不可压缩弹性薄膜球形压痕问题的一种渐近解析解
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O343.3

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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
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    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。

    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.

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焦志安,吴剑,万玲.不可压缩弹性薄膜球形压痕问题的一种渐近解析解[J].重庆大学学报,2019,42(12):74-80.

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  • 收稿日期:2019-07-11
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  • 在线发布日期: 2019-11-21
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