Combustion wave propagation through deformed solids

Solid-phase combustion in a plane stress state. 1. Stationary combustion wave

“…The possibility of solid-phase detonation was demonstrated in [10] through thermodynamic calculations, and the existence of this phenomenon was actually validated in [11,12]. The problem of stability of stationary regimes to thermomechanical perturbations in a coupled formulation was first posed in [13].…”

“…From the last equation in system (13), it follows that d 2 ε yy dx 2 = 0 or ε yy = C 1 x + C 2 , where the constants of integration can be found from the conditions of zero values of the resultant force and the moment of forces [14]. If the plate sizes are large, the integration constants C 1 and C 2 tend to zero.…”

“…Therefore, by analogy with the simplest model (1), the problem reduces to solving a system of two equations: the first equation of system (13) and the stationary heat-conduction equation…”

“…(14), similar to [5,9,13], we obtain the equation for the temperature of the reaction products. As a result, the stationary problem reduces to the problem analyzed above, but its solution has different areas of existence of various conversion modes because of the plane stress state.…”

Solid-phase combustion in a plane stress state. 2. Stability to small perturbations

“…whereΠ = Π/(σ * ε * ); the subscript s indicates the quantities on the surface; z 1 and z 2 are the coefficients of sensitivity of the reaction rate to temperature [2,3] and to the work of stresses [5]:…”