[Portrait] J.R.Barber
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

Campus Address:
3440 GG Brown / 2125

Office Phone: (734) 936-0406

FAX: (734) 615-6647

Brief Biography

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 University of Newcastle upon Tyne, U.K. I moved to the University of Michigan, Department 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 three 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, and co-editor of the Springer book series Solid Mechanics and its Applications.

Current Research

clutch plate after a single engagement 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 Thermoelastic Instability (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, click here.

sinusoidal perturbations in continuous casting 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.

Selected Publications

Click here for a full list of publications.

Ph.D. Graduates