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

by: James M Hill, JL Wegner

Mathematics and Mechanics of Solids, Vol. 9, No. 1. (1 February 2004), pp. 81-95.

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Abstract

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 10.1177/1081286503035200

@article{citeulike:2761068, abstract = {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 10.1177/1081286503035200}, author = {Hill, James M. and Wegner, J. L. }, citeulike-article-id = {2761068}, doi = {10.1177/1081286503035200}, journal = {Mathematics and Mechanics of Solids}, month = {February}, number = {1}, pages = {81--95}, posted-at = {2008-05-06 14:06:44}, priority = {2}, title = {New Families of Exact Nonlinear Waves for the Neo-Hookean Finite Elastic Solid}, url = {http://dx.doi.org/10.1177/1081286503035200}, volume = {9}, year = {2004} }

RIS record

TY - JOUR ID - citeulike:2761068 TI - New Families of Exact Nonlinear Waves for the Neo-Hookean Finite Elastic Solid JF - Mathematics and Mechanics of Solids VL - 9 IS - 1 SP - 81 EP - 95 N2 - 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 10.1177/1081286503035200 AU - Hill, James AU - Wegner, JL PY - 2004/02/01/ UR - http://dx.doi.org/10.1177/1081286503035200 ER -

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