曲率依赖表面张力的Ⅰ/Ⅱ型界面断裂
Curvilinear Mode-I/Mode-II interface fracture with a curvature-dependent surface tension on the boundary
摘要：
以位于无限薄弹性基体中的部分脱粘薄弹性夹杂边界上的混合型曲线界面断裂为例，进一步发展了Sendova和Walton \cite{SendovaWalton2010}，Zemlyanova \cite{Zemlyanova2013}，Zemlyanova和Walton \cite{Zemlyanova2012}提出的断裂力学新模型。材料的纳米结构的效果被纳入模型中的曲率依赖的表面张力作用在断裂的边界上的形式。它示出的表面张力的引入允许消除的顺序$1/2$存在于线弹性断裂力学的经典振荡和功率奇异性。求解该问题的数学方法是基于Muskhelishvili的复位势和Savruk的整表示。将力学问题化为奇异积分微分方程系统，再将奇异积分微分方程系统化为弱奇异积分方程系统。给出了数值计算结果，并与已知结果进行了比较。
英文摘要：
A new model of fracture mechanics considered previously by Sendova and Walton \cite{SendovaWalton2010}, Zemlyanova \cite{Zemlyanova2013}, and Zemlyanova and Walton \cite{Zemlyanova2012} is further developed on the example of a mixed mode curvilinear interface fracture located on the boundary of a partially debonded thin elastic inclusion embedded in an infinite thin elastic matrix. The effect of the nano-structure of the material is incorporated into the model in the form of a curvature-depended surface tension acting on the boundary of the fracture. It is shown that the introduction of the surface tension allows to eliminate the classical oscillating and power singularities of the order $1/2$ present in the linear elastic fracture mechanics. The mathematical methods used to solve the problem are based on the Muskhelishvili's complex potentials and the Savruk's integral representations. The mechanical problem is reduced to the system of singular integro-differential equations which is further reduced to a system of weakly-singular integral equations. The numerical computations and comparison with known results are presented.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
