重庆大学学报2025，Vol.48Issue(4)：40-53,14.DOI:10.11835/j.issn.1000-582X.2024.268
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
摘要
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 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Key words
elliptic thermal inclusion/perfect bonded interface/bi-material/closed-form solution分类
数理科学引用本文复制引用
刘俊,Feodor M.Borodich,吕鼎,金晓清..双材料含椭圆热夹杂的平面应变问题解析解[J].重庆大学学报,2025,48(4):40-53,14.基金项目
超常环境非线性力学全国重点实验室开放基金项目.Supported by Opening Fund of State Key Laboratory of Nonlinear Mechanics. （）
