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Research Papers

Analysis and Inversion of Contact Stress for the Finite Thickness Neo-Hookean Layer

[+] Author and Article Information
Heng Yang, Xue-Feng Yao, Shen Wang, Yu-Chao Ke, Sheng-Hao Huang, Ying-Hua Liu

Applied Mechanics Lab,
Department of Engineering Mechanics,
Tsinghua University,
Beijing 100084, China

1Corresponding author.

Manuscript received April 5, 2018; final manuscript received June 19, 2018; published online July 5, 2018. Assoc. Editor: Yong Zhu.

J. Appl. Mech 85(10), 101008 (Jul 05, 2018) (9 pages) Paper No: JAM-18-1191; doi: 10.1115/1.4040598 History: Received April 05, 2018; Revised June 19, 2018

In this paper, the theoretical analysis and the inversion of the contact stress on the finite thickness rubber contact surface with the friction effect are investigated. First, an explicit expression of deformation and stress on the surface of rubber under a rigid spherical indenter is developed by means of theoretical model, dimensional analysis, and nonlinear finite element simulation. Second, the inverse approach for obtaining the contact stress on the finite thickness rubber contact surface is presented and verified theoretically. Also, the displacement, the stress field, and the friction coefficient are obtained by means of three-dimensional digital image correlation (3D DIC) method. Finally, the applicability to other hyperelastic models, general boundary conditions, and loading modes are discussed. The results will provide an important theoretical and experimental basis for evaluating the contact stress on the finite thickness rubber layer.

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Figures

Grahic Jump Location
Fig. 1

Schematic diagram for the finite thickness rubber contact problems

Grahic Jump Location
Fig. 2

Effects of friction on the contact stress p and the vertical displacement uz under the condition of F/(μ0R2) = 2.0, b/R = 0.5: (a) the vertical displacement uz and (b) the contact stress p

Grahic Jump Location
Fig. 3

The contact stress and vertical displacement on the frictionless contact surface of rubber for different thicknesses under F/(μ0R2)=3.0: (a) the vertical displacement and (b) the contact stress

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Fig. 4

The inversion of the contact stress from displacement field for rubber contact problems: (a) spherical indenter rubber contact and (b) general rubber contact problem

Grahic Jump Location
Fig. 5

Condition number for the inversion of stress under various ratios f and r/a at (a) the thickness ratio b/R of 0.5 and (b) r/a = 0

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Fig. 6

The experimental setup for 3D DIC method and the speckle images of rubber surface: (a) test system on the rubber contact and (b) speckle field in measurement area

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Fig. 7

The measurement results of the vertical displacement uz under the load of 33.0 N and 86.5 N: (a) the vertical displacement uz under the load of 33.0 N and (b) the vertical displacement uz under the load of 86.5 N

Grahic Jump Location
Fig. 8

The vertical displacement uz and the contact stress p along the radius of the experiments and inversion: (a) the vertical displacement and (b) the contact stress

Grahic Jump Location
Fig. 9

The vertical displacement uz of the experiments and inversion results to obtain the friction coefficient in the lubrication interface under F = 50 N

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