A control volume approach to a shock front propagating in laminated hyperelastic media

Abstract

Finite amplitude shock wave front propagating in laminated semi-infinite bodies made of hyperelastic materials is analyzed using the concept of a control volume. The shock front is generated by an impulsive load which is applied to the one end of the semi-infinite body, and propagates steadily in the direction of the lamination. A control volume is therein defined to contain and move with the shock front and a set of steady-state conservation equations is written as in the case of a flow problem. These equations are solved with the aid of the material constitutive relations and the appropriate geometrical and boundary conditions. An illustrative problem of a semi-infinite plate is solved in detail, using rubber-like materials of the Neo-Hookean type. The numerical results for this problem are depicted in graphs, which display a marked non-linear shock Hugoniot relation.