### Abstract

Language | English |
---|---|

Pages | 322-340 |

Number of pages | 18 |

Journal | Journal of Computational and Applied Mathematics |

Volume | 206 |

Issue number | 1 |

DOIs | |

Publication status | Published - Sep 2007 |

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### Keywords

- Hertz contact problem
- Abel's integral equations
- Linear complementarity problem

### Cite this

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*Journal of Computational and Applied Mathematics*, vol. 206, no. 1, pp. 322-340. https://doi.org/10.1016/j.cam.2006.07.008

**The Hertz contact problem, coupled Volterra integral equations and a linear complementarity problem.** / Gauthier, A.; Knight, P.A.; McKee, S.

Research output: Contribution to journal › Article

TY - JOUR

T1 - The Hertz contact problem, coupled Volterra integral equations and a linear complementarity problem

AU - Gauthier, A.

AU - Knight, P.A.

AU - McKee, S.

PY - 2007/9

Y1 - 2007/9

N2 - This paper is concerned with the indentation of an elastic half-space by an axisymmetric punch under a monotonically applied normal force and under the assumption of Coulomb friction with coefficient μ in the region of contact. Within an inner (unknown) circle the contact is adhesive, while in the surrounding annulus the surface moves inwards with increasing load. In this paper it is shown how this problem is equivalent to two coupled Abel's equations with an unknown free point, the inner circumference of the annulus. It is further shown that a product integration finite difference approximation of those integral equations leads to a mixed linear complementarity problem (mixed LCP). A method based on Newton's method for solving non-smooth nonlinear equations is demonstrated to converge under restrictive assumptions on the physical parameters defining the system; and numerical experimentation verifies that it has much wider applicability. The method is also validated against the approach of Spence. The advantage of the mixed LCP formulation is that it provides the radius of the inner adhesive circle directly using the physical parameters of the problem.

AB - This paper is concerned with the indentation of an elastic half-space by an axisymmetric punch under a monotonically applied normal force and under the assumption of Coulomb friction with coefficient μ in the region of contact. Within an inner (unknown) circle the contact is adhesive, while in the surrounding annulus the surface moves inwards with increasing load. In this paper it is shown how this problem is equivalent to two coupled Abel's equations with an unknown free point, the inner circumference of the annulus. It is further shown that a product integration finite difference approximation of those integral equations leads to a mixed linear complementarity problem (mixed LCP). A method based on Newton's method for solving non-smooth nonlinear equations is demonstrated to converge under restrictive assumptions on the physical parameters defining the system; and numerical experimentation verifies that it has much wider applicability. The method is also validated against the approach of Spence. The advantage of the mixed LCP formulation is that it provides the radius of the inner adhesive circle directly using the physical parameters of the problem.

KW - Hertz contact problem

KW - Abel's integral equations

KW - Linear complementarity problem

U2 - 10.1016/j.cam.2006.07.008

DO - 10.1016/j.cam.2006.07.008

M3 - Article

VL - 206

SP - 322

EP - 340

JO - Journal of Computational and Applied Mathematics

T2 - Journal of Computational and Applied Mathematics

JF - Journal of Computational and Applied Mathematics

SN - 0377-0427

IS - 1

ER -