Jon.R. and Beverly S.Holt Professor of Engineering
Arthur F.Thurnau Professor of Mechanical Engineering and Applied Mechanics
Department of Mechanical Engineering
University of Michigan
2350 Hayward Street
Ann Arbor MI 48109-2125
3440 GG Brown / 2125
Office Phone: (734) 936-0406
FAX: (734) 615-6647
I graduated in Mechanical Sciences from the
University of Cambridge in 1963 and
joined British Rail, who later
sponsored my research at Cambridge between 1965 and 1968
on the subject of thermal effects in braking systems. In 1969
I became a Lecturer and later Reader in Solid Mechanics at the
Newcastle upon Tyne, U.K. I moved to the
University of Michigan,
of Mechanical Engineering in 1981. My current
research interests are in solid mechanics with particular
reference to thermoelasticity, contact mechanics and tribology.
I am a Chartered Engineer in the U.K., a Fellow of the Institution
of Mechanical Engineers and have engaged extensively in consulting
work in the field of stress analysis for engineering design. I am
author of two books and numerous articles in the
fields of Elasticity, Thermoelasticity, Contact Mechanics,
Tribology, Heat Conduction and Elastodynamics. I am a member
of the editorial boards of the
International Journal of Mechanical
Sciences and the
Journal of Thermal Stresses.
My research focuses mostly on those aspects of solid mechanics
pertaining to the contact of deformable bodies and particularly
to situations in which non-uniform temperatures result from
frictional heat generation at the interface or from heat flow
across it. In such cases, thermoelastic deformation of the
contacting bodies modifies the contact pressure distribution
and can lead to a rich variety of phenomena including
localization and dynamic instabilities. These effects are
of considerable technological importance, including, for example,
non-uniform contact pressure, high local temperatures
and vibrations in clutches and braking systems: a phenomenon
known as Frictionally-excited
(TEI). The figure on the left shows a transmission clutch plate after
a single engagement. The dark areas correspond to regions in which
high local temperatures have been experienced. The complete
disk in this case exhibits 12 equally spaced hot spots on
each side and they are arranged antisymmetrically. In other words,
the hot spots on the opposite side of the disk are located
in the gaps between those shown in the figure.
My research students and I
have recently developed a finite element description of
the TEI stability problem that predicts the sliding speed at
the onset of instability and the corresponding eigenmode
for practical brake or clutch designs (i.e. the number
and location of hot spots). A
windows-based software package
for estimating the susceptibility of
brake and clutch systems to TEI is available for
purchase from the University of Michigan. For more
information, including sample input and output and
a demonstration that can be downloaded,
The mathematical aspects of thermoelastic contact problems are of considerable
interest and challenge. Contact mechanics is conventionally
defined by the Signorini inequalities precluding tensile
contact tractions and interpenetration of material, but
combination of these boundary conditions with simple
thermal conditions leads to an ill-posed, coupled thermoelastic
problem which exhibits counter examples to both existence and uniqueness
of the steady state. Existence problems can be resolved by
using more sophisticated boundary conditions - for example,
recognizing that the inevitable roughness of the surfaces
will impose a thermal contact resistance that depends upon
contact pressure. The quasi-fractal properties of typical
rough surfaces contributes additional interest to such formulations
and there remain many important unanswered questions about
the effect of fine scale surface statistics on thermal, mechanical and electrical contact. Interaction between thermoelastic
deformation and a pressure dependent thermal contact resistance
can be unstable, leading to non-uniform contact pressure.
The figure on the right shows a section cut from an interrupted
continuous casting process. The sinusoidal perturbation in
the solidification boundary was caused by thermoelastic
instability associated with the mould/casting contact interface.
The classical Coulomb friction law (also governed by instabilities)
introduces additional existence, uniqueness and stability problems.
Frictional vibrations have long been known to occur in many physical
systems, but traditional explanations have depended on the friction
coefficient being a function of sliding speed. Recent work shows
that instabilities (including `stick-slip' vibrations)
can arise with a constant coefficient of friction.
Solution of Elasticity Problems
I have developed Maple and Mathematica files for the solution of boundary-value problems in Elasticity in conjunction with my book `Elasticity'. To explore this resource, start by
clicking on either Programming in Maple or Programming in
Mathematica and then on to `Catalogue of Maple
files' or `Catalogue of Mathematica files'. If you have never used these methods to solve problems,
you will surprised how effective they are. You will however need
to have Mathematica or Maple installed on your computer system.
Software for determining the elastic fields at singular points
An analytical tool has been developed for determining the nature of the stress and displacement fields near a fairly general singular point in linear elasticity. For more information, click here.
Some Recent Publications
Click here for a full list of publications.
- J.R.Barber, Elasticity, Springer, Dordrecht 3rd edn. (2010), 534pp.
Intermediate Mechanics of Materials, Springer, Dordrecht, 2nd edn. (2011), 618pp.
- J.R.Barber and M.Ciavarella, Contact Mechanics, in Research Trends in Solid Mechanics, ( ed. G.Dvorak),
International Journal of Solids and Structures, Vol.37 (2000), pp.29-43.
- M.Ciavarella, G.Demelio, J.R.Barber and Yong Hoon Jang,
Linear elastic contact of the Weierstrass profile, Proceedings of the Royal Society (London), Vol. A 456 (2000), pp. 387-405.
- Yun-Bo Yi, J.R.Barber and P.Zagrodzki, Eigenvalue Solution of Thermoelastic Instability Problems using Fourier Reduction, Proceedings of the Royal Society (London),
Vol. A 456 (2000), pp. 2799-2821.
- Yun-Bo Yi, J.R.Barber and D.L.Hartsock, Thermoelastic
instabilities in automotive disc Brakes - Finite element
analysis and experimental verification, Proc. 3rd Contact
Mechanics International Symposium, Peniche, Portugal, June 2001.
- J.R.Barber, Bounds on the electrical resistance between contacting elastic rough bodies, Proceedings of the Royal Society (London),
Vol. A 459 (2003), pp. 53-66.
- J.R.Barber, Three-dimensional elasticity problems for the prismatic bar Proceedings of the Royal Society (London), Vol.462 (2006), pp.1877--1896.
- J.R.Barber and T.C.T.Ting, Three-dimensional solutions for general anisotropy, Journal of the Mechanics and Physics of Solids, Vol.55 (2007), pp. 1993--2006.
- A.Klarbring, M.Ciavarella and J.R.Barber, Shakedown in elastic contact problems with Coulomb friction, International Journal of Solids and Structures, Vol.44 (2007), pp.8355--8365.
- Jon Kadish, J.R.Barber, P.D.Washabaugh and D.J.Scheeres, Stresses in accreted planetary bodies, International Journal of Solids and Structures, Vol.45 (2008), pp.540--550.
- Jon Kadish, Esteban Rougier, Ante Munjiza and J.R.Barber, Granular temperature as an energy dissipation mechanism in bodies of the Solar System, Proceedings of the Royal Society (London), Vol.463 (2007), pp.2485--2493.
- J.R.Barber, A.Klarbring and M.Ciavarella, Shakedown in frictional contact problems for the continuum, Comptes Rendus Mecanique , Vol.336 (2008), pp.34--41.
- Donghee Lee, N.Triantafyllidis, J.R.Barber and M.D.Thouless, Surface instability of an elastic half space with material properties varying with depth, Journal of the Mechanics and Physics of Solids, Vol.56 (2008), pp.858--868.
- M.Ciavarella and J.R.Barber, Influence of longitudinal creepage and wheel inertia on short pitch corrugation: A resonance-free mechanism to explain the roaring rails pheonomenon, Proceedings of the Institution of Mechanical Engineers, Part J, Journal of Engineering Tribology, Vol.222 (2008), pp.171--181.
- Young Ju Ahn, Enrico Bertocchi, J.R.Barber, Shakedown of coupled two-dimensional discrete frictional systems, Journal of the Mechanics and Physics of Solids, Vol.56 (2008), pp.3433--3440.
- J.R.Barber, M.Davies and D.A.Hills, Frictional elastic contact with periodic loading , International Journal of Solids and Structures, Vol.48 (2011), pp.2041--2047.
- C.Putignano, M.Ciavarella and J.R.Barber, Frictional energy dissipation in contact of nominally flat rough surfaces under harmonically varying loads , Journal of the Mechanics and Physics of Solids, Vol. 59 (2011), pp.2442-2454
- D.A.Hills, A.Thaitirarot, J.R.Barber, and D.Dini, Correlation of fretting fatigue experimental results using an asymptotic approach, International Journal of Fatigue, Vol. 43 (2012) pp. 62–75.
- A.Thaitirarot, R.Flicek, D.A.Hills, and J.R.Barber, The use of static reduction in the solution of two-dimensional frictional contact problems, Journal of Mechanical Engineering Science, Vol. 228 (2014), pp. 1474--1487.
- Yuwei Liu and J. R. Barber, Transient heat conduction between rough sliding surfaces, Tribology Letters, Vol. 55 (2014), pp. 23--33.
- Xiaosun Wang and J.R.Barber, Numerical algorithms for two-dimensional dynamic frictional problems, Tribology International, Vol. 80 (2014), pp. 141--146
- L-E. Andersson, J. R. Barber and A. R. S. Ponter, Existence and uniqueness of attractors in frictional systems with uncoupled tangential displacements and normal tractions, International Journal of Solids and Structures, Vol. 51 (2014), pp. 3710--3714.
- Jae Hyung Kim, Young Ju Ahn, Yong Hoon Jang and J. R. Barber, Contact problems involving beams, International Journal of Solids and Structures, Vol. 51 (2014), pp. 4435--4439.
- R. C. Flicek, D. A. Hills, J. R. Barber, and D. Dini, Determination of the shakedown limit for large, discrete frictional systems, European Journal of Mechanics A/Solids, Vol. 49 (2015), pp. 242--250.
- Zupan Hu, Wei Lu, M. D. Thouless and J. R. Barber, Simulation of wear evolution using fictitious thermal expansion, Tribology International, Vol. 82 (2015), pp. 191--194.
- A. Papangelo, M. Ciavarella and J.R.Barber, Fracture Mechanics implications for apparent static friction coefficient in contact problems involving slip-weakening laws, Proceedings of the Royal Society of London, Vol. A 471 (2015) Issue: 2180 Article Number: 20150271.
- R. Fleury, D. A. Hills and J. R. Barber, A corrective solution for finding the effects of edge-rounding on complete contact between elastically similar bodies. Part I: Contact law and normal contact considerations, International Journal of Solids and Structures, Vol. 85--86 (2016), pp. 89--96.
- R. Fleury, D. A. Hills and J. R. Barber, A corrective solution for finding the effects of edge-rounding on complete contact between elastically similar bodies. Part II: Near-edge asymptotes and the effect of shear, International Journal of Solids and Structures, Vol. 85--86 (2016), pp. 97--104.
- Yongwoo Lee, Yuwei Liu, J.R.Barber and Yong Hoon Jang, Thermal considerations during transient asperity contact, Tribology International, Vol. 94 (2016), pp. 87--91.
- Yongwoo Lee, Yuwei Liu, J.R.Barber and Yong Hoon Jang, Thermal boundary conditions in sliding contact problem, Tribology International, Vol. 103 (2016), pp. 69--72.
- J. R. Barber, Nominally static frictional contacts under periodic loading, Journal of Strain Analysis}, Vol. 51 (2016), pp. 270-278.
- Zupan Hu, Wei Lu, M. D. Thouless and J. R. Barber, Effect of plastic deformation on the evolution of wear and local stress fields in fretting, International Journal of Solids and Structures, Vol. 82 (2016), pp. 1--8.
- Xiaosun Wang and J. R. Barber, Numerical frictional algorithm with implementation of closed form analytical solutions, Computer Methods in Applied Mechanics and Engineering, Vol. 300 (2016), pp. 643--656.
- J. R. Ockendon and J. R. Barber, A model for thermoelastic contact oscillations, IMA Journal of Applied Mathematics, Vol. 81 (2016), pp. 679-687.