Some exact solutions for a class of compressible non-linearly elastic materials |
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Authors: | F.J. Rooney M.M. Carroll |
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Affiliation: | a Bishop O’Dowd, 9500 Stearns Ave, Oakland, CA 94618, USA b Mechanical Engineering and Materials Science MS 321, Rice University, P.O. Box 1892, Houston, TX 77251 1892, USA |
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Abstract: | In this paper we consider exact solutions for plane and axisymmetric deformations for a class of compressible elastic materials we call coharmonic. The coharmonic materials are derived from the harmonic materials by using Shield's inverse deformation theorem. The governing equations for the coharmonic material show the same kind of simplification associated with the harmonic materials. The equations reduce to first-order linear equations depending on an arbitrary harmonic function. They are intractable in general, so various ansätze are investigated. Boundary value problems for the coharmonic materials are compared with the same problems for harmonic materials. For certain boundary value problems, the harmonic materials exhibit well-known problematic behaviour which limits their use as models of material behaviour. The corresponding solutions for the coharmonic materials do not display these non-physical features. |
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Keywords: | Non-linear elasticity Exact solutions Coharmonic materials Shield's theorem |
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