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
3104 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, Linear elasto-statics, in Continuum Mechanics, Jose Merodio and Giuseppe Saccomandi eds., in Encyclopedia of Life Support Systems (EOLSS), Developed under the Auspices of the UNESCO, Eolss Publishers, Oxford ,UK (2008), [http://www.eolss.net ]
- Yong Hoon Jang, J.R.Barber and S.Jack Hu, Electrical conductance between dissimilar materials with temperature-dependent properties, Journal of Physics D Applied Physics, Vol 31 (1998), pp. 3197-3205.
- Hanbum Cho and J.R.Barber, Stability of the three-dimensional Coulomb friction law, Proceedings of the Royal Society (London), Vol. A 455 (1999), pp. 839-861.
- 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.
- M.Ciavarella, A.Baldini, J.R.Barber and A.Strozzi, Reduced dependence on loading parameters in almost conforming contacts, International Journal of Mechanical Sciences, Vol. 48 (2006), pp. 917--925.
- 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.
- J.R.Barber, M.Ciavarella, L.Afferrante and A.Sackfield, Effect of small harmonic oscillations during the steady rolling of a cylinder on a plane, International Journal of Mechanical Sciences, Vol.50 (2008), pp.1344-1353.
- 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.
- Donghee Lee, J.R.Barber and M.D.Thouless, Indentation of an elastic half space with material properties varying with depth, International Journal of Engineering Science, Vol.47 (2009), pp.1274--1283.
- Yong Hoon Jang and J.R.Barber, Multiscale analysis of moving clusters of microcontacts, International Journal of Heat and Mass Transfer, Vol.53 (2010), pp.3817-3822.
- Yong Hoon Jang and J.R.Barber, Frictional energy dissipation in materials containing cracks, Journal of the Mechanics and Physics of Solids, Vol. 59 (2011), pp.583--594.
- Yong Hoon Jang and J.R.Barber, Effect of phase on the frictional dissipation in systems subjected to harmonically varying loads, European Journal of Mechanics A/Solids, Vol.30 (2011), pp.269--274.
- 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.
- M.Paggi and J.R.Barber, Contact conductance of rough surfaces composed of modified RMD patches, International Journal of Heat and Mass Transfer, Vol.54 (2011), pp.4664--4672.
- D.A.Hills, M.Davies and J.R.Barber, An incremental formulation for half-plane contact problems subject to varying normal load, shear and tension , Journal of Strain Analysis, Vol.46 (2011), pp.436-443.
- J.R.Barber, Frictional systems subjected to oscillating loads, Annals of Solid and Structural Mechanics, Vol.2 (2011), pp.45--55.
- 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
- M.Davies, J.R.Barber and D.A Hills, Energy dissipation in a frictional incomplete contact with varying normal load , International Journal of Mechanical Sciences, Vol.55 (2012), pp.13-21, DOI: 10.1016/j.ijmecsci.2011.11.006.
- A.Al-Shabibi and J.R.Barber, Finite element implementation of the eigenfunction series solution for transient heat conduction problems with low Biot number, Journal of Mechanical Engineering Science, Vol.226 (2012), pp.1579--1588, DOI: 10.1177/0954406211423615.
- J.A.Greenwood and J.R.Barber, Indentation of an elastic layer by a rigid cylinder, International Journal of Solids and Structures, Vol.49 (2012), pp.2962--2977. DOI:10.1016/j.ijsolstr.2012.05.036
- 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.
- J.R.Barber, Incremental stiffness and electrical contact conductance in the contact of rough finite bodies, Physical Review E, Vol. 87 (2013), Art. 013203.
- J.R.Barber, Multiscale surfaces and Amontons' law of friction, Tribology Letters, Vol. 49 (2013), pp.539--543.
- L-E.Andersson, J.R.Barber and Y-J Ahn, Attractors in frictional systems subjected to periodic loads, SIAM Journal of Applied Mathematics, Vol.73 (2013), pp.1097--1116.
- J.R.Barber, Similarity considerations in adhesive contact problems, Tribology International, Vol.67 (2013), pp.51--53.
- Yuwei Liu, Yong Hoon Jang and J. R. Barber, Finite element implementation of an eigenfunction solution for the contact pressure variation due to wear, Wear, Vol. 309 (2014), pp. 134--138. http://dx.doi.org/10.1016/j.wear.2013.11.004
- J. R. Barber and M.Ciavarella, JKR solution for an anisotropic half space, Journal of the Mechanics and Physics of Solids, Vol. 64 (2014), pp.367--376.
- 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.
- 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.