The JKR-type adhesive contact problems for transversely isotropic elastic solids
The JKR-type adhesive contact problems for transversely isotropic elastic solids
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DOI：
10.1016/j.mechmat.2014.03.011
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发表时间：
2014-08-01
影响因子：
3.9
通讯作者：
Suarez-Alvarez, Maria M.
中科院分区：
文献类型：
--
作者：
Borodich, Feodor M.;Galanov, Boris A.;Suarez-Alvarez, Maria M.
JKR（约翰逊、肯德尔和罗伯茨）和Boussinesq-Kendall模型描述了两个各向同性弹性球体之间或平端冲头与弹性各向同性半空间之间的无摩擦粘附接触。本文在JKR理论的框架下研究了横观各向同性材料的粘着接触问题。该理论被扩展到更一般的形状接触轴对称固体，即固体之间的距离是由一个单式（幂律）函数的任意程度d >= 1。经典的JKR模型和Boussinesq-Kendall模型可以被看作是这类问题的两种特殊情况，分别是当冲次数d等于2或趋于无穷大时。结果表明，横观各向同性材料的扩展JKR接触模型公式与各向同性材料的相应公式具有相同的数学形式，但不同材料的有效弹性接触模量有不同的表达式。以显式形式给出了实际力、位移和接触半径之间的无量纲关系。横向各向同性材料的纳米压痕的问题的连接进行了讨论。皇冠版权所有（C）2014由爱思唯尔有限公司出版。保留所有权利。
The JKR (Johnson, Kendall, and Roberts) and Boussinesq-Kendall models describe adhesive frictionless contact between two isotropic elastic spheres or between a flat end punch and an elastic isotropic half-space. Here adhesive contact is studied for transversely isotropic materials in the framework of the JKR theory. The theory is extended to much more general shapes of contacting axisymmetric solids, namely the distance between the solids is described by a monomial (power-law) function of an arbitrary degree d >= 1. The classic JKR and Boussinesq-Kendall models can be considered as two particular cases of these problems, when the degree of the punch d is equal to two or it goes to infinity, respectively. It is shown that the formulae for extended JKR contact model for transversely isotropic materials have the same mathematical form as the corresponding formulae for isotropic materials; however the effective elastic contact moduli have different expression for different materials. The dimensionless relations between the actual force, displacements and contact radius are given in explicit form. Connections of the problems to nanoindentation of transversely isotropic materials are discussed. Crown Copyright (C) 2014 Published by Elsevier Ltd. All rights reserved.