular axes lying in the plane perpendicular to the direction of SW propagati on the deformations along these axes being equal. Copyright (C) 1996 E lsevier Science Ltd.