双材料含椭圆热夹杂的平面应变问题解析解  

A closed-form solution to an elliptic cylindrical thermal inclusion in a bi-material under plane strain

作　　者：刘俊[1] Feodor M.Borodich 吕鼎 金晓清[1,2] LIU Jun;Feodor MBorodich;LYU Ding;JIN Xiaoqing(College of Aerospace Engineering,Chongqing University,Chongqing 400044,P.R.China;State Key Laboratory of Mechanical Transmissions,Chongqing University,Chongqing 400044,P.R.China;Department of Biomedical Engineering,Wayne State University,Detroit 48201,America)

机构地区：[1]重庆大学航空航天学院,重庆400044 [2]重庆大学机械传动国家重点实验室,重庆400044 [3]韦恩州立大学生物医学工程系底特律48201

出　　处：《重庆大学学报》2025年第4期40-53,共14页Journal of Chongqing University

基　　金：超常环境非线性力学全国重点实验室开放基金项目。

摘　　要：以含椭圆热夹杂的结合双材料为研究对象,对其平面应变问题进行解析求解和算例讨论。根据Eshelby提出的夹杂分析方法,推导了椭圆夹杂受热本征应变作用引起的弹性场封闭解析解。受Dundurs参数启发,当前解析解引入了1个新的材料参数(范围-1~1)和5个类张量表达式来简洁表达,使之便于实际应用。针对典型的圆形夹杂问题,解析解在形式上可以得到极大简化,且根据得到的解析解给出了双材料界面上位移、应变和应力的跳跃条件。通过调整双材料的杨氏模量和泊松比,当前解可以退化为全平面或半平面含椭圆热夹杂的解析解。本文的数值解与已发表文献中的数值解的一致性证实了所推导解析解的正确性。This article addresses the plane strain problem of a bi-material system containing an elliptical cylindrical thermal inclusion.Using Eshelby’s inclusion analysis method,we derive closed-form analytical solutions for the elastic field induced by the thermal inclusion.Inspired by Dundurs’parameters,we introduce a new material parameter(ranging from-1 to 1)and five tensorially structured expressions to succinctly represent the analytical solution,facilitating its practical applications.For circular inclusion scenarios,the analytical solution simplifies significantly,and we derive explicit jump conditions for displacement,strain,and stress at the bonded interface of the bi-material.By adjusting the Young’s moduli and Poisson’s ratios of the bi-material,the solution can reduce to cases of a full or half-plane containing a thermal elliptical inclusion.The accuracy of the proposed solution is validated through consistency with previously published analytical results and by matching numerical solutions from the literature,confirming the correctness and reliability of the derived analytical expressions.

关 键 词：椭圆热夹杂 完美结合界面 双材料 解析解 

分 类 号：O34[理学—固体力学]