双材料含椭圆热夹杂的平面应变问题解析解

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中图分类号：034 文献标志码：A 文章编号：1000-582X（2025）04-040-14

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

LIU Jun'， Feodor M. Borodich'，LYU Ding2，JIN Xiaoqinglb

（. College of Aerospace Engineering； lb. State Key Laboratory of Mechanical Transmissions， Chongqing

University， Chongqing 40o044， P.R. China； 2.Department of Biomedical Engineering， Wayne State University， Detroit 48201， America）

Abstract： 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 forthe elastic field induced by the thermal inclusion.Inspired by Dundurs' parameters，we introduce a new material parameter （ranging from to 1） and five tensorially structured expressions to succinctly represent the analytical solution， facilitating its practical applications. For circular inclusion scenarios， the analytical solution simplifiessignificantly，and wederiveexplicit jumpconditions fordisplacement，strain，andstres at the bonded interface of thebi-material.Byadjusting theYoung's moduli and Poisson'sratios of thebi-material，the solution can reduce to cases of a full orhalf-plane containing a thermal ellptical 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.

Keywords： elliptic thermal inclusion； perfect bonded interface； bi-material； closed-form solution

双材料问题的研究在许多工程实际中有重要应用，例如，芯片传感器、压电层和压磁层3。（剩余10558字）