Elastic response of surface-loaded half plane with influence of surface and couple stresses

摘要

This paper presents the elastic response of a surface-loaded half plane accounting for the simultaneous influence of surface and couple stresses. The underlying mathematical models for the bulk and the surface material are formulated, respectively, from the couple-stress and Gurtin-Murdoch surface-elasticity theories. A general solution for the elastic field within the bulk is derived in a closed form via the method of Fourier integral transform. All involved unknown coefficients are also determined in a closed form by enforcing the boundary conditions together with the continuity along the surface-bulk interface and the surface governing equation. An efficient quadrature is then adopted to numerically evaluate all involved integrals resulting from Fourier integral inversions. Results from an extensive numerical study have clearly reflected the crucial role of both surface and couple stresses on the elastic response of the half plane as well as the size-dependent characteristics of predicted solutions when the size of loading region is comparable to the internal length scales of the bulk and surface materials.