Analysis of a debonding model of two elastic 2D-bars

Abstract

Abstract This work establishes the existence of a weak solution to a new model for the process of debonding of two elastic 2D-bars caused by humidity and vibrations. A version of the model was first presented in the PCM-CMM-2019 conference in Krakow, Poland, and was published in (Shillor in J. Theor. Appl. Mech. 58(2): 295–305 2020). The existence of a weak solution is proved by regularizing the problem and then setting it in an abstract form that allows the use of tools for pseudo-differential operators and a fixed point theorem. Questions of further analysis of the solutions, effective numerical methods and simulations, as well as possible controls, are unresolved, yet.

Keywords

• 2D bar
• Dynamic contact
• Debonding
• Humidity diffusion