Equilibria and Instabilities of a Slinky: Discrete Model
|D.P. Holmes, A.D. Borum, B.F. Moore III, R.H. Plaut, and D.A. Dillard, Accepted: International Journal of Nonlinear Mechanics, DOI:10.1016/j.ijnonlinmec.2014.05.015, 2014. [PDF] [arXiv]
The Slinky is a well-known example of a highly flexible helical spring, exhibiting large, geometrically nonlinear deformations from minimal applied forces. By considering it as a system of coils that act to resist axial, shearing, and rotational deformations, we develop a discretized model to predict the equilibrium configurations of a Slinky via the minimization of its potential energy. Careful consideration of the contact between coils enables this procedure to accurately describe the shape and stability of the Slinky under different modes of deformation. In addition, we provide simple geometric and material relations that describe a scaling of the general behavior of flexible, helical springs.
Buckling of Dielectric Elastomeric Plates for Soft, Electrically Active Microfluidic Pumps
|B. Tavakol, M. Bozlar, C. Punckt, D.P. Holmes, G. Froehlicher, H.A. Stone, I.A. Aksay, and D.P. Holmes, Soft Matter, 10(27), 4789-4794, 2014. [PDF]
Elastic instabilities, when properly implemented within soft, mechanical structures, can generate advanced functionality. In this work, we use the voltage-induced buckling of thin, flexible plates to pump fluids within a microfluidic channel. The soft electrodes that enable electrical actuation are compatible with fluids, and undergo large, reversible deformations. We quantified the onset of voltage-induced buckling, and measured the flow rate within the microchannel. This embeddable, flexible microfluidic pump will aid in new generation of stand-alone microfluidic devices that require a tunable flow rate.
Effects of Substrate Defects on Lipid Bilayer Compression Dynamics
|A. Fergusson, R. Kappiyoor, G. Balasubramanian, I.K. Puri, and D.P. Holmes, arXiv, 2014. [arXiv]
In vivo and in vitro lipid bilayers are commonly supported by subcellular structures, particles, and artificial substrates. Deformation of the underlying structure can lead to large, localized deformations as the bilayer deforms to avoid stretching. Applications of SLBs commonly assume that the supporting substrate is continuous and defect-free. However, this assumption is unrealistic in vivo. In this work, we consider the effect of defects within the underlying substrate by simulating different bilayers supported by continuous and nanoporous substrates. We show that the bilayer behavior greatly depends on strain rate, and that substrate defects may contribute to the formation of nanotubes for compressed substrates.
Extended Lubrication Theory: Estimation of Fluid Flow in Channels with Variable Geometry
|B. Tavakol, D.P. Holmes, G. Froehlicher, and H.A. Stone, arXiv, 2014. [arXiv]
Lubrication theory is broadly applicable to the flow characterization of thin fluid films and the motion of particles near surfaces. We offer an extension to lubrication theory by considering higher-order terms of the analytical approximation to describe the fluid flow in a channel with features of a modest aspect ratio. We find good agreement between our analytical results and numerical simulations. We show that the extended lubrication theory is a robust tool for an accurate estimate of laminar fluid flow in channels with features on the order of the channel height, accounting for both smooth and sharp changes in geometry.
Dynamics of Snapping Beams and Jumping Poppers
|A. Pandey, D.E. Moulton, D. Vella, and D.P. Holmes, EPL (Europhysical Letters), 105, 24001, 2014. [PDF] [arXiv]
We consider the dynamic snapping instability of elastic beams and shells. We show that the stretchability of the arch plays a critical role in determining not only the post-buckling mode of deformation, but also the timescale of snapping, and the frequency of the arch's vibrations about its final equilibrium state. We show that the growth rate of the snap-through instability, and its subsequent ringing frequency, can both be interpreted physically as the result of a sound wave in the material propagating over a distance comparable to the radius of curvature of the arch. Finally, we extend our analysis of the ringing frequency of indented arches to understand the 'pop' heard when everted shell structures snap-through to their stable state. Remarkably, we find that not only are the scaling laws for the ringing frequencies in these two scenarios identical, but also the respective prefactors are numerically close; this allows us to develop a master curve for the frequency of ringing in snapping beams and shells.
Control and Manipulation of Microfluidic
Fluid Flow via Elastic Deformations
|D.P. Holmes, B. Tavakol, G.
Froehlicher, and H.A. Stone, Soft Matter, 9, 7049, 2013. [PDF]
Special Issue: Emerging Investigators [PDF]
We present a material with internal flexible valves that can
control and direct fluid flow via external mechanical actuation for use
in advanced materials for in situ mixing, chemical reactions, and
rapid, portable chemical analysis. In particular, we microfabricate
internal flexible valves so that macroscopic deformation leads to valve
function that regulates fluid flow and so can direct flow from low to
high regions of external stress. Creating a bio-inspired method for
internal flow regulation will be useful for controlling fluid flow
within multifunctional devices.
Swelling-Induced Deformations: A Materials-Defined Transition from Macroscopic to Microscopic Deformations
|A. Pandey and D.P. Holmes, Soft Matter, 9, 5524, 2013. [PDF]
Swelling-induced deformations are common in many biological
and industrial environments, and the shapes and patterns that emerge can
vary across many length scales. Here we present an experimental study of
a transition between macroscopic structural bending and microscopic
surface creasing in elastomeric beams swollen non-homogeneously with
favorable solvents. We demonstrate how proper tuning of materials and geometry can generate instabilities at
multiple length scales in a single structure.
Elastic Instabilities for Form and
|D.P. Holmes, iMechanica - Journal Club,
February 2012. [Link]
Welcome to February 2012's Journal club,
which will include a discussion on elastic instabilities for form and
function. Not long ago, the loss of structural stability through
buckling generally referred to failure and disaster. It was a phenomenon
to be designed around, and rarely did it provide functionality*. The
increasing focus on soft materials, from rubbers and gels to biological
tissues, encouraged scientists to revisit the role of elastic
instabilities in the world around us and inspired their utilization in
advanced materials. Now the field of elastic instabilities, or extreme
mechanics, brings together the disciplines of physics, mechanics,
mathematics, biology, and materials science to extend our understanding
of structural instabilities for both form and function. In this journal
club, we're going to look at research on the wrinkling, crumpling, and
snapping of soft or slender structures. Read
Mechanics of Surface Area Regulation of
|M. Staykova, D.P. Holmes, C.
Read, and H.A. Stone, Proc. Natl. Acad. Sci, 108 (22),
9084-9088, 2011. [PDF]
Press: Nature Materials
We approach the complex problem of cell
area regulation by using a model membrane system and a novel
experimental setup, which couples a lipid bilayer to the controlled
straining of an elastic sheet to study the response of pure lipid
membranes to lateral stretch and compression. We demonstrate that
even a single component fluid lipid bilayer can controllably regulate
its surface area upon straining by either the absorption of vesicles
upon membrane dilation or through nanotube expulsion upon compression.
The processes of lipid membrane remodeling in our experiments
closely resemble steps in the membrane traffic via exo- and endo-cytosis
observed in biological cells. Our results offer a simple insight
into these complex cell processes as well as into the role of the lipid
bilayer in their regulation and coordination.
Bending and Twisting of Soft Materials
by Non-Homogenous Swelling
D.P. Holmes, M. Roché, T. Sinha, and H.A.
Stone, Soft Matter,
5188, 2011 [PDF]
Soft materials, e.g. biological tissues
and gels, undergo morphological changes, motion, and instabilities when
subjected to external stimuli. Tissues can exhibit residual internal
stresses induced by growth, and generate elastic deformations to move in
response to light or touch, curl articular cartilage, aid in seed
dispersal, and actuate hygromorphs, such as pine cones. Understanding
the dynamics of such osmotically driven movements, in the influence of
geometry and boundary conditions, is crucial to the controlled
deformation of soft materials. We examine how thin elastic plates
undergo rapid bending and buckling instabilities after exposure to a
solvent that swells the network. A circular disc bends and buckles with
multiple curvatures, and a large-amplitude travelling wave rotates
azimuthally around the disc.
A Wrinkle to Fold Transition
|D.P. Holmes and A.J.
Crosby, Physical Review
Letters, 105, 038303, 2010.
[PDF] [Supplemental Material]
Press: Science News,
Discovery News, Physics
polymer film draping over a point of contact will wrinkle due to the
strain imposed by the underlying substrate. The wrinkle wavelength
is dictated by a balance of material properties and geometry; most
directly the thickness of the draping film. At a critical strain,
the stress in the film will localize, causing hundreds of wrinkles to
collapse into several discrete folds. In this paper, we examine
the deformation of an axisymmetric sheet and quantify the force required
to generate a fold. The onset of folding, in terms of a critical force
or displacement, scales as the thickness to the four-ninth power, which
we predict from the energy balance of the system. The folds
increase the tension in the remainder of the film causing the radial
stress to increase, thereby decreasing the wavelength of the remaining
D.P. Holmes, M. Ursiny, and A.J. Crosby. Soft
Matter, 4, 82, 2008. [PDF]
The topographic control of pattern
features is of great interest for a range of applications including the
generation of ultrahydrophobic surfaces, microfluidic devices, and the
control and tuning of adhesion. In these areas, surface patterning is
achieved by a variety of techniques including: photolithography, imprint
lithography, and surfaces wrinkling. In this paper, we present a
scalable patterning method based on surface plate buckling, or
crumpling, to generate a variety of topographies that can dynamically
change shape and aspect ratio in response to
|D.P. Holmes and A.J.
Crosby. Advanced Materials, 19,
3589, 2007 [PDF]
Discovery News, Wired
The responsive mechanism
of the Venus flytrap has captured the interest of scientists for
centuries. Although a complete understanding of the mechanism
controlling the Venus flytrap movement has yet to be determined, a
recent publication highlights the importance of geometry and material
properties for this fast, stimuli-responsive movement.
Specifically, the movement is attributed to a snap-through elastic
instability whose sensitivity is dictated by the length scale, geometry,
and materials properties of the features. Here, we use lessons
from the Venus flytrap to design surfaces that dynamically modify their
topography. We present a simple, biomimetic responsive surface
based on an array of microlens shells that snap from one curvature to
another when a critical stress develops in the shell
||email: dpholmes at vt.
Slender structures are ubiquitous. Commonly described by rods, plates, and shells, these thin
structures are embodied by carbon nanotubes, air plane wings, blood vessels, spider silk, contact lenses, and human hair. The
mechanics of these thin objects are fascinating because geometric nonlinearities will
arise even as the material properties remain linear - hair will curl and tangle, skin will wrinkle, and soda cans will crumple. We are interested in understanding and controlling the mechanics, physics, and geometry of these thin structures.
|Mechanics of Deformable
||Summer I 2014
|Mechanics of Deformable
|Theory of Plates and
|Mechanics of Deformable
|Mechanics of Deformable
|Mechanical Behavior of