{"title":"用A - ν0图分析简单物质立方晶体的弹性性质","authors":"A. I. Epishin, D. S. Lisovenko","doi":"10.1134/S0025654425602551","DOIUrl":null,"url":null,"abstract":"<p>The graphical diagram <i>A</i> – ν<sub>0</sub> proposed earlier by the authors was used to analyze the elastic properties of cubic crystals of simple substances. The elastic properties of crystals both at room temperature and their temperature dependences are considered. As the temperature increases, a general trend is observed for most crystals of simple substances: the points (<i>A</i>, ν<sub>0</sub>) characterizing the elastic properties of crystals shift in the direction towards the limiting angle of the diagram (<i>A</i> = 1.5, <span>\\({{\\nu }_{0}} = 0.5)\\)</span>, i.e., in the towards of the region of special extrema being typical for metastable crystals, for example, such as crystals with shape-memory effect. The use of the <i>A</i> – ν<sub>0</sub> diagram made it possible to graphically represent and explain the relationships between the basic values of the elastic moduli of cubic crystals: Young’s modulus <span>\\({{E}_{0}}\\)</span>, shear modulus <span>\\({{G}_{0}}\\)</span>, and volumetric modulus of elasticity <span>\\(B\\)</span>.</p>","PeriodicalId":697,"journal":{"name":"Mechanics of Solids","volume":"60 4","pages":"2385 - 2397"},"PeriodicalIF":0.9000,"publicationDate":"2025-10-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Analysis of Elastic Properties of Cubic Crystals of Simple Substances Using the Diagram A – ν0\",\"authors\":\"A. I. Epishin, D. S. Lisovenko\",\"doi\":\"10.1134/S0025654425602551\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>The graphical diagram <i>A</i> – ν<sub>0</sub> proposed earlier by the authors was used to analyze the elastic properties of cubic crystals of simple substances. The elastic properties of crystals both at room temperature and their temperature dependences are considered. As the temperature increases, a general trend is observed for most crystals of simple substances: the points (<i>A</i>, ν<sub>0</sub>) characterizing the elastic properties of crystals shift in the direction towards the limiting angle of the diagram (<i>A</i> = 1.5, <span>\\\\({{\\\\nu }_{0}} = 0.5)\\\\)</span>, i.e., in the towards of the region of special extrema being typical for metastable crystals, for example, such as crystals with shape-memory effect. The use of the <i>A</i> – ν<sub>0</sub> diagram made it possible to graphically represent and explain the relationships between the basic values of the elastic moduli of cubic crystals: Young’s modulus <span>\\\\({{E}_{0}}\\\\)</span>, shear modulus <span>\\\\({{G}_{0}}\\\\)</span>, and volumetric modulus of elasticity <span>\\\\(B\\\\)</span>.</p>\",\"PeriodicalId\":697,\"journal\":{\"name\":\"Mechanics of Solids\",\"volume\":\"60 4\",\"pages\":\"2385 - 2397\"},\"PeriodicalIF\":0.9000,\"publicationDate\":\"2025-10-08\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Mechanics of Solids\",\"FirstCategoryId\":\"5\",\"ListUrlMain\":\"https://link.springer.com/article/10.1134/S0025654425602551\",\"RegionNum\":4,\"RegionCategory\":\"工程技术\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MECHANICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mechanics of Solids","FirstCategoryId":"5","ListUrlMain":"https://link.springer.com/article/10.1134/S0025654425602551","RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MECHANICS","Score":null,"Total":0}
Analysis of Elastic Properties of Cubic Crystals of Simple Substances Using the Diagram A – ν0
The graphical diagram A – ν0 proposed earlier by the authors was used to analyze the elastic properties of cubic crystals of simple substances. The elastic properties of crystals both at room temperature and their temperature dependences are considered. As the temperature increases, a general trend is observed for most crystals of simple substances: the points (A, ν0) characterizing the elastic properties of crystals shift in the direction towards the limiting angle of the diagram (A = 1.5, \({{\nu }_{0}} = 0.5)\), i.e., in the towards of the region of special extrema being typical for metastable crystals, for example, such as crystals with shape-memory effect. The use of the A – ν0 diagram made it possible to graphically represent and explain the relationships between the basic values of the elastic moduli of cubic crystals: Young’s modulus \({{E}_{0}}\), shear modulus \({{G}_{0}}\), and volumetric modulus of elasticity \(B\).
期刊介绍：
Mechanics of Solids publishes articles in the general areas of dynamics of particles and rigid bodies and the mechanics of deformable solids. The journal has a goal of being a comprehensive record of up-to-the-minute research results. The journal coverage is vibration of discrete and continuous systems; stability and optimization of mechanical systems; automatic control theory; dynamics of multiple body systems; elasticity, viscoelasticity and plasticity; mechanics of composite materials; theory of structures and structural stability; wave propagation and impact of solids; fracture mechanics; micromechanics of solids; mechanics of granular and geological materials; structure-fluid interaction; mechanical behavior of materials; gyroscopes and navigation systems; and nanomechanics. Most of the articles in the journal are theoretical and analytical. They present a blend of basic mechanics theory with analysis of contemporary technological problems.
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