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 critical load at which buckling occurs elastically, often following a significant delay period from the time of load application. 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 centred 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 deflection at instability and the time delay 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 behaviour 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.

Buckling of lipidic ultrasound contrast agents under quasi-static load

“…Viscous phenomena must, in general, be taken into account [76,77]. A macroscopic experiment showed recently that delay in buckling of visco-elastic shells is strongly related to the dynamics at the level of the defect where buckling initially nucleated [66]. Delay in buckling may lead to apparent perception of buckling threshold knock-up, by contrast with the usual knock-down observed in the presence of defects [43,64,65,78,80].…”

Influence of Initial Imperfections on PMMA Spherical Shell

“…Numerical results of axisymmetric large deflection behavior of the ideal sphere are presented, and the role of axisymmetric defects in reducing buckling pressure is widely analyzed. Stein Montalvo et al [16] conducted dynamic pressure buckling tests on defective spherical shells made of viscoelastic materials, proving that the lower critical load can be determined by material characteristics. An empirical model is introduced to show that reducing critical load caused by viscoelastic creep deformation is in the same way as reducing critical load affected by increasing defects in the elastic shell.…”