A dynamic thermoviscoelastic contact problem with friction and wear

• Published in: International journal of engineering science Vol. 35; no. 14; pp. 1291 - 1309
• Main Authors: Andrews, Kevin T., Shillor, M., Wright, S., Klarbring, A.
• Format: Journal Article
• Language: English
• Published: Oxford Elsevier Ltd 01-11-1997; Elsevier
• Subjects: Exact sciences and technology; Fundamental areas of phenomenology (including applications); Mechanical contact (friction...); Physics; Solid mechanics; Structural and continuum mechanics; Tribology and mechanical contacts; Dynamic contact; Weak solution; Heat equation; Variational inequality; Thermoviscoelasticity; Variational calculus; Thermomechanical properties; Numerical method; Mechanical contacts; Uniqueness theorem; Sliding friction
• ISSN: 0020-7225; 1879-2197
• DOI: 10.1016/S0020-7225(97)87426-5

We prove the existence of a unique solution to a dynamic frictional contact problem involving a thermoviscoelastic body that may undergo wear on the contacting surface. The viscosity is assumed to be of the Kelvin-Voigt type, the contact is modeled by the normal compliance condition, and the wear by Archard's law. The problem consists of the elasticity system in the form of a variational inequality for the displacements, the heat equation for the temperature, and a first order equation for the wear function. The existence of a weak solution is established by considering a sequence of regularized approximations. These approximations may serve as the basis for a convergent numerical scheme. Under additional conditions on the data we establish the uniqueness of the weak solution.