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Surface Green's Functions for an Incompressible, Transversely Isotropic Elastic Half-Space

Richard S. Chadwick, Brett Shoelson and Hongxue Cai
SIAM Journal on Applied Mathematics
Vol. 64, No. 4 (Apr. - Jun., 2004), pp. 1186-1197
Stable URL: http://www.jstor.org/stable/4095977
Page Count: 12
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Surface Green's Functions for an Incompressible, Transversely Isotropic Elastic Half-Space
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Abstract

The surface displacements produced by normal and tangential point loads applied to the surface of an incompressible, transversely isotropic material are considered when anisotropy is produced by a single family of fibers oriented perpendicular to the surface normal. Three elastic constants (two shear moduli and a fiber modulus) characterize the linear elasticity of such a material. The problems are solved analytically in two-dimensional Fourier transform space, and explicit surface displacement formulae are given for the inverses in physical space. Simple relations are given as asymptotic expansions for weak anisotropy. Computed surface displacement patterns are illustrated, and the application of the results to atomic force microscopy is discussed.

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