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Mathematical modelisation of machining process: abrasion and wetting

Abstract : This PhD work is dedicated to a study of a viscoelastic model with unilateral constraints modeled as a Kelvin-Voigt material. The chapter one is dedicated to the monodimensional case: we approximate the solution of the problem by penalization, which leads to a theorem of existence of a weak solution. A result of regularity of the traces enables to show that the solution is strong. The chapter two includes a numerical scheme, we prove the convergence of this scheme to a weak solution. The chapters three and four enable to construct a strong solution in a semi-infinite monodimensional domain. We establish an energy relation for this solution: the only losses are purely viscous. The problem is reduced to a variational inequality at the boundary involving a pseudodifferential operator which principal term is a derivation of order 3/2. The chapters five and six include the trace theorems for a damped waves equation and an operator of viscoelasticity in a half-space, with application to strong solutions.
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Contributor : Adrien Petrov <>
Submitted on : Tuesday, March 9, 2004 - 8:53:56 PM
Last modification on : Wednesday, July 8, 2020 - 12:42:05 PM
Long-term archiving on: : Friday, April 2, 2010 - 7:51:38 PM


  • HAL Id : tel-00005277, version 1


Adrien Petrov. Mathematical modelisation of machining process: abrasion and wetting. Mathematics [math]. Université Claude Bernard - Lyon I, 2002. English. ⟨tel-00005277⟩



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