### Abstract

The accuracy of the geometric assumptions in the Johnson- Kendall-Roberts (JKR) theory of adhesion are examined in this work. In particular, the effect of surface curvature on the validity of the JKR theoryis analyzed by developing a perturbation solution to the problem of two cylinders in contact. The pressure distribution inside the contact zone as predicted by the JKR theory is shown to be accurate toorder ε2, where ε is the ratio of the contact width to the radius of the smaller cylinder. The relative normal approach of the cylinders is also given in a closed form. Based on these results, a correction to the normal approach is derived for the case of three-dimensional contact of hemispheres. The validity of these correction terms and of the JKR theory for hemispheres is investigated numericallyusing a non-linear finite element method capable of simulating large strains. The effect of thin lenses on the validity of the JKR theory is also examined using the FEM.

Original language | English |
---|---|

Pages (from-to) | 1297-1319 |

Number of pages | 23 |

Journal | Journal of Adhesion Science and Technology |

Volume | 14 |

Issue number | 10 |

DOIs | |

Publication status | Published - 2000 Jan 1 |

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### All Science Journal Classification (ASJC) codes

- Chemistry(all)
- Mechanics of Materials
- Surfaces and Interfaces
- Surfaces, Coatings and Films
- Materials Chemistry

### Cite this

*Journal of Adhesion Science and Technology*,

*14*(10), 1297-1319. https://doi.org/10.1163/156856100742203

}

*Journal of Adhesion Science and Technology*, vol. 14, no. 10, pp. 1297-1319. https://doi.org/10.1163/156856100742203

**The accuracy of the geometric assumptions in the jkr (johnson–kendall–roberts) theory of adhesion.** / Hui, C. Y.; Lin, Yu-Yun; Baney, J. M.; Jagota, A.

Research output: Contribution to journal › Article

TY - JOUR

T1 - The accuracy of the geometric assumptions in the jkr (johnson–kendall–roberts) theory of adhesion

AU - Hui, C. Y.

AU - Lin, Yu-Yun

AU - Baney, J. M.

AU - Jagota, A.

PY - 2000/1/1

Y1 - 2000/1/1

N2 - The accuracy of the geometric assumptions in the Johnson- Kendall-Roberts (JKR) theory of adhesion are examined in this work. In particular, the effect of surface curvature on the validity of the JKR theoryis analyzed by developing a perturbation solution to the problem of two cylinders in contact. The pressure distribution inside the contact zone as predicted by the JKR theory is shown to be accurate toorder ε2, where ε is the ratio of the contact width to the radius of the smaller cylinder. The relative normal approach of the cylinders is also given in a closed form. Based on these results, a correction to the normal approach is derived for the case of three-dimensional contact of hemispheres. The validity of these correction terms and of the JKR theory for hemispheres is investigated numericallyusing a non-linear finite element method capable of simulating large strains. The effect of thin lenses on the validity of the JKR theory is also examined using the FEM.

AB - The accuracy of the geometric assumptions in the Johnson- Kendall-Roberts (JKR) theory of adhesion are examined in this work. In particular, the effect of surface curvature on the validity of the JKR theoryis analyzed by developing a perturbation solution to the problem of two cylinders in contact. The pressure distribution inside the contact zone as predicted by the JKR theory is shown to be accurate toorder ε2, where ε is the ratio of the contact width to the radius of the smaller cylinder. The relative normal approach of the cylinders is also given in a closed form. Based on these results, a correction to the normal approach is derived for the case of three-dimensional contact of hemispheres. The validity of these correction terms and of the JKR theory for hemispheres is investigated numericallyusing a non-linear finite element method capable of simulating large strains. The effect of thin lenses on the validity of the JKR theory is also examined using the FEM.

UR - http://www.scopus.com/inward/record.url?scp=0033684185&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0033684185&partnerID=8YFLogxK

U2 - 10.1163/156856100742203

DO - 10.1163/156856100742203

M3 - Article

VL - 14

SP - 1297

EP - 1319

JO - Journal of Adhesion Science and Technology

JF - Journal of Adhesion Science and Technology

SN - 0169-4243

IS - 10

ER -