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]

SlinkyThe 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]

DielectricElastic 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]

Lipid Bilayer CompressionIn 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]

Extended Lubrication TheoryLubrication 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]

Dynamics of Snapping Beams and Jumping PoppersWe 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]

Control and
Manipulation of Microfluidic Fluid Flow via Elastic DeformationsWe 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-InducedSwelling-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 Function   

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 More...


Mechanics of Surface Area Regulation of Cell Membranes   

M. Staykova, D.P. Holmes, C. Read, and H.A. Stone, Proc. Natl. Acad. Sci, 108 (22), 9084-9088, 2011. [PDF]
Selected PressNature Materials 

Controlled Vesicle Adsorption and Tether Formation of Lipid BilayersWe 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, 7, 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.  


Draping Films: A Wrinkle to Fold Transition    

D.P. Holmes and A.J. Crosby, Physical Review Letters105, 038303, 2010.  [PDF] [Supplemental Material]

Selected Press: Science News, Discovery NewsPhysics

Draping Films: A Wrinkle to Fold Transition

A 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 wrinkles.  


Crumpled Surface Structures    

D.P. Holmes, M. Ursiny, and A.J. Crosby.  Soft Matter, 4, 82, 2008. [PDF]

Crumpled Surface
StructuresThe 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 stimuli.


Snapping Surfaces    

D.P. Holmes and A.J. Crosby. Advanced Materials19, 3589, 2007 [PDF]
Selected Press Discovery NewsWired

SurfacesThe 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 structure.

Assistant Professor
Engineering Science & Mechanics
Virginia Tech
222 Norris Hall
Blacksburg, VA 24060
(540) 231-7814
Soft Mechanical Structures Blog


  email:  dpholmes at vt. edu [CV]


Research Interests

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.

News & Highlights
Recent Events, Press, and Awards
06/16/2014 Conference: USNCTAM - Mechanics and Physics of Soft Matter Materials
05/22/2014 Workshop: AmeriMech 2014 - Mechanics in Biology II
03/17/2014 UNH Inquiry: Celebrating Ten Years in Publication
03/03/2014 Co-Organizer: APS March Meeting - Invited Session: Toy Mechanics and Mechanisms
01/06/2014 Workshop: Princeton-Oxford Collaborative Workshop
11/24/2013 Conference: APS 66th Annual DFD Meeting
10/22/2013 Seminar: Boston University - Mechanical Engineering
10/21/2013 Seminar: Brown University - Applied Mathematics
09/19/2013 Seminar: James Madison University - Physics & Astronomy
08/01/2013 Visiting Scholar: OCCAM - Oxford University
07/01/2013 Visiting Professor: UPMC - Paris 6
06/24/2013 Conference: American Society for Engineering Education
05/22/2013 Conference: Pan American Congress of Applied Mechanics
03/29/2013 ASEE: Ferdinand P. Beer & E. Russell Johnston, Jr. Outstanding New Mechanics Educator
03/18/2013 Co-Organizer: APS March Meeting - Extreme Mechanics
03/15/2013 Workshop: NECF - Mechanics of Thin Sheets
02/19/2013 NSF CMMI Award: Swelling-Induced Origami
01/07/2013 Workshop: Princeton-Oxford Collaborative Workshop
12/10/2012 Workshop: AmeriMech 2012: Mechanics in Biology I
11/30/2012 Seminar: California Institute of Technology: GALCIT
10/05/2012 Physics: Connecting a Thin-Shell's Stiffness with Its Geometry
02/01/2012 iMechanica: Elastic Instabilities for Form & Function
11/02/2011 Science: Jumping Rope by the Numbers
07/22/2011 Nature Materials: Vesicles in and Tubes Out


Mechanics of Deformable Bodies Online ESM 2204 Summer I 2014
Mechanics of Deformable Bodies ESM 2204 Spring 2014
Theory of Plates and Shells ESM 6044 Fall 2013
Mechanics of Deformable Bodies Video Blog ESM 2204 Spring 2013
Mechanics of Deformable Bodies ESM 2204 Fall 2012
Mechanical Behavior of Materials ESM 3054 Spring 2012

Research Group

Ph.D. Students
Anupam Pandey Behrouz Tavakol
Masters Students
Callan Gillespie Austin Fergusson