Shock Waves (1992) 2 : 189-200 9Springer-Verlag 1992 Head-on collision between normal shock waves and a rubber-supported plate, a parametric study O. Igra, G. Ben-Dor, G. Mazor and M. Mond The Pearlstone Center for Aeronautical Engineering Studies, Department of Mechanical Engineering, Ben-Gurion University of the Negev, Beer Sheva, Israel Received January 15, i992; accepted July 20, 1992 Abstract. The equations governing the flow resulting from a ihead-on collision between a normal shock wave and a rubber-supported plate are listed. The non-dimensional pa- rmfieters that may affect the resulting flow are specified and their influence on I;he post-collision flow and waves is stud- ied numerically. It is shown that changes in: the area-ratio between the gas m~d the rubber cross-sections, the incident shock wave Mach number and the mass ratio between the rubber and the plate it supports, all have significant effects on the post-collision gas and rubber responses. Changes in the rubber elasticity constant also affect the post-collision flow. The extent of the effect that changes in the above men- tioned parameters ihave on the post-collision flow responses depends upon the loading mode used. Three different modes were studied; uni-axial stress loading, bi-axial stress loading and uni-axial strain loading. Key words: Shock in rubber, Multiple Media, Stress wave 1. Introduction and theoretical background In a recent paper Mazor et al. (1992) studied the flow field resulting from the head-on collision between a normal shock wave and a rubber-supported rigid plate. The impact of the shock-loaded plate at the rubber column is absorbed by the rubber in either of the following idealized modes: 1. "Uni-axial stress"; in this case the rubber movement is constrained only at its rear end, along the x-axis, where it is attached to a rigid boundary. The rubber is free to expand laterally along the y and z-axis, and its leading edge moves with the plate along the z-axis (see Fig. la). In this case ~ry=~r~=0ande v=e~r 2. "Bi-axial stress"; in this case an additional constraint to the rubber movements is added by rigid walls normal to the y-axis. (Due to its attachment to rigid boundaries at these locations, see Fig. lb). The rubber is free to expand along the z-axis and its leading edge can move along the z-axis. Correspondence to: O. l:gra In this case Crz = 0 and cy = 0. Friction between the nlbber column and the sicle walls is assumed negligibly small. In both, the uni-axial and hi-axial stress loadings the air pressure around the rubber rod (behind the plate) is kept at atmospheric level throughout the interaction process between the incident shock wave and the plate. 3. "Uni-axial strain"; in this case the rubber lateral move- ments in both the y- and z-axis are constrained by rigid walls (see Fig. lc). Only the rubber leading edge can move along the z-axis. In this case e~ = ez = 0 and (rz, ~y and a~ ~ 0. Friction between the rubber column sliding along side walls is assumed negligibly small. For each of the above mentioned loading cases an ap- propriate stress-strain relation was suggested by Mazor et al. (1992). These relations, along with the conservation equa- tions serve as a basis for a Lagrangian numerical scheme for computing the post-collision flow in the gas and in the rub- ber. Mazor et al. (1992) numerically soNed the conservation equations for specified initial and boundary conditions. The numerical results obtained for a hi-axial stress loading were compared with experimental findings. The good agreement obtained between these two results confirms the validity of the proposed physical model (conservation and constitutive equations) and the adequacy of the numerical scheme used for obtaining the numerical solution. In the following the conservation and the constitutive equations, used by Mazor et al. (1992), are listed in a non-dimensional form. The non- dimensional variables (having asterisks) were derived using the following definitions: . ta~ tco p. = ~ ~. = = L---;' t; = p la ,' P o4 * Pg , * Pr z* z S* S Pg =-- Pr = - = 1, =--, = ~, Pgl Pro L1 L~o u;= U" u;: T* , Ar al ~ C0 a2 ' Ar Art . hg . hr hg = pglL1A ~, h r proL~A~ ~