S. A. Nassar, K. T. Andrews, S. Kruk, and M. Shillor

Abstract. 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.