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Influence of surface energy effect on elastic field of layered elastic medium

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Document pages: 11 pages

Abstract: In this paper, the influence of surface energy effect on layered elastic half space under axisymmetric surface load is analyzed. Based on the classical linear elastic theory and the complete Gurtin Murdoch constitutive relation, the boundary value problems of volume and surface are established. Using the analytical methods of love representation and Hankel integral transformation, the integral solutions of displacement field and stress field are derived. Then an effective numerical quadrature is applied to accurately calculate all involved integrals. Numerical results are selected to describe the effects of various parameters on the elastic field. The numerical results show that the surface stress has a significant effect on both displacementsacement and stress fields. It is also found that the layered half space becomes stiffer with the presence of surface stresses. In addition, unlike the classical elasticity solution, size-dependent behavior of elastic fields is noted. The present analytical solutions provide fundamental understanding of the influence of surface energy on layered elastic materials. It can also be used as a benchmark solution for the development of numerical techniques such as FEM and BEM, for analysis of more complex problems involving a layered medium under the influence of surface energy effects.

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