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 $\eta $ , 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 $0<\delta <1$ . The appropriate limiting problem with respect to η $\eta $ , with fixed δ $\delta $ , 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 $x=\delta $ . This approximate solution determines, up to first order, the energy release rate on δ $\delta $ , giving the critical value for the gel thickness at which it becomes unstable against debonding.

中文翻译：

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从刚性基材上剥离凝胶

我们考虑了薄凝胶域从刚性基材上剥离的问题。从涉及凝胶总能量的变分方法开始，我们在二维空间中制定控制方程的边值问题。我们考虑纵横比 η $\eta $（薄膜厚度与其长度的商）非常小的情况。我们假设凝胶在由 0 < δ < 1 $0<\delta <1$ 表示的无量纲水平位置部分脱粘。关于 η $\eta $ 的适当限制问题，具有固定的 δ $\delta $ ，产生一个近似解对应于在凝胶的粘合部分和脱粘部分都是均匀的变形，但其梯度和垂直分量在界面 x = δ $x=\delta $ 上是不连续的。