表面応力と表面弾性特性を考慮した表面グリーン関数 : Stroh形式の三次元等方性弾性体への適用

Abstract

Surface stress and surface elasticity are related to an organization of surface pattern and reconstruction of surface atoms. Recently, nanotechnology such as quantum dot and carbon nano fiber is developed and is used for new advanced devices and industrial products. When the size of material reduces to a nanometer level, a ratio of surface to volume increases. Then, surface stress and surface elasticity influence on mechanical responce near surface for an external force on the surface. Stroh formalism is very useful for analyzing the stress and displacement in anisotropic materials. When the Stroh formalism is applied to isotropic materials, the eigen matrix dervied from equilibrium equation yields a triple root of i (i: imaginary unit), and then an independent eigen vector corresponding to the eigen value can not be determined. It is very hard to derive a three-dimensional solution for isotropic materials using Stroh formalism. In this paper, surface Green function for isotropic materials is derived using Stroh formalism. The derived Green function without surface stress nor surface elasticity agrees with the solution of Boussinesq. The surface Green function is used for analyzing the displacement fields in amorphous silicon considering surface stress and surface elasticity. It was found that the displacements considering surface stress and elasticity were less than those not considering them.