Modeling, analysis and simulations of debonding of bonded rod-beam system caused by humidity and thermal effects
Texas State University, Department of Mathematics
This work models, analyses and simulates a one-dimensional process of debonding of a structure made of two viscoelastic bonded slabs that is described by a rod-beam system. It is motivated, primarily, by the degradation of adhesively bonded plates in automotive applications and studies the effects of the humidity, horizontal and vertical vibrations and temperature on the debonding process. The existence of a weak solution to the model is established by using approximate problems, existence theorems for differential inclusions, and a fixed point theorem. An implicit finite differences algorithm for the problem is developed and used to simulate the system dynamics. It is found that the qualitative behavior of the system correlates well with experimental results. Moreover, it indicates that using the shifts in the spectrum, as described by the FFT of one component of the solution, may be used to measure nondestructively the integrity of the bonds and their deterioration.
Rod-beam system, Debonding, Single lap joint, Differential inclusions, Existence, Simulations, Spectrum shifts
Kuttler, K. L., Kruk, S., Marcinek, P., & Shillor, M. (2017). Modeling, analysis and simulations of debonding of bonded rod-beam system caused by humidity and thermal effects. <i>Electronic Journal of Differential Equations, 2017</i>(301), pp. 1-42.