Lagrangian equations of motion for finite amplitude azimuthal shear wave propagation in a compressible isotropic hyperelastic solid are obtained in conservation form with a source term. A Godunov-type finite difference procedure is used along with these equations to obtain numerical solutions for wave propagation emanating from a cylindrical cavity, of fixed radius, whose surface is subjected to the sudden application of a spatially uniform azimuthal shearing stress. Results are presented for waves propagating radially outwards; however, the numerical procedure can also be used to obtain solutions if waves are reflected radially inwards from a cylindrical outer surface of the medium. A class of strain energy functions is considered, which is a compressible generalization of the Mooney-Rivlin strain energy function, and it is shown that, for this class, an azimuthal shear wave can not propagate without a coupled longitudinal wave. This is in contrast to the problem of finite amplitude plane shear wave propagation with the neo-Hookean generalization, for which a shear wave can propagate without a coupled longitudinal wave. The plane problem is discussed briefly for comparison with the azimuthal problem.
Finite Amplitude Azimuthal Shear Waves in a Compressible Hyperelastic Solid
Contributed by the Applied Mechanics Division of THE AMERICAN SOCIETY OF MECHANICAL ENGINEERS for publication in the ASME JOURNAL OF APPLIED MECHANICS. Manuscript received by the ASME Applied Mechanics Division, July 22, 1999; final revision, June 1, 2000. Associate Technical Editor: A. K. Mal. Discussion on the paper should be addressed to the Technical Editor, Professor Lewis T. Wheeler, Department of Mechanical Engineering, University of Houston, Houston, TX 77204-4792, and will be accepted until four months after final publication of the paper itself in the ASME JOURNAL OF APPLIED MECHANICS.
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Haddow, J. B., and Jiang, L. (June 1, 2000). "Finite Amplitude Azimuthal Shear Waves in a Compressible Hyperelastic Solid ." ASME. J. Appl. Mech. March 2001; 68(2): 145–152. https://doi.org/10.1115/1.1334862
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