Adhesion behavior of an extensible soft thin film-substrate system based on finite deformation theory

In this paper, we study the adhesion behavior of a circular and extensible plate adhered to a rigid substrate based on the finite deformation theory. The energy method is used to derive the governing equations associated with boundary conditions. Due to the highly nonlinear nature of the problem and undetermined parameters on the boundary conditions, we solve the system of equations by an optimization-based approach which has never been used to study the thin film-substrate system. We also perform a comparative study on the deformation of the plate based on the finite deformation theory, finite deformation theory assuming that the adhered part is inextensible and the infinitesimal theory. The results demonstrate that when the plate is very soft, the adhesion force is very large or the detachment between the substrate and plate is very large, the inextensibility of the adhered part of the circular plate will induce large error in predicting the mechanical response of the adhered slender structure.