Analytical solutions for inflation of pre-stretched elastomeric circular membranes under uniform pressure

Elastomeric membranes are frequently used in several emerging fields such as soft robotics and flexible electronics. For convenience of the structural design, it is very attractive to find simple analytical solutions to well describe their elastic deformations in response to external loadings. However, both the material/geometrical nonlinearity and the deformation inhomogeneity due to boundary constraints make it much challenging to get an exact analytical solution. In this paper, we focus on the inflation of a pre-stretched elastomeric circular membrane under uniform pressure, and derive an approximate analytical solution of the pressure–volume curve based upon a reasonable assumption on the shape of the inflated membrane. Such an explicit expression enables us to quantitatively design the material and geometrical parameters of the pre-stretched membrane to generate a target pressure–volume curve with prescribed peak point and initial slope. This work would be of help in the simplified mechanical design of structures involving elastomeric membranes.