Analytical solutions for a surface-loaded isotropic elastic layer with surface energy effects

• Published in: International journal of engineering science 2009-11, Vol.47 (11), p.1433-1444
• Main Authors: Zhao, X.J., Rajapakse, R.K.N.D.
• Format: Article
• Language: English
• Subjects: Condensed matter: structure, mechanical and thermal properties; Constants; Displacements; Elastic layers; Elasticity; Exact sciences and technology; Exact solutions; Fluid surfaces and fluid-fluid interfaces; Fundamental areas of phenomenology (including applications); Integrals; Mathematical analysis; Mathematical models; Nanomechanics; Physics; Size-effects; Solid mechanics; Static elasticity (thermoelasticity...); Structural and continuum mechanics; Surface energy; Surface energy (surface tension, interface tension, angle of contact, etc.); Surface stress; Surfaces and interfaces; thin films and whiskers (structure and nonelectronic properties); Transforms
• ISSN: 0020-7225; 1879-2197
• DOI: 10.1016/j.ijengsci.2008.12.013

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.