【作者】 杨勇；

【导师】 唐立强；

【作者基本信息】 哈尔滨工程大学 ， 固体力学， 2006， 硕士

【摘要】 随着科学技术的发展，在工程实践中迫切需要解决微米和亚微米的设计和制造问题。最近发展的应变梯度理论为解决这些问题奠定了良好的基础。 本文综述了发展应变梯度理论的背景及意义，综述了四种应变梯度理论（CS应变梯度理论、SG应变梯度理论、MSG应变梯度理论和一种新的应变梯度理论）的特点及其相互关系，推导了四种应变梯度理论的平衡方程、几何方程、本构方程和应变能函数。综述了各种应变梯度理论在断裂力学中的应用以及各种应变梯度理论的发展现状。 本文综述了引入偶应力和转动梯度的偶应力理论，推导了一般偶应力理论的本构方程及其简化的偶应力边界条件。 应用偶应力理论和应变梯度理论求解了弹性—刚性Ⅲ型界面裂纹问题，利用偶应力理论的简化边界条件推导了弹性—刚性Ⅲ型界面裂纹问题的边界条件，采用量级分析，得到了位移场、应变场、对称应力场和反称应力场，高阶应力场具有r^-3的奇异性。本文所得到的位移场、应变场、对称应力场和反称应力场和文献[103]给出的Ⅲ型裂纹局部解相似。 本文的结果，为进一步研究应变梯度理论在断裂力学中的应用提供了良好的基础。更多还原

【Abstract】 There is an impending need to deal with design and manufacturing issues at the level of micros and submicros, along with science and technology developing. Good foundation can be given by the recent strain gradient theory, which can solve those problems.The background and the significance of the strain gradient are expatiated in this paper. The characteristic and interrelation of four strain gradient theories, such as CS strain gradient theory, SG strain gradient theory, MSG strain gradient theory and a new strain gradient theory are given. The equilibrium equation, the geometric equation, the constitutive equation and the strain energy function are obtained. Applications in fracture mechanics and the status of the four strain gradient theories are also expatiated in this paper.In this paper, the couple stress and rotational gradient vector are introduced, and the couple stress theory are expatiated. the constitutive equations and simple boundary conditions of couple stress theory are obtained.The mode Ⅲ interfacial crack between elasticity and rigidity is studied by the couple stress theory and the strain gradient theory. The boundary conditions are obtained in the simple boundary conditions of the couple stress theory. By asymptotically analyzing, the stress, strain and displacement of the mode Ⅲ interfacial crack-tip between elasticity and rigidity are obtained. And the high singulary stress has r^-3 singularity near the interfacial crack-tip. The symmetric stress and the anti-symmetric stress, strain and displacement of the mode Ⅲ interfacial crack-tip between elasticity and rigidity are similar to local solution on mode Ⅲ crack-tip by Reference [103].The foundation for further studying the strain gradient theory and applying the strain gradient theory to the fracture mechanics can be given by the result of this paper.更多还原