Elastic Displacements and Viscous Flows in Wedge-Shaped Geometries with a Straight Edge: Green’s Functions for Perpendicular Forces

IF 1.4 3区工程技术 Q2 ENGINEERING, MULTIDISCIPLINARY

Journal of Elasticity Pub Date : 2025-06-19 DOI:10.1007/s10659-025-10146-4

Abdallah Daddi-Moussa-Ider, Andreas M. Menzel

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引用次数: 0

Abstract

Edges are abundant when elastic solids glide in guiding rails or fluids are contained in vessels. We here address induced displacements in elastic solids or small-scale flows in viscous fluids in the vicinity of one such edge. For this purpose, we solve the governing elasticity equations for linearly elastic, potentially compressible solids, as well as the low-Reynolds-number flow equations for incompressible fluids. Technically speaking, we derive the associated Green’s functions under confinement by two planar boundaries that meet at a straight edge. The two boundaries both feature no-slip or free-slip conditions, or one of these two conditions per boundary. Previously, we solved the simpler case of the force being oriented parallel to the straight edge. Here, we complement this solution by the more challenging case of the force pointing into a direction perpendicular to the edge. Together, these two cases provide the general solution. Specific situations in which our analysis may find application in terms of quantitative theoretical descriptions are particle motion in confined colloidal suspensions, dynamics of active microswimmers near edges, or actuated distortions of elastic materials due to activated contained functionalized particles.

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具有直边的楔形几何中的弹性位移和粘性流动：垂直力的格林函数

当弹性固体在导轨中滑动或流体在容器中包含时，边缘丰富。我们在此讨论弹性固体中的诱导位移或在此类边缘附近的粘性流体中的小规模流动。为此，我们求解了线性弹性、潜在可压缩固体的控制弹性方程，以及不可压缩流体的低雷诺数流动方程。从技术上讲，我们导出了在两个平面边界的约束下的相关格林函数。两个边界都具有无滑移或自由滑移条件，或者每个边界具有这两个条件中的一个。之前，我们解决了力方向平行于直边的简单情况。在这里，我们通过更具有挑战性的情况来补充这个解决方案，即力指向垂直于边缘的方向。这两种情况一起提供了一般解决方案。我们的分析可以在定量理论描述方面找到应用的具体情况是：受限胶体悬浮液中的粒子运动，边缘附近活性微游泳者的动力学，或由于活化的含有功能化颗粒而引起的弹性材料的致动变形。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Elasticity 工程技术-材料科学：综合

CiteScore

3.70

自引率

15.00%

发文量

审稿时长

>12 weeks

期刊介绍： The Journal of Elasticity was founded in 1971 by Marvin Stippes (1922-1979), with its main purpose being to report original and significant discoveries in elasticity. The Journal has broadened in scope over the years to include original contributions in the physical and mathematical science of solids. The areas of rational mechanics, mechanics of materials, including theories of soft materials, biomechanics, and engineering sciences that contribute to fundamental advancements in understanding and predicting the complex behavior of solids are particularly welcomed. The role of elasticity in all such behavior is well recognized and reporting significant discoveries in elasticity remains important to the Journal, as is its relation to thermal and mass transport, electromagnetism, and chemical reactions. Fundamental research that applies the concepts of physics and elements of applied mathematical science is of particular interest. Original research contributions will appear as either full research papers or research notes. Well-documented historical essays and reviews also are welcomed. Materials that will prove effective in teaching will appear as classroom notes. Computational and/or experimental investigations that emphasize relationships to the modeling of the novel physical behavior of solids at all scales are of interest. Guidance principles for content are to be found in the current interests of the Editorial Board.