Adhesion of a gas-filled membrane on a stretched substrate

A two-dimensionally adhesive contact model is established, in which a gas-filled elastic membrane adheres on a stretched substrate. The free energy of the system is achieved, minimization of which leads to the relationship between the contact width and the global substrate strain. The contact solution exhibits three distinct regimes characterized by two threshold strains: (i) the contact size is hardly affected by the external loading acted on the substrate when the global substrate strain is below the first threshold value; (ii) the size of the contact is reduced quickly as the force is between the two threshold levels; (iii) the contact size tends to vanish when the global substrate strain exceeds the second threshold level. All the results share a number of common features with the experimental observation of cell orientation on a stretched substrate. Effects of the internal pressure, the tensile stiffness of the membrane and the interface work of adhesion on the two threshold levels are further discussed. The finding in the present paper should be helpful for deep understanding of adhesion mediated deformation sensing mechanism by which cells can detect mechanical signals in extracellular matrices and the design of adhesion mediated deformation sensors.