{"title":"模拟塑性材料力学行为的矩形有限元","authors":"Alexey V. Mazaev","doi":"10.1016/j.ijengsci.2025.104290","DOIUrl":null,"url":null,"abstract":"<div><div>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.</div></div>","PeriodicalId":14053,"journal":{"name":"International Journal of Engineering Science","volume":"213 ","pages":"Article 104290"},"PeriodicalIF":5.7000,"publicationDate":"2025-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Rectangular finite elements for modeling the mechanical behavior of auxetic materials\",\"authors\":\"Alexey V. Mazaev\",\"doi\":\"10.1016/j.ijengsci.2025.104290\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>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.</div></div>\",\"PeriodicalId\":14053,\"journal\":{\"name\":\"International Journal of Engineering Science\",\"volume\":\"213 \",\"pages\":\"Article 104290\"},\"PeriodicalIF\":5.7000,\"publicationDate\":\"2025-05-08\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"International Journal of Engineering Science\",\"FirstCategoryId\":\"5\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0020722525000771\",\"RegionNum\":1,\"RegionCategory\":\"工程技术\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"ENGINEERING, MULTIDISCIPLINARY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Journal of Engineering Science","FirstCategoryId":"5","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0020722525000771","RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"ENGINEERING, MULTIDISCIPLINARY","Score":null,"Total":0}
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.
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.