Gel Debonding from a Rigid Substrate

We consider the problem of debonding of a thin gel domain from a rigid substrate. Starting with a variational approach involving the total energy of a gel, we formulate the boundary value problem of the governing equations in two-space dimensions. We consider the case that the aspect ratio, η, the quotient of the thickness of the film with respect to its length, is very small. We assume that the gel is partially debonded at the dimensionless horizontal location denoted by 0 < δ< 1. The appropriate limiting problem with respect to η, with fixed δ, yields an approximate solution corresponding to a deformation that is homogeneous both on the bonded part and on the debonded part of the gel, but whose gradient and vertical component are discontinuous across the interface x= δ. This approximate solution determines, up to first order, the energy release rate on δ, giving the critical value for the gel thickness at which it becomes unstable against debonding.