借助平面应变问题的Green函数,可推导出任意弱形状夹杂的Eshelby张量表达式。利用该Eshelby张量,给出了由温度本征应变在夹杂内、外产生的应变场和应力场理论解。目的是利用大型有限元软件ADINA和AN-SYS数值模拟含任意弱形状夹杂内、外部的应变场和应力场,验证我们的应力场理论解,为任意形状夹杂Eshelby张量的研究提供数值实验验证方法。计算结果表明:对于任意弱形状夹杂,我们的应力场理论解与ADINA和AN-SYS数值模拟结果吻合的很好。
By Green' s function on plane strain problems,we derive an explicit expression of Eshelby tensor for any weakly anisotropie shape inclusion. Using the Eshelby' s expression, we give expressions of the stress fields and the strain fields inside and outside the inclusions. The goal of this paper is to use ADINA program and ANSYS program for FEM to simulate the stress fields and to check our theoretical expressions. The simulating method based on FEM can be used to verify the results of any shape Eshelby tensor. Our theoretical expressions are consistent with the computational results simulated by ADINA and ANSYS.