
Accession Number : ADP004935
Title : Discontinuous Dependence of Solution on Boundary Conditions for Large Amplitude Shock Waves,
Corporate Author : ILLINOIS UNIV AT CHICAGO CIRCLE DEPT OF CIVIL ENGINEERING MECHANICS AND METALLURGY
Personal Author(s) : Ting,T. C. T.
Report Date : FEB 1985
Pagination or Media Count : 11
Abstract : Plane waves of finite amplitude in a simple elastic solid which occupies the half space x > or = 0 are studied. For isotropic materials there are two plane polarized simple waves as well as two shock waves and one circularly polarized simple wave which can be regarded as a shock wave. Using combination of simple waves and/or shock waves is needed to satisfy the initial and boundary conditions. For hyperelastic materials, the wave curves associated with different wave speed are orthogonal to each other. Examples are presented for second order hyperelastic materials. In one example we show that the solution requires as many as four simple waves. In another, when the amplitude of the applied shock is large enough, the solution, though does not blow up with time, does not depend continuously on the boundary conditions. Mathematically, this may create difficulties for a numerical solution of the problem. Physically, this means that if the applied load at the boundary is not properly controlled, any slight deviations in the applied load would result in a finite jump in the material response. (Author)
Descriptors : *SHOCK WAVES, *PLANE WAVES, ISOTROPISM, SOLIDS, ELASTIC PROPERTIES, SOLUTIONS(GENERAL)
Distribution Statement : APPROVED FOR PUBLIC RELEASE