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A Quasistatic Contact Problem with Slip Dependent Coefficient of Friction for Elastic Materials

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Published/Copyright: June 7, 2010
Journal of Applied Analysis
From the journal Journal of Applied Analysis Volume 8 Issue 1

Abstract

We consider a mathematical model which describes the frictional contact between a deformable body and an obstacle, say a foundation. The body is assumed to be linear elastic and the contact is modeled with a version of Coulomb's law of dry friction in which the normal stress is prescribed on the contact surface. The novelty consists here in the fact that we consider a slip dependent coefficient of friction and a quasistatic process. We present two alternative yet equivalent formulations of the problem and establish existence and uniqueness results. The proofs are based on a new result obtained in [Motreanu and Sofonea, Abstr. Appl. Anal. 4: 255–279, 1999] in the study of evolutionary variational inequalities.

Key words and phrases.: Elastic material; quasistatic process; Coulomb's law; slip dependent friction; variational inequality; weak solution
Received: 2000-10-24
Revised: 2001-07-24
Published Online: 2010-06-07
Published in Print: 2002-June

© Heldermann Verlag

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  1. The Infinite Dimensional Henstock Integral and Problems of Black-Scholes Expectation
  2. An Explicit Formula for Solutions of Some System of Linear Delay Difference Equations
  3. Existence and Controllability Results for Nonlinear Differential Inclusions with Nonlocal Conditions in Banach Spaces
  4. Results on Singular Distribution Products of Mikusiński Type
  5. A Quasistatic Contact Problem with Slip Dependent Coefficient of Friction for Elastic Materials
  6. Linear Fredholm Integral Equations and the Integral of Kurzweil
  7. On Trigonometric-Like Decompositions of Functions with Respect to the Cyclic Group of Order n
  8. The Existence and Uniqueness of Solution of One Coupled Plate Thermomechanics Problem
  9. On the Stationary Flow of the Power Law Fluid in 2D
https://doi.org/10.1515/JAA.2002.63
Keywords for this article
Elastic material; quasistatic process; Coulomb's law; slip dependent friction; variational inequality; weak solution

Articles in the same Issue

  1. The Infinite Dimensional Henstock Integral and Problems of Black-Scholes Expectation
  2. An Explicit Formula for Solutions of Some System of Linear Delay Difference Equations
  3. Existence and Controllability Results for Nonlinear Differential Inclusions with Nonlocal Conditions in Banach Spaces
  4. Results on Singular Distribution Products of Mikusiński Type
  5. A Quasistatic Contact Problem with Slip Dependent Coefficient of Friction for Elastic Materials
  6. Linear Fredholm Integral Equations and the Integral of Kurzweil
  7. On Trigonometric-Like Decompositions of Functions with Respect to the Cyclic Group of Order n
  8. The Existence and Uniqueness of Solution of One Coupled Plate Thermomechanics Problem
  9. On the Stationary Flow of the Power Law Fluid in 2D
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