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.

在本文中，我们基于有限变形理论研究了粘附在刚性基板上的圆形可延展板的粘附行为。能量方法用于导出与边界条件相关的控制方程。由于问题的高度非线性性质和边界条件上不确定的参数，我们采用基于优化的方法求解方程组，该方法从未用于研究薄膜-基板系统。我们还基于有限变形理论，假定粘附部分不可扩展的有限变形理论和无限小理论对板的变形进行了比较研究。结果表明，当板很软时，粘附力很大，或者基板与板之间的分离很大，