本文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，当前解析解引入了一个新的材料参数（范围从-1到1）和五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，本文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本文推导解析解的正确性。

This article focuses on the analysis and solution of the plane strain problem of bi-material containing an elliptical cylindrical thermal inclusion. Following the inclusion analysis method proposed by Eshelby, we derive closed-form analytical solutions for the elastic field induced by an elliptical thermal inclusion. Inspired by Dundurs' parameters, we introduce a new material parameter (ranging from -1 to 1) and five tensorial structured expressions to succinctly represent the current analytical solution, facilitating practical applications. For typical circular inclusion problems, our analytical solution can be greatly simplified, and we derive jump conditions for displacement, strain, and stress at the bonded interface of the bi-material. By adjusting Young's moduli and Poisson's ratios of the bi-material, the current solutions can degenerate into analytical solutions for a full or half-plane containing a thermal elliptical inclusion. The consistency of these solutions with previously published analytical solutions for specific cases, along with the numerical solutions presented in this article matching those in the literature, confirms the correctness of the derived analytical solutions in this study.

O34

考虑材料微观结构的复杂接触分析研究