Bi-Modular Rods: Vanishing Shock Velocity

It is known that the propagation of infinitesimal elastic waves in a one-dimensional bi-modular rod implies the appearance of discontinuities in strain, stress and the propagation velocity, if one part of the wave pulse overtakes another. These discontinuities are known as strong shock wave fronts, or strong shocks. Applying the Hadamard compatibility equation, it was found that under certain conditions the velocity of the moving shock wave front can approach to zero. This result was confirmed numerically using the Marlow hyperelastic potential coupled with a finite element model. It is shown that the existence of slowly moving surface of discontinuity (strong shock) implies local heat release with the corresponding slowly moving heat source.