Axisymmetric frictionless indentation of a rigid stamp into a semi-space with a surface energetic boundary

Author:

Zemlyanova Anna Y.1ORCID,White Lauren M.1

Affiliation:

1. Department of Mathematics, Kansas State University, Manhattan, KS, USA

Abstract

An axisymmetric problem for a frictionless contact of a rigid stamp with a semi-space in the presence of surface energy in the Steigmann–Ogden form is studied. The method of Boussinesq potentials is used to obtain integral representations of the stresses and the displacements. Using the Hankel transform, the problem is reduced to a single integral equation of the first kind on a contact interval with an additional condition. The integral equation is studied for solvability. It is shown that for the classic problem in the absence of surface effects and for the problem with the Gurtin–Murdoch surface energy without surface tension, the obtained equation represents a Cauchy singular integral equation. At the same time, for the Gurtin–Murdoch model with a non-zero surface tension and for the general Steigmann–Ogden model, the problem results in the integral equation of the first kind with a weakly singular or a continuous kernel, correspondingly. Hence, the contact problem is ill-posed in these cases. The integral equation of the first kind with an additional condition is solved approximately by using Gauss–Chebyshev quadrature for evaluation of the integrals. Numerical results for various values of the parameters are reported.

Funder

Simons Foundation

Publisher

SAGE Publications

Subject

Mechanics of Materials,General Materials Science,General Mathematics

Cited by 13 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

同舟云学术

1.学者识别学者识别

2.学术分析学术分析

3.人才评估人才评估

"同舟云学术"是以全球学者为主线,采集、加工和组织学术论文而形成的新型学术文献查询和分析系统,可以对全球学者进行文献检索和人才价值评估。用户可以通过关注某些学科领域的顶尖人物而持续追踪该领域的学科进展和研究前沿。经过近期的数据扩容,当前同舟云学术共收录了国内外主流学术期刊6万余种,收集的期刊论文及会议论文总量共计约1.5亿篇,并以每天添加12000余篇中外论文的速度递增。我们也可以为用户提供个性化、定制化的学者数据。欢迎来电咨询!咨询电话:010-8811{复制后删除}0370

www.globalauthorid.com

TOP

Copyright © 2019-2024 北京同舟云网络信息技术有限公司
京公网安备11010802033243号  京ICP备18003416号-3