考虑界面应力时含椭圆孔正交异性材料的反平面问题研究

Study on orthotropic materials containing elliptic cavity under anti-plane shear due to interface stress

研究了远场作用反平面剪切载荷时含纳米椭圆孔正交异性材料问题。基于Gurtin-Murdoch表面/界面理论模型引入界面应力,利用复变弹性理论和保角映射方法,给出了考虑界面应力时含椭圆孔正交异性材料反平面问题的解析解答,获得了应力场的闭合解。研究表明:当椭圆孔在纳米量级时,正交异性材料内应力场受孔隙尺寸影响显著。随着椭圆孔尺寸的增大,界面效应对应力场的影响逐渐减弱,趋近于经典弹性理论的解答。界面效应对正交异性材料内应力场的影响随着材料弹性主方向比55/44的增大逐渐减弱。

A theoretical study on the orthotropic materials containing nano elliptic cavity under anti-plane shear is reported. Interface stress is introduced based on the theory of Gurtin-Murdoch surface/interface model. A rigorous whole-field solution is presented by using the complex variable elasticity theory and the conformal mapping method, in terms of which closed-form solutions of the stress field is obtained. The results reveal that the stress fields in the orthotropic materials are size dependent when the size of the nano elliptic cavity is on the order of nanometer. The present solution approaches to the classical elasticity theory results with the increase of the nano elliptic cavity. The influence of the interfacial effects on the stress fields in the orthotropic materials decrease with the increase of the ratio of elastic main direction 55/ 44.