A mode III arc-shaped crack with surface elasticity

被引：32
|
作者：
Wang, Xu [1 ]
机构：
[1] E China Univ Sci & Technol, Sch Mech & Power Engn, Shanghai 200237, Peoples R China
来源：
ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK | 2015年 / 66卷 / 04期
基金：
中国国家自然科学基金;
关键词：
Arc-shaped crack; Antiplane deformation; Surface elasticity; Conformal mapping; Logarithmic singularity; Square root singularity; Cauchy singular integro-differential equation; CLARIFICATION; SOLIDS;
D O I：
10.1007/s00033-014-0482-x
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We study the effect of surface elasticity on an arc-shaped crack in a linearly elastic isotropic homogeneous material under antiplane shear deformation. The surface mechanics is incorporated by using a continuum-based surface/interface model of Gurtin and Murdoch. We obtain a complete solution by reducing the problem to two decoupled first-order Cauchy-type singular integro-differential equations. It is shown that different from the case of a straight crack, the stresses exhibit both the weak logarithmic and the strong square root singularities at the tips of the arc crack.
引用
收藏
页码：1987 / 2000
页数：14
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