{"title":"On a Contact Problem for a Homogeneous Plane with a Finite Crack under Friction","authors":"V. N. Hakobyan, A. A. Amirjanyan, L. V. Hakobyan","doi":"10.1134/S0025654423601593","DOIUrl":null,"url":null,"abstract":"<p>An exact solution to the contact problem of indentation of an absolutely rigid stamp with a straight base, taking into account friction, into one of the edges of a finite crack located in a homogeneous elastic plane is constructed. It is assumed that tangential contact stresses are directly proportional to normal contact pressure. In this case, it is believed that the friction coefficient is directly proportional to the coordinates of the contacting points of the contacting surfaces. The defining system of equations for the problem is derived in the form of an inhomogeneous Riemann problem for two functions with variable coefficients and its closed solution in quadratures is constructed. Simple formulas for contact stresses and the normal dislocation component of displacements of crack edge points are obtained. The patterns of changes in contact stresses and crack opening depending on the maximum value of the friction coefficient have been studied.</p>","PeriodicalId":697,"journal":{"name":"Mechanics of Solids","volume":"59 2","pages":"711 - 722"},"PeriodicalIF":0.6000,"publicationDate":"2024-09-12","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/S0025654423601593","RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MECHANICS","Score":null,"Total":0}
引用次数: 0
Abstract
An exact solution to the contact problem of indentation of an absolutely rigid stamp with a straight base, taking into account friction, into one of the edges of a finite crack located in a homogeneous elastic plane is constructed. It is assumed that tangential contact stresses are directly proportional to normal contact pressure. In this case, it is believed that the friction coefficient is directly proportional to the coordinates of the contacting points of the contacting surfaces. The defining system of equations for the problem is derived in the form of an inhomogeneous Riemann problem for two functions with variable coefficients and its closed solution in quadratures is constructed. Simple formulas for contact stresses and the normal dislocation component of displacements of crack edge points are obtained. The patterns of changes in contact stresses and crack opening depending on the maximum value of the friction coefficient have been studied.
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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