Interplay of elastic instabilities and viscoelasticity in the finite deformation of thin membranes

Pneumatic structures and actuators are found in a variety of natural and engineered systems such as dielectric actuators, soft robots, plants and fungi cells, or even the vocal sac of frogs. These structures are often subjected to mechanical instabilities arising from the thinning of their cross section and that may be harvested to perform mechanical work at a low energetic cost. While most of our understanding of this unstable behavior is for purely elastic membranes, real materials including lipid bilayers, elastomers, and connective tissues typically display a time-dependent viscoelastic response. This paper thus explores the role of viscous effects on the nature of this elastic instability when such membranes are dynamically inflated. For this, we first introduce an extension of the transient network theory to describe the finite strain viscoelastic response of membranes, enabling an elegant formulation while keeping a close connection with the dynamics of the underlying polymer network. We then combine experiments and simulations to analyze the viscoelastic behavior of an inflated blister made of a commercial adhesive tape (VHB 4905). Our results show that the viscous component induces a rich spectrum of behaviors bounded by two well-known elastic solutions corresponding to very high and very low inflation rates. We also show that membrane relaxation may induce unwanted buckling when it is subjected to cyclic inflations at certain frequencies. These results have clear implications for the inflation and mechanical work performed by time-dependent pneumatic structures and instability-based actuators.