A liquid inclusion having an n-fold axis of symmetry in an infinite isotropic elastic matrix

IF 1.9 4区工程技术 Q3 MECHANICS Continuum Mechanics and Thermodynamics Pub Date : 2023-12-24 DOI:10.1007/s00161-023-01274-0

Xu Wang, Peter Schiavone

引用次数: 0

Abstract

We first study the plane strain problem associated with an incompressible liquid inclusion having an n-fold axis of symmetry which is embedded in an infinite isotropic elastic matrix subjected to uniform remote hydrostatic stresses. A closed-form solution is derived using Muskhelishvili’s complex variable formulation, a four-term conformal mapping function and the application of analytic continuation. The pair of analytic functions characterizing the elastic field in the matrix is completely determined in elementary closed-form. Explicit expressions are obtained and graphically illustrated for the internal uniform hydrostatic stresses within the liquid inclusion and the hoop stress along the liquid–solid interface on the matrix side. The closed-form solution for a linearly compressible liquid inclusion having an n-fold axis of symmetry is also obtained.

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无限各向同性弹性基体中具有 n 折对称轴的液态包合物

我们首先研究了与具有 n 折对称轴的不可压缩液体包含体相关的平面应变问题，该液体包含体嵌入到无限各向同性弹性矩阵中，受到均匀的远程静水压力。利用 Muskhelishvili 的复变公式、四项保角映射函数和解析延续的应用，得出了闭式解。矩阵中表征弹性场的一对解析函数完全以基本闭合形式确定。对于液体包裹体内部的均匀静水应力和矩阵一侧沿液固界面的箍应力，我们获得了明确的表达式，并用图形进行了说明。此外，还得到了具有 n 折对称轴的线性可压缩液体包容体的闭式解。

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来源期刊

Continuum Mechanics and Thermodynamics 物理-力学

CiteScore

5.30

自引率

15.40%

发文量

审稿时长

>12 weeks

期刊介绍： This interdisciplinary journal provides a forum for presenting new ideas in continuum and quasi-continuum modeling of systems with a large number of degrees of freedom and sufficient complexity to require thermodynamic closure. Major emphasis is placed on papers attempting to bridge the gap between discrete and continuum approaches as well as micro- and macro-scales, by means of homogenization, statistical averaging and other mathematical tools aimed at the judicial elimination of small time and length scales. The journal is particularly interested in contributions focusing on a simultaneous description of complex systems at several disparate scales. Papers presenting and explaining new experimental findings are highly encouraged. The journal welcomes numerical studies aimed at understanding the physical nature of the phenomena. Potential subjects range from boiling and turbulence to plasticity and earthquakes. Studies of fluids and solids with nonlinear and non-local interactions, multiple fields and multi-scale responses, nontrivial dissipative properties and complex dynamics are expected to have a strong presence in the pages of the journal. An incomplete list of featured topics includes: active solids and liquids, nano-scale effects and molecular structure of materials, singularities in fluid and solid mechanics, polymers, elastomers and liquid crystals, rheology, cavitation and fracture, hysteresis and friction, mechanics of solid and liquid phase transformations, composite, porous and granular media, scaling in statics and dynamics, large scale processes and geomechanics, stochastic aspects of mechanics. The journal would also like to attract papers addressing the very foundations of thermodynamics and kinetics of continuum processes. Of special interest are contributions to the emerging areas of biophysics and biomechanics of cells, bones and tissues leading to new continuum and thermodynamical models.