The membrane–membrane contact mechanics plays an important role in several biological processes, such as drug delivery, cell infection, cell destruction, etc. at microscales. The problem at macroscales is relevant to air inflated and air supported structures. In this work, we have chosen a simple system in which contact mechanics of two inflated membranes (initially flat circular membranes parallelly placed, fixed circumferentially and pressurized in opposite direction to make contact) has been studied. Friction and effects of adhesion are neglected for simplicity. We have considered the Mooney–Rivlin hyperelastic membrane material. The governing equations are derived using the principle of minimum potential energy. The problem has been solved separately for contacting and non-contacting region and joined by appropriate junction and boundary conditions. Indentation on the low-pressure membrane by the high-pressure membrane for different loading and rigidity constants has been studied. We observe a critical radius of contact of the low-pressure membrane, which depends upon the characteristics of high-pressure membrane, beyond which the stretch and stress values start to rise with indentation. At this critical radius, maximum meridional curvature discontinuity jump exists. Variation of contact force, along with principal stretches and stresses, are also discussed.

膜-膜接触力学在多种生物过程中起着重要作用，例如微尺度的药物递送、细胞感染、细胞破坏等。宏观尺度的问题与充气和空气支撑结构有关。在这项工作中，我们选择了一个简单的系统，其中研究了两个充气膜（最初是平行放置的扁平圆形膜，周向固定并在相反方向加压以进行接触）的接触力学。为简单起见，忽略摩擦和粘附效应。我们已经考虑了 Mooney-Rivlin 超弹性膜材料。控制方程是使用最小势能原理推导出来的。该问题已针对接触和非接触区域分别解决，并通过适当的结和边界条件连接。研究了不同载荷和刚度常数下高压膜在低压膜上的压痕。我们观察到低压膜的临界接触半径，这取决于高压膜的特性，超过这个半径，拉伸和应力值开始随着压痕而上升。在这个临界半径处，存在最大子午曲率不连续跳跃。还讨论了接触力的变化以及主要的拉伸和应力。我们观察到低压膜的临界接触半径，这取决于高压膜的特性，超过这个半径，拉伸和应力值开始随着压痕而上升。在这个临界半径处，存在最大子午曲率不连续跳跃。还讨论了接触力的变化以及主要的拉伸和应力。我们观察到低压膜的临界接触半径，这取决于高压膜的特性，超过这个半径，拉伸和应力值开始随着压痕而上升。在这个临界半径处，存在最大子午曲率不连续跳跃。还讨论了接触力的变化以及主要的拉伸和应力。