Indentation of elastomeric membranes by sphere-tipped indenters: Snap-through instability, shrinkage, and puncture

Elastomeric membranes are flexible and stretchable, commonly found in soft devices, soft robotics, and flexible electronics. The indentation of free-standing elastomeric membranes induces large transverse deflection, leading to the puncture of elastomeric membranes. In this paper, we study the indentation and puncture of elastomeric membranes by sphere-tipped indenters. Effects of the indenter tip size, indenter-membrane friction, and equi-biaxial pre-stretch of the membrane on the indentation depth-force curve, deformed membrane profile, puncture depth and force, and shape of the puncture site are studied both experimentally and theoretically. In the experiments, we observe an abnormal decrease of indentation force with increasing indentation depth, similar to the spontaneous expansion of a rubber balloon at a critical pressure. We call this phenomenon the snap-through instability in the indentation of elastomeric membranes. The profile of the lubricated membrane shrinks around the indenter tip with increasing indentation depth. The puncture depth and force of lubricated membranes are smaller than those of pristine membranes by several times. Indenters prefer to penetrate lubricated membranes by a line crack instead of a circular hole for pristine membranes. Our theoretical model successfully predicts the snap-through instability, puncture depth and force, and shrinkage of elastomeric membranes. Also, the shape of the membrane's puncture site is explained. These experimental findings and theoretical formulations reveal the new characteristics of the indentation and puncture of elastomeric membranes.