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主办单位:重庆大学
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国际标准刊号:ISSN 1000-582X
国内统一刊号:CN 50-1044/N
邮发代号:国内78-16 国外 M355
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不可压缩弹性薄膜球形压痕问题的一种渐近解析解
焦志安, 吴剑, 万玲
重庆大学 航空航天学院, 重庆 400044
摘要:
针对刚性基底上不可压缩弹性薄膜的轴对称球形压痕问题,采用了一种基于Kerr模型的简单解析求解方法。在该方法中,薄膜上表面的接触压强与位移为线性微分关系。之后利用贝蒂互等定理,求解了该问题的高阶渐近解,推导了接触力、压痕深度和接触半径之间的显式关系。当忽略高阶项时,得出的高阶渐近解与现有研究中的低阶解相同。此外还建立了有限元模型来验证渐近解的精度。结果显示,与已有的低阶渐近解相比,高阶渐近解与现有的数值计算结果和有限元分析结果吻合得更好。
关键词:  球形压痕  不可压缩  Kerr模型  贝蒂互等定理  弹性薄膜  接触
DOI:10.11835/j.issn.1000-582X.2019.12.009
分类号:O343.3
基金项目:国家自然科学基金项目(11802043);重庆市留学人员创新资助项目(51204067);重庆市基础科学与前沿技术研究专项项目(cstc2016jcyjA0058)。
An asymptotic analytical solution to the spherical indentation problem of incompressible elastic thin film
JIAO Zhian, WU Jian, WAN Ling
College of Aerospace Engineering, Chongqing University, Chongqing 400044, P. R. China
Abstract:
In order to solve the problem of axisymmetric indentation of an incompressible elastic film on a rigid substrate, a simple analytical method based on Kerr-model is derived, in which the differential relation between the contact pressure and the displacement of the film's upper surface is established. Then, the high-order asymptotic solution to the problem is solved by using Betti's reciprocal theorem and the explicit relation between contact pressure, indentation depth and contact radius is built. When the high-order term is ignored, the present asymptotic solution is the same as the existing low-order solution. In addition, a finite element model is established to verify the accuracy of the asymptotic solution. The result shows that, compared with the existing low-order asymptotic solutions, the higher-order asymptotic solution agrees better with the existing numerical results and the newly developed numerical simulation results.
Key words:  spherical indentation  incompressible  Kerr-model  Betti's reciprocal theorem  elastic film  contact
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