Analysis of oblique shock waves in solids using shock polars

Graphical solutions of shock reflections in gases have long been used to gain insight into such phenomena. These shock polar solutions provide a simple means of visualizing the complex nonlinear nature of shock wave interactions. This methodology, however, is not limited to the treatment of an ideal gas. While the framework can be extended to a completely general equation of state, the emphasis here will be on the description of oblique shocks in a hydrodynamic Mie-Gruneisen solid. The oblique shock relations for the principal Hugoniot, second shock Hugoniot, and release isentrope are presented and used to solve two different shock reflection problems. First, the oblique shock reflection from an inclined interface is examined using the shock polar methodology. Specifically, the shock interactions at a copper and beryllium oblique interface are addressed to compare the shock polar methodology with a recent study which utilizes a Lagrangian analytical approach in conjunction with numerical simulations. The second problem examined is the so-called Mach lens configuration, which can be used to generate a steady Mach reflection. Shock polar solutions are generated for a copper target using various confinements and compared to numerical simulations. Similarly, an iron target is examined in which the resulting polymorphic phase transition can also be described through the shock polar methodology.