Hot-spot thermal explosion in deformed solids

A model for hot-spot thermal explosion is proposed taking into account the coherence of deformation and temperature fields and the dependence of the reaction rate on the work of the deformation force. The problem is considered in terms of thermal elasticity theory. The solution is performed using matched asymptotic expansions in various particular cases. The temperature, displacement, deformation and stress fields, the hot-spot radius corresponding to the boundary of ignition and extinction regimes, and the ignition time are determined under critical conditions.