Delayed buckling of spherical shells due to viscoelastic knockdown of the critical load

Abstract

We performed dynamic pressure buckling experiments on defect-seeded spherical shells made of a common silicone elastomer. Unlike in quasi-static experiments, shells buckled at ostensibly subcritical pressures (i.e. below the experimentally-determined load at which buckling occurs elastically), often following a significant time delay. While emphasizing the close connections to elastic shell buckling, we rely on viscoelasticity to explain our observations. In particular, we demonstrate that the lower critical load may be determined from the material properties, which is rationalized by a simple analogy to elastic spherical shell buckling. We then introduce a model centered on empirical quantities to show that viscoelastic creep deformation lowers the critical load in the same predictable, quantifiable way that a growing defect would in an elastic shell. This allows us to capture how both the critical deflection and the delay time depend on the applied pressure, material properties, and defect geometry. These quantities are straightforward to measure in experiments. Thus, our work not only provides intuition for viscoelastic behavior from an elastic shell buckling perspective, but also offers an accessible pathway to introduce tunable, time-controlled actuation to existing mechanical actuators, e.g. pneumatic grippers.

The Extreme Mechanics of Viscoelastic Metamaterials

“…Yet, the opposite can also be true. Stein-Moldavo et al recently showed that the buckling pressure of spherical shells could also drop due to viscoelastic effects [44]. When a negative pressure was kept stable just below the elastic buckling limit, a viscoelastic shell would still buckle after relaxation.…”

“…As such, dissipative vibration transmissions has been studied extensively in acoustic metamaterials featuring wave propagation and band gap structures [21,22,23,24,25,26,27,28,29,30] as well vibration and shock control [31,32,33,34,35,36]. However, although the effect of the constitutive materials' dissipation on mechanical instabilities has been well studied [37,38,39,40,41,42,43,44], the role of dissipation in the instabilities that underpin the extreme mechanics of mechanical metamaterials remains poorly understood (Fig 1). Yet, there is growing evidence that dissipation can play a key role in the response of mechanical metamaterials that are based on buckling [45,46].…”