Gert van der Heijden

Centre for Nonlinear Dynamics and its Applications

Department of Civil, Environmental and Geomatic Engineering

University College London

Gower Street
London WC1E 6BT, UK
Tel: +44-(0)20-7679-2727
Fax: +44-(0)20-7380-0986

"Many a golden opportunity to remain silent has been squandered by anti-prophets who do not realise that the grounds for declaring something impossible or inconceivable may be undermined by new ideas that cannot be foreseen."

Peter Medawar (1965)

EPSRC DTP studentship available on the project `Vibration and stability of slender structures under moving masses' (start date: Sep 2023). Apply here.
The project can be found in the Project Catalogue under the Research Theme 'Engineering' (number 2228bd1125).
(Closing date for applications: 26 Jan 2023, 12:00.)

Studentships available:
I'm looking for recent graduates interested in research into the nonlinear dynamics of large-deformation structures (bifurcations, stability, post-buckling behaviour). Get in touch if any of the research projects highlighted below look interesting or if you have ideas for a project.

Call for papers:
10th European Nonlinear Dynamics Conference (ENOC 2020), 5-10 July 2020, Lyon, France
including a Minisymposium on Nonlinear Dynamics in Biological Systems (MS-13)
(postponed to 17-22 July 2022)

Recent event:
Analysis, Simulation and Modeling of Elastic Curves (Curves 2019), 6-8 May 2019, Freiburg, Germany

Recent event:
Summer School and Workshop
Biology, Analysis, Geometry, Energies, Links [bagel19]: A Program on Low-dimensional Topology, Geometry and Applications
17-28 June 2019, IMA (Institute for Mathematics and its Applications), University of Minnesota, USA

Recent event:
8th Symposium on the Mechanics of Slender Structures (MoSS 2019), 24-26 May 2019, Changsha, P.R. China

EPSRC grant awarded on the project `Modelling the Mechanics of Animal Whiskers (MMEAW)'
as part of this there is a Postdoc position available at London South Bank University
(closing date for applications: 5 November 2017)

Summer school:
XLII Summer School on Mathematical Physics, 4-16 September 2017, Ravello, Italy

Call for papers:
9th European Nonlinear Dynamics Conference (ENOC 2017), 25-30 June 2017, Budapest
including a Minisymposium on Nonlinear Dynamics in Biological Systems (MS-13)

Recent event:
Symposium on the Mechanics of Slender Structures (MoSS 2015), 21-22 September 2015, Northampton, UK

Recent event:
8th European Nonlinear Dynamics Conference (ENOC 2014), 6-11 July 2014, Vienna
including a Minisymposium on Nonlinear Dynamics in Biological Systems (MS-13)

Recent event:
Symposium on the Mechanics of Slender Structures (MoSS 2012), 23-25 July 2012, Harbin, P.R. China

Recent event:
7th European Nonlinear Dynamics Conference (ENOC 2011), 24-29 July 2011, Rome
including a Minisymposium on Nonlinear Dynamics of Biological Systems (MS-13)

EPSRC grant awarded on the project `A chiral theory of DNA supercoiling'
(as part of this there is a PhD studentship available at Imperial College London)
(position filled)

EPSRC-funded DTA studentship available on the project `Collagen: a nanoscale rope made of twisted bundles of fibres' (position filled)
(read more)

Recent event:
Workshop `Nonlinear Dynamics of Chemical and Biochemical Reaction Networks'
28 May 2008
(check here for more information)

EPSRC-funded 2-year postdoc position available! (position filled)
(read more)

Call for Papers (closed)
Symposium on the Mechanics of Slender Structures (MoSS 2008), 23-25 July 2008, UMBC

Call for Papers (closed)
for a Special Issue on 'Nonlinear Mechanics and Dynamics of Macromolecules' of the International Journal of Non-Linear Mechanics

Recent event:
Workshop `Nonlinear Dynamics of Biological Filaments'
1 June 2007
(check here for more information)

Latest news (August 2004):
EPSRC-funded 3-year postdoc position available! (position filled)
(read more)

Workshop `Modern Trends in Theoretical and Applied Mechanics'
23-24 April 2003
(view the flyer or click here to read more)
group picture

Curriculum Vitae

Research Interests:

Generally the geometrically exact description and analysis of slender structures in constrained environments
  • Nonlinear mechanics of slender elastic structures, both 1D (rods, strings) and 2D (strips, ribbons): post-buckling behaviour, large deformations, (multi-pulse) localisation, statical and dynamical stability, bifurcation, constrained deformation (self-contact and surface contact), interaction, discontinuities (kinks), writhing, whirling, transport, ply formation, multi-strand structures, boundary layers, topological properties such as link and writhe. Applications both in engineering (pipe lay, twisted cables, (electrodynamic) space tethers, drill strings, wire rope, rotated and transported textile yarn, nanotube junctions) and in biology (supercoiled DNA, deformations under screened electrostatic interactions, cholesterol ribbons, plied proteins, collagen fibres). Read more in the research overview article (dated 2007). For prize-winning experiments on rods, by former student Geoff Goss, click here.
  • Constrained variational calculus, conjugate point theory, variational inequalities, non-smooth mechanical systems
  • Hamiltonian mechanics, integrability, Melnikov theory
  • Computational (numerical as well as analytical) dynamical systems: normal forms, (homoclinic) bifurcations
  • Numerical continuation and bifurcation analysis, computer software
  • Nonlinear rotordynamics, coupled oscillators, chaotic dynamics


Highlights in pictures (old)


Some current research projects:

  • Statical and dynamical behaviour of electrodynamic space tethers:

  • Electrodynamic tethers connect spacecraft to other orbiting bodies and are designed to use the earth's magnetic field, rather than chemical fuel, for thrust and drag. Some tethers are spun about their axis for gyroscopic stability and therefore must resist bending and twisting. Such tethers need to be described by an elastic rod rather than the traditional string. Of particular interest are whirling and other instabilities.

    J. Phys. A paper (2008) (on the integrability of a rod in a magnetic field) [arXiv preprint]

    J. Phys. A paper (2009) (on spatial chaos of an EXTENSIBLE rod in a magnetic field) [arXiv preprint]

    J. Nonl. Sci. paper (2010) (on magnetically-induced buckling of electrodynamic space tethers) [arXiv preprint]

    J. Phys. A paper (2011) (on a Melnikov method and nonintegrability of an extensible rod in a magnetic field) [arXiv preprint]

    Physica D paper (2014) (on localised electrodynamic space tether solutions and their bifurcations)

    As a spin-off, in this ZAMP paper (2014) we give the first correct proof that the nonsymmetric top, and hence the anisotropic rod, is chaotic.


  • Complicated dynamics of rotor systems with bearing clearance:

  • Bearing clearance introduces a nonlinearity into rotor dynamics, which gives rise to complicated dynamics. We study resonances and mode-locking of (quasi-)periodic solutions and have foound an interesting new interaction between mode-locking and homoclinic phenomena (coined the zipper bifurcation).

    [ J. Nonlinear Sci. (1995)] (on resonance and mode-locking)

    [ Dynamics and Stability of Systems (2000)] (on interaction between mode-locking and homoclinic behaviour - the zipper)

    [ Chaos, Solitons & Fractals (1993)] (application to drill string dynamics - resonant and chaotic drill string whirl)


  • Writhing instabilities of transported textile yarns in spinning and texturing:

  • We study snarling and other twist-induced instabilities of transported textile yarns in such industrial processes as ring-spinning and texturing. We are also trying to get a better understanding of the mechanical properties of textile yarns (such as the twist-stretch coupling) in terms of the properties of the composing fibres.

    [ J. Eng. Math. (2007)] (paper on the snarling instability)

    [ J. Text. Inst. (2008)] (paper on multi-ply textile yarns)

    [ J. Text. Inst. (2010)] (paper on torsional properties of plied yarns)


  • Collagen nanofibres and fibrillogenesis:

  • The structural support protein collagen is the most abundant protein in the animal kingdom and helps tissues such as bone and tendon to withstand stretching. Models of multi-strand plied structures are applied to the rope-like collagen fibrils recently discovered in UCL's Medicine Department.

    [ Biophysical Journal 92, 70-75 (2007)] (nanoscale ropes)


  • Variational analysis of rods subject to surface constraints - from drill strings to DNA packing:

  • Configurations and bifurcations of rods on or inside surfaces are studied (i.e., equality or inequality constraints). An example of the latter is a drill string bouncing inside a borehole. This work is also relevant for structural problems in molecular biology (for instance, in the supercoiling and packing of DNA).

    [ Proc. R. Soc. Lond. A 457, 695-715 (2001)] (derives and analyses the equations for an isotropic rod deforming on a cylinder - heteroclinic connection)]

    [ Int. J. Solids Struct. 39, 1863-1883 (2002)] (anisotropic rod on a cylinder - spatial chaos (heteroclinic tangle), Maxwell critical load for transition to periodic buckling)

    [ Arch. Rat. Mech. Anal. 182, 471-511 (2006)] (on energy-minimising self-contacting rods on a cylinder) [arXiv preprint]

    [ Quart. Appl. Math. 65, 385-402 (2007)] (on end rotation, twist and writhe for large-deformation rods) [early arXiv preprint]

    By modelling a rod on a cylinder as a special case of a two-strand braid (see theory below), we now also have a complete theory of static friction, allowing us to determine the dependence of critical loads of constrained cylindrical buckling on friction parameters:

    [ J. Mech. Phys. Solids 173, 105224 (2023) ]

    The braid modelling also allows us to study the buckling and lift-off of a heavy rod compressed into a cylinder with arbitrary inclination relative to the direction of gravity. Gravity becomes an internal torque to the braid. Buckling in near-horizontal cylinders is found to be dominated by mode-switching, while buckling in near-vertical cylinders is dominated by self-weight buckling at tensile loads. We show how the inclination angle interpolates between these two scenarios.

    [ J. Mech. Phys. Solids , 105464 (2023) ]


  • Braided rods with applications to DNA supercoiling:

  • We have developed a general theory of elastic two-strand structures. The strands are assumed to have circular cross-section and to be in continuous (frictionless) contact, but we make no assumption about the shape of the contact curve, i.e., the axis of the ply is free to adopt any configuration under the action of end loads. Local interaction between the rods is also incorporated and we are applying the theory to study DNA supercoiling (both open braided DNA and closed minicircles) due to chiral DNA-DNA interactions.

    Below are three ideal shapes with hard-core contact only, i.e., without electrostatic forces: a link, a knot and a braid. In each case we verify that the contact pressure is everywhere positive, meaning that the shapes are physical: the strands are naturally in contact and would require a force to be pulled apart.

    4link 9knot braid

    [ Journal of the Mechanics and Physics of Solids 64, 83-132 (2014)] (equilibrium equations for elastic braids)

    [ Soft Matter 9, 9833-9848 (2013)] (application to dual-DNA braiding experiments)


  • Localised lateral and upheaval thermal buckling of subsea pipelines:

  • Subsea pipelines under high-temperature conditions tend to relieve their axial compressive stress by forming localised lateral or upheaval buckles. This type of buckling has traditionally been studied as a kind of imperfect column buckling problem. The first paper below studies lateral buckling as a genuine localised buckling phenomenon governed by a different static instability (a Hamiltonian-Hopf bifurcation) with a different critical load and with post-buckling shapes described by homoclinic orbits. These homoclinic orbits give analytical buckle decay rates without the need for ad hoc assumptions on pipeline imperfections.

    We also investigate by means of parameter studies how buckling can be controlled by sleepers or buoyancy sections. We furthermore carry out stability analyses that reveal a limit to the temperature difference for safe operation of the pipeline.

    [ Thin-Walled Structures 120, 408-420 (2017)] (localised lateral buckling of partially embedded subsea pipelines with nonlinear soil resistance)

    [ Thin-Walled Structures 122, 17-29 (2018)] (lateral buckling of pipelines with sleepers as buckle initiators)

    [ Marine Structures 58, 199-222 (2018)] (on distributed buoyancy sections to control lateral buckling)

    [ Marine Structures 60, 165-185 (2018)] (localised upheaval buckling of buried subsea pipelines)

    [ Engineering Structures 168, 447-461 (2018)] (on a different lateral buckling mode of pipelines with sleeper)

    The paper below studies the shock sensitivity of a trenched pipeline (for instance under irregular fluid flow inside the pipe, landslides or earthquakes), i.e., the nonlinear stability under finite disturbances rather than the usual linear stability under infinitesimal perturbations.

    [ Journal of the Mechanics and Physics of Solids 143, 104044 (2020)]


  • Animal and robotic whiskers:

  • We study the shape and mechanics of animal whiskers and analogous robotic sensing devices.

    [ Science Advances (2020) (open access) paper on their universal shape]

    [ Journal of Morphology (2020) (open access) paper with more on whisker shape]

    [ Journal of Morphology (2023) (open access) paper on the variation of whisker shape between species]

    [ Soft Robotics (2023) on selecting appropriate base measurements in whisker sensing]




  • Dynamics of beams and cables under moving loads and masses:

  • We are developing a general theory of computational rod dynamics using numerical discretisation based on Cosserat theory. The theory allows for arbitrary deformations and we are particularly interested in the effects of moving loads and masses on slender structures. Moving load problems occur in various engineering applications: vehicle-bridge interaction, cable cars, cranes, launch systems, space structures, etc.

    A few early examples:

    Spring pulled at the end: movie 1

    Spring subject to a moving load: movie 2

    In-plane collapse of shallow arch under slowly-moving load: movie 3

    Non-collapse of shallow arch under same load at higher speed: movie 4

    Out-of-plane collapse of deep arch under slowly-moving load: movie 5

    [ Meccanica 50, 1419-1429 (2015)] (dynamics of a tapered beam carrying a moving mass)

    [ Journal of Physics: Conference Series 721, 012016 (2016)] (beams and rods carrying a moving mass, 3D theory)

    [ Journal of Sound and Vibration 412, 309-325 (2017)] (large-deformation rods carrying a moving load or mass, 2D theory)


  • Twisted strips - states of an inextensible sheet:

  • We study the mechanics of inextensible strips with applications to paper crumpling, fabric draping as well as general sheet processing. Geometrically this leads to the study of developable surfaces (surfaces flat in one direction). As part of this work we solved the long-standing problem of finding the shape of a Möbius strip.

    animated Escher Escher Lk=3/2 animated Moebius Nature Materials cover

    Our paper `The shape of a Möbius strip' has now appeared in Nature Materials (2007)

    (a preprint can be found here, Supplementary Information here; or read the abstract, or UCL's top story)

    See Eugene's page for publicity

    Extending this work, we have discovered and described a new triangular buckling pattern of twisted inextensible strips held in tension with edge stress concentration similar to that of the Möbius strip (Proc. R. Soc. A (2010) paper, arXiv preprint):

    strip buckling strip computed

    We have also computed equilibrium shapes of knotted one-sided ribbons such as these (2,5) and (3,7) torus knots:

    (2,5) torus knot (3,7) torus knot

    By contrast, the (2,3) (trefoil) and (4,7) knots look like:

    (2,3) torus knot (4,7) torus knot common trefoil knot

    (note that one-sided closed inextensible ribbons need to have an odd number of inflection/switching points (with accompanying singularity in the bending energy density); the (2,3) trefoil knot has these on the outside and therefore looks somewhat different from the usual shape (right), requiring a wider berth to accommodate them; we call it a type II torus knot)

    For more on such strips with topology different from the Möbius one, see our paper in the Journal of Elasticity (2015)

    A singular perturbation analysis of these universal cone-like singularities on the edge of the strip has been published in the Journal of the Mechanics and Physics of Solids (2023)

    The method for deriving convenient equilibrium equations for general one-dimensional elastic problems (i.e., for geometric variational problems on curves) is discussed in our paper in Physical Review E (2009) [arXiv preprint]

    Quantum eigenstates of a particle confined to the surface of a Möbius strip (or other one-sided surface) reveal curvature trapping in regions (creases) of high curvature as the strip's width-to-length ratio is increased. This could be important for transport properties of Möbius-type structures in nanoscale devices. See our paper in the Journal of Physics: Condensed Matter (2009) [arXiv preprint]

    We have also applied our methods to helical ribbons and discovered tension-induced multistability and phase separation (straightening) as observed in cholesterol ribbons. The results may also be relevant for nanobelts and the design of nanoswitches [Physical Review Letters 101, 084301 (2008)] [arXiv preprint]:

    stretched helix

    How to shed a loop in a kinked helical spring:

    stretched helix

    Helical nanoribbons of various types of material (SiO2, ZnO, Si/Cr, SiGe/Si, SiGe/Si/Cr) have been fabricated for use in nano-electromechanical systems (NEMS) such as nanoinductors, resonators, actuators, etc. Of particular interest are nanosprings of very low pitch as they allow for a large magnetic flux density. Such low-pitch springs when pulled may not simply unwind but instead show a highly nonlinear force-extension response dominated by sequential multi-loop pop-out. [J. Mech. Phys. Solids 57, 959-969 (2009)] [arXiv preprint]


  • Folding of thin annular strips:

  • Closed annular strips can be folded into compact shapes in 'regular' or 'inverted' fashion. Wide-strip equilibrium configurations can be either inflectional or non-inflectional. Inflectional solutions have stress localisations, with diverging strain energy density, on the edge of the strip.







    [J. Mech. Phys. Solids 169, 105054 (2022)]


Research students, postdocs and visitors:

  • Rehan Shah (EPSRC-funded PhD student; rods deforming on surfaces, 2018-2022; thesis title: Nonlinear mechanics of elastic rods constrained to deform on rigid tubular surfaces)
  • Eugene Starostin (EPSRC Research Fellow, Jul. 2005 - Sep. 2009 - Sep. 2012; Honorary Research Fellow, 2012-present; writhing structures, geometry and mechanics of strips, plies and bundles, applications to biofilaments, DNA supercoiling, annular strips, animal and robotic whiskers)
  • Xingwei Zhao (Tongji University, Shanghai, China; PhD student funded by the China Scholarship Council, Nov. 2013 - Nov. 2015; vibrations of beams and cables with moving loads and masses)
  • Zhenkui Wang (Tianjin University, Tianjin, China; PhD student funded by the National Key Basic Research Program of China, Jan. 2016 - Jan. 2017; post-doctoral Fellow funded by the China Postdoctoral Council, Oct. 2018 - Oct. 2020; localised thermal buckling of subsea pipelines)
  • Anthony Korte (EPSRC Research Fellow, Apr. 2008 - Apr. 2010; HFSP, Apr. 2010 - Mar. 2013; quantum eigenstates and transport properties of Möbius-type nanostructures, curvature trapping, buckling and instabilities of twisted strips; chiral effects in DNA supercoiling)
  • Mark Peletier (EPSRC Visiting Fellow, 6 weeks 2002; global energy minimisers, constrained rods, Link-Twist-Writhe)
  • Geoff Goss (part-time PhD student, finished Sep. 2003; thesis title: Snap buckling, writhing and loop formation in twisted rods [PDF file, 7.8 MB])
  • Juan Valverde (Royal Society Visiting Research Fellow, Seville, Jul.-Dec. 2004; buckling of conducting rods in a magnetic field, instabilities of whirling electrodynamic space tethers)
  • Qiguo Sun (Royal Society KC Wong China Fellow, Nov. 2005 - Oct. 2006; fluid-structure interactions in whirling tether and rotor systems; also Royal Society China-UK 1 Year Networking grant visitor, periodically, Apr. 2009 - Aug. 2010; control of space tethers)
  • Kazuyuki Yagasaki (London Mathematical Society, Mar. 2006; multi-pulse homoclinic orbits, spatial chaos)
  • Pedro Ribeiro (on sabbatical leave from the University of Porto, Jan. - Aug. 2007)
  • Barrie Fraser (EPSRC Visiting Fellow, periodically, 2005 - 2008; instabilities in whirling and transported rods and textile yarns)
  • David Sinden (EPSRC-funded PhD student, 2004-2008; thesis title: Integrability, localisation and bifurcation of an elastic conducting rod in a uniform magnetic field; now a Research Assistant in UCL's Department of Mechanical Engineering)
  • David Lane (EPSRC-funded PhD student, 2006-2010; thesis title: Stability of discontinuous elastic rods with applications to nanotube junctions)
  • Caifa Guo (College of Aerospace and Materials Engineering, National University of Defense Technology, Changsha, China; PhD student funded by the China Scholarship Council, Oct. 2011 - Sep. 2013; bifurcation and stability of electrodynamic space tethers)
  • Colin Taylor (EPSRC-funded PhD student on 4-year EngD in Molecular Modelling and Materials Science, 2009-2014; bundle models for collagen and other biofilaments; thesis title: Interacting elastic rods)
  • Zhe Wang (Tianjin University, Tianjin, China; PhD student funded by the China Scholarship Council, Mar. 2015 - Mar. 2017; localised lateral and upheaval buckling of deep-sea pipelines)
  • Guiqin He (School of Astronautics, Harbin Institute of Technology, Harbin, China; PhD student funded by the China Scholarship Council, 2021; structural vibrations of manoeuvring satellites equipped with solar panels)



  • 2002-2011: MECH3004 Applied Mechanics (Mechanical Engineering)
    (now with solution movies!)
  • Autumn Terms 2005-2019: MATH0086 Computational and Simulation Methods (introduction to finite-element modelling), as part of the MSc in Mathematical Modelling (Mathematics)
  • Spring Terms 2010-2020: CEGE0038 Finite Element Modelling and Numerical Methods (4th-year/MSc, Civil and Environmental Engineering)
  • Spring Term 2013, Autumn Terms 2013-2015: CEGEG090/CEGEM090 Advanced Structural Analysis (plates, membranes, shells) (4th-year/MSc, Civil and Environmental Engineering)
  • Autumn Term 2016-2019: CEGE0040 Structural Dynamics (4th-year/MSc, Civil and Environmental Engineering)
  • December 2010: MSc course `Computational and Simulation Methods' (KAUBM04), Department of Mathematics, King Abdulaziz University, Jeddah, Saudi Arabia
  • June-July 2016: Short Course `Introduction to nonlinear dynamics with applications to slender structures', Shanghai Maritime University, Nanhui New City, Shanghai, P.R. China
  • January 2017: Short Course `Introduction to nonlinear dynamics with applications to slender structures', Harbin Institute of Technology, Harbin, P.R. China
  • July 2017: Short Course `Nonlinear mechanics of plates and shells', Harbin Institute of Technology, Harbin, P.R. China
  • December 2017 - January 2018: Short Course `Nonlinear dynamics of slender structures', Harbin Institute of Technology, Harbin, P.R. China
  • August 2018: Short Course `Nonlinear dynamics of slender structures', Harbin Institute of Technology, Harbin, P.R. China
  • December 2018 - January 2019: Short Course `Vibration of continuous systems (strings, beams and chains)', Shanghai Maritime University, Nanhui New City, Shanghai, P.R. China
  • June 2013: Summer School Course `Introduction to nonlinear dynamics with applications to space tethers', International Summer School on Aerospace Technologies (ISSAT 2013), National University of Defense Technology, Changsha, P.R. China
  • September 2017: Summer School Course `Nonlinear mechanics of sheets and filaments - interplay between geometry and mechanics', XLII Summer School on Mathematical Physics, Ravello, Italy
  • June 2019: Summer School Course `Nonlinear mechanics of rods, sheets and ribbons - interplay between geometry and mechanics', IMA programme on Biology, Analysis, Geometry, Energies, Links [bagel19]: A Program on Low-dimensional Topology, Geometry, and Applications , University of Minnesota, Minneapolis, USA


Further professional activities:


Other interests:


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