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New Families of Exact Nonlinear Waves for the Neo-Hookean Finite Elastic Solid

School of Mathematics and Applied Statistics, University of fWllongong, Wollongong, NSW 2522, Australia

J. L. Wegner

Department of Mechanical Engineering, University of JKctoria, British Columbia, Canada V8W3P6

For the perfectly elastic neo-Hookean material, two well known partial solutions are extended to produce new families of exact nonlinear waves. For plane strain deformations, new results are presented for longitudinal and shear waves, while for axially symmetric defornations incorporating torsion, new results are presented for longitudinal and torsional waves. The plane dynamic deformations also apply to the more general Mooney strain-energy function, while the solutions given for the axially symmetric dynamic deformations incorporating torsion can be similarly deternined for the Mooney material, except that the details are far more complicated and involve elliptic functions. Both families of solutions are illustrated graphically

Key Words: Perfectly elastic materials • new exact nonlinear waves • neo-Hookean elastic solid • shear • longitudinal and torsional waves

Mathematics and Mechanics of Solids, Vol. 9, No. 1, 81-95 (2004)
DOI: 10.1177/1081286503035200


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