Calculus of Variations and Geometric Measure Theory

E. Bonetti - G. Bonfanti - R. Rossi

Analysis of a temperature-dependent model for adhesive contact with friction

created by rossi on 20 Jul 2012


Submitted Paper

Inserted: 20 jul 2012
Last Updated: 20 jul 2012

Year: 2012


We propose a model for (unilateral) contact with adhesion between a viscoelastic body and a rigid support, encompassing thermal and frictional effects. Following Fremond's approach, adhesion is described in terms of a surface damage parameter $\chi$. The related equations are the momentum balance for the vector of small displacements, and parabolic-type evolution equations for $\chi$ and for the absolute temperatures of the body and of the adhesive substance on the contact surface. All of the constraints on the internal variables, as well as the contact and the friction conditions, are rendered by means of subdifferential operators. Furthermore, the temperature equations, derived from an entropy balance law, feature singular functions. Therefore, the resulting PDE system has a highly nonlinear character.

The main result of the paper states the existence of global-in-time solutions to the associated Cauchy problem. It is proved by passing to the limit in a carefully tailored approximate problem, via variational techniques.