Detonation type waves in phase (chemical) transformation processes in condensed matter

Fast self sustained waves (autowaves) associated with chemical or phase tra nsformations are observed in many situations in condensed matter. They are governed neither by diffusion of matter or heat (as in combustion processes ) nor by a travelling shock wave (as in gaseous detonation). Instead, they result from a coupling between phase transformation and the stress field, a nd may be classified as gasless detonation autowaves in solids. We propose a simple model to describe these regimes. The model rests oil the classical equations of elastic deformations in a 1-dimensional solid bar, with the e xtra assumption that the phase (chemical) transformation induces a change o f the sound velocity. The transformations are assumed to occur through a ch ain branched mechanism; which starts when the mechanical stress exceeds a g iven threshold. Our investigation shows that supersonic autowaves exist in this model. In the absence of diffusion (dissipation factor, losses), a con tinuum of travelling wave solutions is found. In the presence of diffusion, a steady state supersonic wave solution is found, along with a slower wave controlled by diffusion.