40 research outputs found
Dynamics of viscoelastic snap-through
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 in the literature. Combining these approaches
suggests that our conclusions may also extend to more complex viscoelastic
structures used in morphing applications.Comment: Main text 37 pages, Appendices 13 page
Pull-in dynamics of overdamped microbeams
We study the dynamics of MEMS microbeams undergoing electrostatic pull-in. At
DC voltages close to the pull-in voltage, experiments and numerical simulations
have reported `bottleneck' behaviour in which the transient dynamics slow down
considerably. This slowing down is highly sensitive to external forces, and so
has widespread potential for applications that use pull-in time as a sensing
mechanism, including high-resolution accelerometers and pressure sensors.
Previously, the bottleneck phenomenon has only been understood using lumped
mass-spring models that do not account for effects such as variable residual
stress and different boundary conditions. We extend these studies to
incorporate the beam geometry, developing an asymptotic method to analyse the
pull-in dynamics. We attribute bottleneck behaviour to critical slowing down
near the pull-in transition, and we obtain a simple expression for the pull-in
time in terms of the beam parameters and external damping coefficient. This
expression is found to agree well with previous experiments and numerical
simulations that incorporate more realistic models of squeeze film damping, and
so provides a useful design rule for sensing applications. We also consider the
accuracy of a single-mode approximation of the microbeam equations --- an
approach that is commonly used to make analytical progress, without systematic
investigation of its accuracy. By comparing to our bottleneck analysis, we
identify the factors that control the error of this approach, and we
demonstrate that this error can indeed be very small.Comment: 18 page
Delayed pull-in transitions in overdamped MEMS devices
We consider the dynamics of overdamped MEMS devices undergoing the pull-in
instability. Numerous previous experiments and numerical simulations have shown
a significant increase in the pull-in time under DC voltages close to the
pull-in voltage. Here the transient dynamics slow down as the device passes
through a meta-stable or bottleneck phase, but this slowing down is not well
understood quantitatively. Using a lumped parallel-plate model, we perform a
detailed analysis of the pull-in dynamics in this regime. We show that the
bottleneck phenomenon is a type of critical slowing down arising from the
pull-in transition. This allows us to show that the pull-in time obeys an
inverse square-root scaling law as the transition is approached; moreover we
determine an analytical expression for this pull-in time. We then compare our
prediction to a wide range of pull-in time data reported in the literature,
showing that the observed slowing down is well captured by our scaling law,
which appears to be generic for overdamped pull-in under DC loads. This
realization provides a useful design rule with which to tune dynamic response
in applications, including state-of-the-art accelerometers and pressure sensors
that use pull-in time as a sensing mechanism. We also propose a method to
estimate the pull-in voltage based only on data of the pull-in times.Comment: 17 page
Passive control of viscous flow via elastic snap-through
We demonstrate the passive control of viscous flow in a channel by using an
elastic arch embedded in the flow. Depending on the fluid flux, the arch may
`snap' between two states --- constricting and unconstricting --- that differ
in hydraulic conductivity by up to an order of magnitude. We use a combination
of experiments at a macroscopic scale and theory to study the constricting and
unconstricting states, and determine the critical flux required to transition
between them. We show that such a device may be precisely tuned for use in a
range of applications, and in particular has potential as a passive
microfluidic fuse to prevent excessive fluxes in rigid-walled channels.Comment: Main text 5 pages, Supplementary Information 14 page
A computational framework for the morpho-elastic development of molluskan shells by surface and volume growth
Mollusk shells are an ideal model system for understanding the morpho-elastic
basis of morphological evolution of invertebrates' exoskeletons. During the
formation of the shell, the mantle tissue secretes proteins and minerals that
calcify to form a new incremental layer of the exoskeleton. Most of the
existing literature on the morphology of mollusks is descriptive. The
mathematical understanding of the underlying coupling between pre-existing
shell morphology, de novo surface deposition and morpho-elastic volume growth
is at a nascent stage, primarily limited to reduced geometric representations.
Here, we propose a general, three-dimensional computational framework coupling
pre-existing morphology, incremental surface growth by accretion, and
morpho-elastic volume growth. We exercise this framework by applying it to
explain the stepwise morphogenesis of seashells during growth: new material
surfaces are laid down by accretive growth on the mantle whose form is
determined by its morpho-elastic growth. Calcification of the newest surfaces
extends the shell as well as creates a new scaffold that constrains the next
growth step. We study the effects of surface and volumetric growth rates, and
of previously deposited shell geometries on the resulting modes of mantle
deformation, and therefore of the developing shell's morphology. Connections
are made to a range of complex shells ornamentations.Comment: Main article is 20 pages long with 15 figures. Supplementary material
is 4 pages long with 6 figures and 6 attached movies. To be published in PLOS
Computational Biolog
The role of topology and mechanics in uniaxially growing cell networks
In biological systems, the growth of cells, tissues, and organs is influenced
by mechanical cues. Locally, cell growth leads to a mechanically heterogeneous
environment as cells pull and push their neighbors in a cell network. Despite
this local heterogeneity, at the tissue level, the cell network is remarkably
robust, as it is not easily perturbed by changes in the mechanical environment
or the network connectivity. Through a network model, we relate global tissue
structure (i.e. the cell network topology) and local growth mechanisms (growth
laws) to the overall tissue response. Within this framework, we investigate the
two main mechanical growth laws that have been proposed: stress-driven or
strain-driven growth. We show that in order to create a robust and stable
tissue environment, networks with predominantly series connections are
naturally driven by stress-driven growth, whereas networks with predominantly
parallel connections are associated with strain-driven growth
Mechanics reveals the role of peristome geometry in prey capture in carnivorous pitcher plants (Nepenthes)
Carnivorous pitcher plants (Nepenthes) are a striking example of a natural pitfall trap. The trap’s slippery rim, or peristome, plays a critical role in insect capture via an aquaplaning mechanism that is well documented. Whilst the peristome has received significant research attention, the conspicuous variation in peristome geometry across the genus remains unexplored. We examined the mechanics of prey capture using Nepenthes pitcher plants with divergent peristome geometries. Inspired by living materials, we developed a mathematical model that links the peristomes’ three-dimensional geometries to the physics of prey capture under the laws of Newtonian mechanics. Linking form and function enables us to test hypotheses related to the function of features such as shape and ornamentation, orientation in a gravitational field, and the presence of ‘teeth’, while analysis of the energetic costs and gains of a given geometry provides a means of inferring potential evolutionary pathways. In a separate modeling approach, we show how prey size may correlate with peristome dimensions for optimal capture. Our modeling framework provides a physical platform to understand how divergence in peristome morphology may have evolved in the genus Nepenthes in response to shifts in prey diversity, availability, and size
Active shape control by plants in dynamic environments
Plants are a paradigm for active shape control in response to stimuli. For
instance, it is well-known that a tilted plant will eventually straighten
vertically, demonstrating the influence of both an external stimulus, gravity,
and an internal stimulus, proprioception. These effects can be modulated when a
potted plant is additionally rotated along the plant's axis, as in a rotating
clinostat, leading to intricate shapes. We use a morphoelastic model for the
response of growing plants to study the joint effect of both stimuli at all
rotation speeds. In the absence of rotation, we identify a universal planar
shape towards which all shoots eventually converge. With rotation, we
demonstrate the existence of a stable family of three-dimensional dynamic
equilibria where the plant axis is fixed in space. Further, the effect of axial
growth is to induce steady behaviors, such as solitary waves. Overall, this
study offers new insight into the complex out-of-equilibrium dynamics of a
plant in three dimensions and further establishes that internal stimuli in
active materials are key for robust shape control