螺位错场的非线性力学解

A Screw Dislocation by Nonlinear Continuum Mechanics

本文以非线性连续体几何场论为理论基础，分析了无限大体中一个螺位错引起的应力场。结果揭示了非线性高阶效应的影响。当不考虑高阶效应时，所求得的应力场可退化为经典线弹性理论的结果。本文还对螺位错引起的体力矩场进行了求解。获得了无限大体中单个螺位错引起的体力矩的解析表达式。作为理论结果的应用，本文研究了界面附近螺位错的应力场和体力矩场。揭示了它们对界面力学性能的影响。

Based on the nonlinear geometry field theory of continuum mechanics,this paper analyzes the stress field due to a screw dislocation in an infinite medium.The results reveal the high-order effect of the stress field.When this effect is small,the result can be reduced to one of the classical linear elasticity. The body couple field of the screw dislocation is also investigated in this paper.The analytical expression of the body couple due to a screw dislocation is obtained with small rotation deformation. As the application of theoretical results,the stress and the body couple at the interface of the crystals are calculated when the screw dislocation is near the interface.