模拟塑性材料力学行为的矩形有限元

IF 5.7 1区 工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY
Alexey V. Mazaev
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引用次数: 0

摘要

本文致力于探索矩形有限元模拟具有负泊松比的各向同性和正交异性材料的应力-应变状态的能力。通过在平面应力公式中引入线弹性,利用基于位移的有限元方法,对描述静力剪切和压痕作用下塑性材料力学行为的线性相容和二次不相容形状函数进行了评价。此外,对不相容矩形有限元的解析表达式进行了调整,以适应正交各向异性的情况。利用有效材料常数的解析表达式,将六手性和可重入蜂窝结构建模为具有均质特性的连续介质。研究结果表明,虽然经典的形状函数可能足以进行位移建模,但它们在准确预测材料的特征缺失行为和应力分布方面是无效的。相反,不相容形状函数在两种情况下都能有效地提供适当的应力模型。这项工作强调了不相容矩形有限元在具有负泊松比的先进材料分析中的相关性。为消声蜂窝结构及其复合材料的计算提供了有效的计算方法。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Rectangular finite elements for modeling the mechanical behavior of auxetic materials
This paper is devoted to the exploration of rectangular finite elements’ ability to model the stress-strain state of isotropic and orthotropic materials with a negative Poisson’s ratio, known as auxetic materials. By employing linear elasticity in the plane stress formulation, the research evaluates the linear compatible and the quadratic incompatible shape functions in describing the mechanical behavior of auxetic materials within a displacement-based finite element method under static shear and indentation. Additionally, the analytical expression of an incompatible rectangular finite element is adapted to accommodate an orthotropic case. Hexachiral and re-entrant honeycomb structures, characterized by auxetic behavior, are modeled as continuous media with homogenized properties using analytical expressions for their effective material constants. The findings reveal that while the classical shape functions may be sufficient for displacement modeling, they are ineffective in accurately predicting the characteristic auxetic behavior and stress distributions in auxetic materials. In contrast, the incompatible shape functions prove to be effective in providing appropriate stress modeling in both cases. This work underscores the relevance of the incompatible rectangular finite elements in the analysis of advanced materials with a negative Poisson’s ratio. It provides computationally efficient approaches for the calculation of auxetic honeycomb structures and multilayer composites based on them.
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来源期刊
International Journal of Engineering Science
International Journal of Engineering Science 工程技术-工程:综合
CiteScore
11.80
自引率
16.70%
发文量
86
审稿时长
45 days
期刊介绍: The International Journal of Engineering Science is not limited to a specific aspect of science and engineering but is instead devoted to a wide range of subfields in the engineering sciences. While it encourages a broad spectrum of contribution in the engineering sciences, its core interest lies in issues concerning material modeling and response. Articles of interdisciplinary nature are particularly welcome. The primary goal of the new editors is to maintain high quality of publications. There will be a commitment to expediting the time taken for the publication of the papers. The articles that are sent for reviews will have names of the authors deleted with a view towards enhancing the objectivity and fairness of the review process. Articles that are devoted to the purely mathematical aspects without a discussion of the physical implications of the results or the consideration of specific examples are discouraged. Articles concerning material science should not be limited merely to a description and recording of observations but should contain theoretical or quantitative discussion of the results.
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