Shock waves in Materials with Nonlinear Instantaneous Response.
CALIFORNIA UNIV BERKELEY STRUCTURAL ENGINEERING LAB
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Shock propagation in solids which exhibit a nonlinear stress strain curve when subjected to instantaneous loadings is studied. General three-dimensional shock waves are first examined and then specialized to the one-dimensional case. The method of solution involves two steps, the generation of an infinite set of coupled nonlinear ordinary differential equations to replace the original partial differential equations and the solution of this system. Explicit solutions are exhibited for a restricted class of materials using a series solution for the system and also a perturbation technique. The two methods are compared showing that a low order perturbation solution can give good results for the decay of the wave front. A way of extending the method to a general type of material is shown and the effect of the boundary conditions on the shock decay is calculated. A steady state solution is also obtained. Author