We study wetting of an elastic membrane whose surface can resist stretch by surface stress. Through energy minimization, we obtain the general equilibrium equations and a configurational energy balance equation at the contact line, i.e., the Young equation, modified for an elastic membrane. We use a 3D large deformation formulation with general elastic constitutive behavior for the membrane and its surfaces. Our results allow for non-flat reference membrane shape, non-uniform and anisotropic tension and dependence of surface stress on surface strain – the generalized Shuttleworth effects. We use two examples to demonstrate the application of our theory: plane strain and axisymmetric wetting of an initially flat elastic membrane. A large deformation solution for an axisymmetric droplet on a deformable membrane is obtained numerically. We show that when surface elastic moduli for solid–vapor and solid–liquid interfaces are different, continuity of membrane strain, a key assumption used in many previous studies, no longer holds at the contact line.

我们研究了弹性膜的润湿性，该弹性膜的表面可以抵抗表面应力引起的拉伸。通过能量最小化，我们获得了接触线处的一般平衡方程和结构能平衡方程，即针对弹性膜修改的杨氏方程。我们对膜及其表面使用具有一般弹性本构行为的3D大变形公式。我们的结果考虑到了非平坦的参考膜形状，不均匀且各向异性的张力以及表面应力对表面应变的依赖性-广义的Shuttleworth效应。我们用两个例子来证明我们的理论的应用：最初的平面弹性膜的平面应变和轴对称润湿。数值获得了可变形膜上轴对称液滴的大变形解。