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Zhao, X.J.; Rajapakse, R.K.N.D.
International journal of engineering science, 11/2009, Letnik: 47, Številka: 11Journal Article
Consideration of surface (interface) energy effects on the elastic field of a solid material has applications in several modern problems in solid mechanics. The Gurtin–Murdoch continuum model M.E. Gurtin, A.I. Murdoch, Arch. Ration. Mech. Anal. 57 (1975) 291–323; M.E. Gurtin, J. Weissmuller, F. Larché, Philos. Mag. A 78 (1998) 1093–1109 accounting for surface energy effects is applied to analyze the elastic field of an isotropic elastic layer bonded to a rigid base. The surface properties are characterized by the residual surface tension and surface Lame constants. The general solutions of the bulk medium expressed in terms of Fourier integral transforms and Hankel integral transforms are used to formulate the two-dimensional and axisymmetric three-dimensional problems, respectively. The generalized Young–Laplace equation for a surface yields a set of non-classical boundary conditions for the current class of problems. An explicit analytical solution is presented for the elastic field of a layer. The layer solution is specialized to obtain closed-form solutions for semi-infinite domains. Selected numerical results are presented to show the influence of surface elastic constants and layer thickness on stresses and displacements.
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