The effect of applying different surface elasticity models related to the Gurtin–Murdoch and Steigmann–Ogden theories to the problem on an interaction of a dislocation row with a flat surface of a semi-infinite three-dimensional body is analyzed in the paper. The boundary conditions in the case of an arbitrary shape of a cylindrical surface under the plane strain are derived within the framework of the Steigmann–Ogden model involving all simplified versions of the Gurtin–Murdoch model and the Gurtin–Murdoch model itself. The boundary condition used in the paper for the flat surface is a particular case of the general one. The analytical solution of the corresponding boundary value problem is obtained in the paper in a closed form for the elastic field. Based on this solution, some numerical examples of the stress distribution at the surface and the image force acting on each dislocation are presented. It is shown that incorporating the bending resistance of the surface in the Steigmann–Ogden model leads to the decrease of some stresses and increase the other ones at the surface and to the decrease of the image force, as compared with those obtained by the Gurtin–Murdoch membrane theory of the surface.

本文分析了应用与 Gurtin-Murdoch 和 Steigmann-Ogden 理论相关的不同表面弹性模型来解决位错列与半无限三维体平面相互作用问题的效果。平面应变下任意形状的圆柱表面情况下的边界条件是在 Steigmann-Ogden 模型的框架内导出的，涉及 Gurtin-Murdoch 模型的所有简化版本和 Gurtin-Murdoch 模型本身。论文中使用的平面边界条件是一般边界条件的一种特殊情况。文中以弹性场的封闭形式得到了相应边值问题的解析解。基于该解，给出了表面应力分布和作用在每个位错上的镜像力的一些数值示例。结果表明，与 Gurtin-Ogden 模型相比，在 Steigmann-Ogden 模型中加入表面抗弯力会导致表面的一些应力减少，而其他应力增加，从而导致像力减小。默多克表面膜理论。