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Mathematics and Mechanics of Solids
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Irrotational Deformations in Finite Compressible Elasticity

Jeremiah G. Murphy

Department of Science, R. TC. Tallaght, Dublin 24, Ireland

This paper examines nonhomogeneous deformations of homogeneous, isotropic, compressible, nonlinearly elastic solids. It is assumed that the deformation is the gradient of a scalar field, and then determine the equation satisfied by this field from the equation of equilibrium. The strain energy function assumed is a generalization of the harmonic material and the generalized Varga material. For the special case of the generalized Varga material, a similarity solution is found for the scalar field. This solution describes the deformation of regions bounded by a family of surfaces which includes circles, ellipses, and hyperbolas in two and three dimensions. The solution is then partially extended to the more general elastic material.

Mathematics and Mechanics of Solids, Vol. 2, No. 4, 491-502 (1997)
DOI: 10.1177/108128659700200406
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