Exact solution to the formation and propagation problem of a non-stationary shock wave in bilinear media

An exact solution is presented for the formation and propagation problem of a nonstationary plane shock wave in a continuous medium with a concave characteristic sigma minus epsilon, approximated by the bilinear model. The form of a shock wave in the loading and unloading zone is explicitly defined. Exact formulas are derived for the parameters of state and motion of the medium behind the wave front. The solution constitutes the starting point for the construction of a closed-form solution to the interaction of nonstationary shock waves with contact discontinuities.