Dynamics of viscoelastic snap-through

Abstract

We study the dynamics of snap-through when viscoelastic effects are present. To gain analytical insight we analyse a modified form of the Mises truss, a single-degree-of-freedom structure, which features an 'inverted' shape that snaps to a 'natural' shape. Motivated by the anomalously slow snap-through shown by spherical elastic caps, we consider a thought experiment in which the truss is first indented to an inverted state and allowed to relax while a specified displacement is maintained; the constraint of an imposed displacement is then removed. Focussing on the dynamics for the limit in which the timescale of viscous relaxation is much larger than the characteristic elastic timescale, we show that two types of snap-through are possible: the truss either immediately snaps back over the elastic timescale or it displays 'pseudo-bistability', in which it undergoes a slow creeping motion before rapidly accelerating. In particular, we demonstrate that accurately determining when pseudo-bistability occurs requires the consideration of inertial effects immediately after the indentation force is removed. Our analysis also explains many basic features of pseudo-bistability that have been observed previously in experiments and numerical simulations; for example, we show that pseudo-bistability occurs in a narrow parameter range at the bifurcation between bistability and monostability, so that the dynamics is naturally susceptible to critical slowing down. We then study an analogous thought experiment performed on a continuous arch, showing that the qualitative features of the snap-through dynamics are well captured by the truss model. In addition, we analyse experimental and numerical data of viscoelastic snap-through times reported previously in the literature. Combining these approaches suggests that our conclusions may also extend to more complex viscoelastic structures used in morphing applications.

Flexible Microfluidics: Fundamentals, Recent Developments, and Applications

“…These PI micropumps are incorporated in Gomez et al used embedded flexible arches in a channel to achieve passive control in the microfluidic device via elastic snap-through [142]. Snap-through is an instability, where a rapid transition from one condition to another occurs [143][144][145]. The flow of the fluid in a flexible microchannel has a corresponding pressure gradient.…”

Predicting delayed instabilities in viscoelastic solids

“…Nonetheless, the virtual work of displacements performed over a short period Δ t → 0, coincides with the instantaneous elastic energy functional ( 16 ) where the elastic strain is . Typically, the elastic response time scale in elastomers is much smaller than the viscoelastic relaxation time [sometimes referred to as the large Deborah number limit ( 18 )]. In these cases, we can eliminate inertia from the system and approximate the motion of the material by the quasi-static evolution between elastic equilibrium states.…”

“…Varying the kernel may lead to varying rate of divergence of the flipping time between the stable and acquired stability region, yet the location of this divergence will remain unchanged. The divergence of flipping times was addressed in ( 8 ), and more recently, the rate of divergence was studied in ( 18 ).…”

Viscoelastic ribbons

“…Increasing the solvent viscosity smooths the snap-through, at least up to η s = 0.1 or so, highlighting how this dissipative effect controls the dynamics here (cf. Gomez et al 2019). For higher solvent viscosities (η s above 0.15), the dissipation slows the dynamics so much that snap-through is prevented entirely.…”