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

TL;DR

This study investigates how viscoelasticity causes delayed buckling in spherical shells, revealing that material properties lower the critical load and enable time-dependent control, with implications for tunable actuation.

Contribution

The paper introduces a viscoelastic model that predicts delayed buckling and load reduction in spherical shells, linking material properties to buckling behavior.

Findings

Viscoelasticity causes shells to buckle below elastic critical loads.

Delay time and buckling deflection depend on pressure, material, and defect size.

The model accurately predicts experimental observations.

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.