Summary
Some aspects of the wave propagation, resulting from the spherically symmetric expansion of a thick walled hyperelastic shell and the limiting case of expansion of a cavity in an unbounded medium, are investigated. It is assumed that the shell is isotropic and uniform in the natural reference state and its strain energy function is a particular compressible generalization of that for the neo-Hookean solid. The response of a compressible shell, due to a spatially uniform time dependent application of internal pressure, is compared with that for the neo-Hookean shell taken as a limiting case of the compressible shell. This is also done for an unbounded medium.
A finite difference method which uses the relation along one of the families of characteristics is used to obtain numerical results. In order to implement this method the governing equations are expressed as a system of first order partial differential equations in conservation form.
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Janele, P., Haddow, J.B. & Mioduchowski, A. Finite amplitude spherically symmetric wave propagation in a compressible hyperelastic solid. Acta Mechanica 79, 25–41 (1989). https://doi.org/10.1007/BF01181478
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DOI: https://doi.org/10.1007/BF01181478