Vol. 8, No. 1, 2013

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Transient 3D singular solutions for use in problems of prestressed highly elastic solids

Louis Milton Brock

Vol. 8 (2013), No. 1, 37–49

The dynamic perturbation of a neo-Hookean solid in an initial equilibrium state of finite deformation can be viewed as the superposition of infinitesimal strains upon large ones. Three transient 3D singular problems whose solutions are useful in generating the former are studied. The first and second concern, respectively, a concentrated force and a point displacement discontinuity in an unbounded solid; the third problem involves a concentrated force applied at a point on the surface of a half-space. The governing equations resemble those for a linear anisotropic solid. Analytic solutions are obtained, as well as formulas and calculations for anisotropic wave speeds. Formulation of the problems is in terms of Cartesian coordinates, but expressions for the solutions and wave speeds make use of a quasipolar coordinate system.

neo-Hookean, dynamic perturbation, 3D singular solution, transient
Received: 7 August 2012
Revised: 19 November 2012
Accepted: 22 November 2012
Published: 28 March 2013
Louis Milton Brock
Department of Mechanical Engineering
University of Kentucky
265 Ralph G. Anderson Building
Lexington KY 40506-0503
United States