Thermomechanical behaviour of a damageable beam in contact with two stops

Abstract

A model for the thermomechanical behaviour of a beam which allows for the general evolution of material damage is presented and investigated. One end of the beam is fixed while the other is constrained to move between two stops. The contact of the free tip with the stops is modelled by the normal compliance condition. The thermal interaction between the stops and the free tip is described by a heat exchange condition where the heat transfer coefficient is a general function of the gaps between the tip and the stops. The effects on the mechanical properties of the material due to crack expansion are described by a damage field, which measures the decrease in the load-bearing capacity of the material. The damage evolves as a constrained diffusion process in which the microcracks that develop may grow or disappear. The mathematical model consists of a coupled system of energy--elasticity equations together with a nonlinear parabolic inclusion for the damage field. The existence of a local solution is established using truncation, penalization, and a priori estimates.

Keywords:

• Dynamic
• Contact
• Vibrations
• Stops
• Viscoelastic beam
• Parabolic inclusion
• Normal compliance
• Damage
• Constrained diffusion process

Keywords:

• 2000 Mathematics Subject Classifications: Primary: 74H20
• Secondary: 35Q72
• 74F05
• 74K10
• 74M15