两个非均匀弹性体接触的赫兹和粘着平面模型

IF 4.6 Q2 MATERIALS SCIENCE, BIOMATERIALS
Y. Antipov, S. Mkhitaryan
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引用次数: 1

摘要

以往幂律梯度材料的接触研究涉及刚体(冲床)与弹性非均匀基础的接触,其非均匀性的特征是杨氏模量随深度变化为幂函数。本文建立了两个不同指数的非均匀幂律梯度弹体的赫兹接触和黏着接触模型。这个问题是由两个不同幂函数的积分方程控制的。提出了一种求解Gegenbauer正交多项式的非标准方法。它导致了一个特殊结构的线性代数方程组的无穷系统。给出了系统系数的积分表示,并研究了系统的性质。结果表明,当指数重合时,无限系统存在一个简单的精确解,该解对应于杨氏模不同而指数相同的情况。以方便计算的形式得到了接触区长度、压力分布和接触体表面法向位移的计算公式。研究了杨氏模指数失配的影响。通过对赫兹接触模型和黏着接触模型的对比分析,阐明了表面能密度对接触压力、接触区尺寸和接触区外接触体轮廓的影响。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Hertzian and adhesive plane models of contact of two inhomogeneous elastic bodies
Previous study of contact of power-law graded materials concerned the contact of a rigid body (punch) with an elastic inhomogeneous foundation whose inhomogeneity is characterised by the Young modulus varying with depth as a power function. This paper models Hertzian and adhesive contact of two elastic inhomogeneous power-law graded bodies with different exponents. The problem is governed by an integral equation with two different power kernels. A nonstandard method of Gegenbauer orthogonal polynomials for its solution is proposed. It leads to an infinite system of linear algebraic equations of a special structure. The integral representations of the system coefficients are evaluated, and the properties of the system are studied. It is shown that if the exponents coincide, the infinite system admits a simple exact solution that corresponds to the case when the Young moduli are different but the exponents are the same. Formulas for the length of the contact zone, the pressure distribution and the surface normal displacements of the contacting bodies are obtained in the form convenient for computations. Effects of the mismatch in the Young moduli exponents are studied. A comparative analysis of the Hertzian and adhesive contact models clarifies the effects of the surface energy density on the contact pressure, the contact zone size and the profile of the contacting bodies outside the contact area.
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来源期刊
ACS Applied Bio Materials
ACS Applied Bio Materials Chemistry-Chemistry (all)
CiteScore
9.40
自引率
2.10%
发文量
464
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