Regular reflection of plane detonation waves from an elastic half-space

An effective method for the approximate solution of the Eq. [1] for the intensity of a reflected shock wave in the case of oblique incidence of a detonation wave on an elastic half-space is described; the elastic half-space is described by a certain specific form of the equation of state. Formulas relating the front and particle velocities behind the transmitted wave front to physical parameters are derived. Values of the wave intensity and other quantities determined with the aid of a Ural-2 computer are cited.The author of [1, 2] investigated the regular reflection of shock waves from the boundary between two bodies. In the present paper we solve the analogous problem in the case of oblique incidence of a detonation wave on an elastic half-space. The detonation wave deforms the elastic half-space, which assumes the position OK₁ (Fig. 1) forming the angle to the initial direction KO of the halfspace boundary. We assume that the acoustic stiffness of the halfspace is larger than the acoustic stiffness of the explosive. In this case, both reflected wave 2 and transmitted wave 3 are shock waves [3]. Let us denote the velocities of propagation of the detonation, reflected, and transmitted waves by U_i(i=1, 2, 3), respectively; let the pressure be p_i and let the density bep_i(i=0, 1, 2, 3, 4). The quantities U₁, ₁, ₀, and ₄ are given. We determine the intensities of waves 2 and 3, their velocities of propagation, and the angles ₂, ₃ and . The parameters are constant within each of the domains a, b, c, d, and e. In domains a and e the medium is stationary, i.e., u₀=u₄ =0. The basic equations of the problem express the conditions at the wave fronts and the dynamic and kinematic relationships.