Modelling and simulations of a bonded rod

This work models, analyzes, and simulates the process of adhesive bonding between a rod or a slab and an object. The process is assumed to be quasistatic and the model consists of an evolution equation for the rod, a nonstandard boundary condition describing the adhesive traction, and an ordinary differential equation for the adhesive evolution. The object may be reactive or rigid, and the rod elastic or viscoelastic. The equations are shown to decouple and once the adhesion field is found, the displacements are obtained in a closed form. Numerical simulations provide insight into the behavior of structures with this model of adhesion. These include the reversible process which may be history dependent. It is found that when the bonding field is weak, the assumptions underlying the quasistatic approximation are violated, and intrinsically the model predicts that either the debonding process stops, or complete debonding can be obtained only asymptotically.