两个圆形不可压缩液体包裹体

ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik Pub Date : 2024-01-19 DOI:10.1002/zamm.202300679

Xu Wang, P. Schiavone

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引用次数: 0

摘要

我们应用 Muskhelishvili 的复变方法来求解与嵌入无限各向同性弹性矩阵中的两个圆形不可压缩液体夹杂物有关的平面应变问题，该矩阵受到均匀的远程平面内法向应力。我们主要借助保角映射和解析延续推导出了该问题的解析解。为了证明我们的解析解，我们给出了详细的数值结果，描述了两个液体内含物内部的均匀静水压力、沿基体侧两个圆形液固界面的非均匀箍应力以及两个圆形液体内含物内部的非均匀刚体旋转。

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Two circular incompressible liquid inclusions

We apply Muskhelishvili's complex variable method to solve the plane strain problem associated with two circular incompressible liquid inclusions embedded in an infinite isotropic elastic matrix subjected to uniform remote in‐plane normal stresses. An analytical solution to the problem is derived primarily with the aid of conformal mapping and analytic continuation. To demonstrate our analytical solution, we present detailed numerical results characterizing the internal uniform hydrostatic stresses within the two liquid inclusions, the nonuniform hoop stresses along the two circular liquid‐solid interfaces on the matrix side and the nonuniform rigid body rotations within the two circular liquid inclusions.

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ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik

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