Large Deformation Behavior of Plane Periodic Truss Networks. Part 1. Closed-Form Solution for Single Node Cells

IF 1.8 3区工程技术 Q2 ENGINEERING, MULTIDISCIPLINARY

Journal of Elasticity Pub Date : 2025-01-23 DOI:10.1007/s10659-025-10109-9

Massimo Cuomo, Claude Boutin, Carmelo Pannitteri

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Abstract

This article focuses on the derivation of explicit descriptions of networks in large deformation through the homogenization method of discrete media. Analytical models are established for the in-plane behavior of a planar periodic truss, whose cell contains a single node, as frequently encountered in practice. The cell is composed of bars that support only axial forces and are connected by perfect hinges. For the considered type of trusses, (given that the equilibrium conditions of the node and of the cell coincide) closed-form expressions for the local behaviour in the case of large deformations can be derived. This case makes it possible to combine the non-linearities arising from large deformations on the one hand and rheological characteristics on the other, and to compare their respective effects as a function of cell morphology. The results are illustrated by the shear and extension responses of specific trusses. The analysis is carried out for bars with stiffening, linear or softening behavior. The combination of the effects of geometrical non-linearities, rheological non-linearities and anisotropy results in particularly rich behaviors of the network.

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平面周期性桁架网络的大变形特性。第1部分。单节点单元的封闭形式解决方案

本文主要讨论了用离散介质均匀化方法推导大变形网络的显式描述。建立了在实际应用中经常遇到的单元为单节点的平面周期桁架的面内特性分析模型。该单元由仅支持轴向力的杆组成，并通过完美的铰链连接。对于所考虑的桁架类型，（假设节点和单元的平衡条件一致）可以导出大变形情况下局部行为的封闭形式表达式。这种情况使得将一方面由大变形引起的非线性和另一方面由流变特性引起的非线性结合起来，并比较它们各自作为细胞形态函数的影响成为可能。结果由特定桁架的剪切和拉伸响应来说明。对具有加劲、线性或软化行为的杆进行了分析。几何非线性、流变非线性和各向异性的共同作用使网络具有特别丰富的行为。

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.