Superseismic Loading and Shock Polars: an Example of Fluid-solid Coupling

We propose a two-dimensional problem involving fluid-solid coupling where a solution is given in closed form. The upper half of the domain is modeled as an isotropic solid; the lower part as a compressible gas. The loading of the solid at the fluid-solid boundary is called superseismic when its speed is larger than the speed of propagation of disturbances in the bulk of the material. The loading is modeled by a shock coupled to the deformation of the boundary. The problem is relevant to high explosive applications, since it is very similar to the interaction between an explosive and the casing in a cylinder test experiment. Within this framework, we show the existence of self-similar solutions in the reference frame moving with the shock wave.