Antiplane shear crack in a prestressed elastic medium based on the couple stress theory  

作　　者：Jian CHEN Yawei WANG Xianfang LI 

机构地区：[1]School of Civil Engineering,Central South University,Changsha 410075,China

出　　处：《Applied Mathematics and Mechanics(English Edition)》2023年第4期583-602,共20页应用数学和力学（英文版）

基　　金：Project supported by the National Natural Science Foundation of China(Nos.11672336,12072374)。

摘　　要：A prestressed elastic medium containing a mode-Ⅲcrack is studied by means of the couple stress theory(CST).Based on the CST under initial stresses,a governing differential equation along with a mixed boundary value problem is established.The singularities of the couple stress and force stress near the crack tips are analyzed through the asymptotic crack-tip fields resulting from the characteristic expansion method.To determine their intensity,a hypersingular integral equation is derived and numerically solved with the help of the Chebyshev polynomial.The obtained results show a strong size-dependence of the out-of-plane displacement on the crack and the couple stress intensity factor(CSIF)and the force stress intensity factor(FSIF)around the crack tips.The symmetric part of the shear stress has no singularity,and the skew-symmetric part related to the couple stress exhibits an r^(-3/2)singularity,in which r is the distance from the crack tip.The initial stresses also affect the crack tearing displacement and the CSIF and FSIF.

关 键 词：couple stress theory(CST) initial stress antiplane shear crack SINGULARITY hypersingular integral equation 

分 类 号：O346.1[理学—固体力学]