### Abstract

Punches with or without friction sliding along the surface of an anisotropic elastic half-plane are considered. A general unified solution for the full field stresses and displacements is derived by the complex-variable formulation. The solution obtained is valid not only for punches which slide slowly but also for the punches which are in equilibrium. Thus, the word 'sliding' as used here has a generalized meaning which includes the cases when punches are in equilibrium. And the applied horizontal forces may have any value less than the maximum friction force. With this general full field solution, special reductions are made for the contact pressure, surface deformation, frictionless surface, orthotropic and isotropic media. In order to show the generality of our solutions, three typical examples are solved completely and their related stress contours, surface deformations and contact pressures are also plotted to help us see more clearly the physical behaviours of the sliding-punch problems. Based upon these new results for particular sliding-punch problems, several phenomena are discussed in detail such as the order and strength of the stress singularity at a punch end, complete and incomplete indentation, interactions between two punches, dependence of the singular order on the material properties and friction conditions or the ratio of horizontal force to normal force, independency of the singular order for the frictionless surface, generalization of the horizontal force, arbitrariness of the punch profiles, etc.

Original language | English |
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Pages (from-to) | 159-177 |

Number of pages | 19 |

Journal | Quarterly Journal of Mechanics and Applied Mathematics |

Volume | 51 |

Issue number | 1 |

DOIs | |

Publication status | Published - 1998 Feb |

### All Science Journal Classification (ASJC) codes

- Condensed Matter Physics
- Mechanics of Materials
- Mechanical Engineering
- Applied Mathematics