Contact mechanics of inflated circular membrane under large deformation: Analytical solutions

Abstract

Pressurization of thin elastomeric membranes has been exploited as a key actuation mechanism in soft robotics, leading to soft pneumatic actuators that can deform reversibly upon inflation and deflation. The contact mechanics of an inflated membrane with another object underlies several important functionalities of soft pneumatic actuators such as gripping, haptic feedback and locomotion. Motivated by the technological relevance, we study the contact between an inflated circular membrane consisting of incompressible neo-Hookean solid and a substrate that is: i) flat and rigid, ii) spherically curved and rigid, iii) flat and elastic, or iv) spherically curved and elastic. By assuming that the contact interface is adhesionless and frictionless and that the membrane is subjected to very large stretch ratios, we obtained approximate analytical solutions for the membrane’s deformation profile as well as the relationship between the applied force, displacement and contact radius. These solutions agree well with results of numerical simulations. In particular, when the substrate is elastic, we obtained a dimensionless parameter γ that captures the transition between two limiting cases, i.e., either the substrate or the inflated membrane is effectively rigid relative to the other component and thus experiences negligible deformation upon contact. The analytical solutions provided in this work can offer insights towards designing soft pneumatic actuators with desired contact compliance.