One Hundred Years of Hertz Contact

Hertz H. Uber die Berührung fester elastischer Körper. (On the contact of elastic solids). J. reine und angewandte Mathematik, 1882, 92, 156–171. (For English trans, see Misc. papers by H. Hertz, Jones and Schott, Macmillan, London, 1896).

Hertz H. Uber die Berührung fester elastische Körper und uber die Härte. (On the contact of rigid elastic solids and on hardness). Verhandlungen des Vereins zur Beförderung des Gewerbefleisses, Leipzig, Nov. 1882. (For English trans. see Misc. papers by H. Hertz, Jones and Schott, Macmillan, London, 1896).

Hertz Johanna Heinrich Hertz: memoirs, letters, diaries, 2nd edition (Mathilde Hertz and Charles Susskind) in English and German, San Francisco Press, Ca, 1977.

Fessler H. Ollerton E. Contact stresses in toroids under radial loads. Brit. J. App. Phys., 1957, 8, 387.

Persson A. On the stress distribution of cylindrical elastic bodies in contact. Doctoral dissertation, Chalmers Univ. of Tech., Gothenburg, 1964.

Goodman L. E. Keer L. M. The contact stress problem for an elastic sphere indenting an elastic cavity. Int. J. Solids & Structures, 1965, 1, 407.

Timoshenko S. P. Goodier J. N. Theory of elasticity, McGraw-Hill, 1951.

Huber M. T. Zur Theorie der Berührung fester elastische Körper, Ann. der Phys., 1904, 14, 153.

Huber M. T. Fuchs S. Spannungsverleitung bei der Berührung zweier elastische Zylinder. Phys. Zeitschr., 1914, 15, 298.

Thomas M. R. Hoersch V. A. Stresses due to the pressure of one elastic solid upon another. Univ. of Illinois Engineering Expt. Sta. Bull. No. 212, 1930.

Davies R. M. The determination of static and dynamic yield stress. Proc. R. Soc., 1949, A197, 416.

Tabor D. The hardness of metals, Clarendon, 1951.

Andrews H. I. The contact between a locomotive driving wheel and the rail. Wear, 1958–9, 2, 468.

Lundberg G. Odquist F. K. G. Proc. R. Swed. Inst. Engng. Res., 1932, No. 116.

Lundberg G. Sjövall H. Stress and deformation in elastic contacts. Chalmers Univ. of Tech., Gothenburg, 1958.

Lundberg G. Palmgren A. Dynamic capacity of rolling bearings. Acta Polytechnica, 1947, No. 7.

Nikpur K. Gohar R. Deflection of a roller compressed between platens. Tribology International, 1975, 8, 2.

Lundberg G. Elastiche Berührung zweir Helbraüme. Forsh. a. d. Geb. das Ing. wesen, 1939, 10, 201.

Kalker J. J. Surface displacement of an elastic half-space in a slender, bounded, curved surface region. J. Inst. Maths. Apples., 1977, 19, 127.

Dundurs J. Lee M-S. Stress concentration at a sharp edge in contact problems. J. of Elasticity, 1972, 2, 109.

Nayak L. Johnson K. L. Pressure between elastic bodies having a slender area of contact and arbitrary profiles. Int. J. Mech. Sci., 1979, 21, 237.

Johns P. M. Gohar R. Roller bearings under radial and eccentric loads. Tribology International, 1981, 14, 131.

Hartnett M. J. Kannel J. Contact stresses between elastic cylinders. Trans. ASME, J. Lub. Tech., 1981. 103, 40.

Paul B. Hashemi J. (a) Contact geometry associated with arbitrary rail and wheel profiles. Symp. on Rolling Contact, AMD-40, 93, ASME, New York, 1980.

Contact pressures on closely conforming elastic bodies. Symp. on Solid Contact and Lubrication, AMD-39. ASME, New York, 1980.

Kalker J. J. van Randen Y. A minimum principle for frictionless elastic contact with application to non-Hertzian half-space contact problems. J. Engng. Math., 1972, 6, 193.

Muskhelishvili N. I. Some basic problems in the mathematical theory of elasticity, English trans., edited by Radok Noordhoff , 1953.

McEwen E. Stresses in elastic cylinders in contact along a generatrix. Phil. Mag., 1949, 40, 454.

Poritsky H. Stresses and deflexions of cylindrical bodies in contact. Trans. ASME, J. Appl. Mech., 1950, 18, 191.

Smith J. O. Liu G. K. Stresses due to tangential and normal loads on an elastic solid. Trans. ASME, J. Appl. Mech., 1953, 21, 157.

Hamilton G. M. Goodman L. E. The stress field created by a circular sliding contact. Trans. ASME, J. Appl. Mech., 1966, 33, 371.

Bryant M. D. Keer L. M. Rough contact between elastically and geometrically similar curved bodies. Trans. ASME, J. Appl. Mech., 1982, 49, 345.

Sackfield A. Hills D. A. Some useful results in the classical Hertz contact problem. To be published in J. Strain Analysis..

Cattaneo C. Sul contatto di corpi elastici. Acad. dei Lincei, Rendiconti, Ser. 6, 1938, 27, 342–348, 434–436, 474–478.

Mindlin R. D. Compliance of elastic bodies in contact. Trans. ASME, J. Appl. Mech., 1949, 17, 259.

Mindlin R. D. Deresiewicz H. Elastic spheres under varying oblique forces. Trans. ASME, J. Appl. Mech., 1953, 21, 237.

Deresiewicz H. Oblique contact of non-spherical bodies. Trans. ASME, J. Appl. Mech., 1951, 25, 623.

Deresiewicz H. Mechanics of granular materials. Progress in Appl. Mech., 1958, 5, 233.

Goodman L. E. A review of progress in analysis of interfacial slip damping. Proc. ASME Coll. on Structural Damping, Edited by Ruzicka J. E. Pergamon, 1960.

Johnson K. L. O'Connor J. J. The mechanics of fretting. Proc. Instn. Mech. Engrs., App. Mech. Convention, Newcastle, 1964.

Johnson K. L. Energy dissipation at spherical surfaces in contact transmitting oscillating forces. J. Mech. Engng. Sci., 1961, 3, 362.

Carter F. W. On the action of a locomotive driving wheel. Proc. R. Soc. A, 1926, 112, 151.

Kalker J. J. On the rolling contact of two elastic bodies in contact. Doctoral Dissertation, Tech. Univ. Delft, 1967.

Kalker J. J. A survey of wheel-rail rolling contact theory, Vehicle System Dynamics, 1979, 5, 317.

Wickens A. H. Gilchrist A. O. Railway vehicle dynamics—the emergence of a practical theory, CEI MacRobert Award Lecture, 1977.

Spence D. A. The Hertz contact problem with finite friction. J. of Elasticity, 1975, 5, 297.

Johnson K. L. O'Connor J. J. Woodward A. C. The effect of indenter elasticity on the Hertzian fracture of brittle materials. Proc. R. Soc. A, 1973, 334, 95.

Reynolds O. On rolling friction. Phil. Trans. R. Soc., 1875, 166, 155.

Bentall R. H. Johnson K. L. Slip in the rolling contact of dissimilar rollers. Int. J. Mech. Sci., 1967, 9, 389.

Hunter S. C. Energy absorbed by elastic waves during impact. J. Mech. Phys. Solids, 1956–7, 5, 162.

Maw N. Barber J. R. Fawcett J. N. The oblique impact of elastic spheres. Wear, 1976, 38, 101.

Maw N Barber J. R. Fawcett J. N. The role of elastic tangential compliance in oblique impact. Trans. ASME, J. Lub. Tech., 1981, 103, 74.

Greenwood J. A. Williamson J. B. P. The contact of nominally flat surfaces. Proc. R. Soc. A, 1966, 295, 300.

Greenwood J. A. Tripp J. H. The elastic contact of rough spheres. Trans. ASME, J. Appl. Mech., 1967, 35, 153.

Johnson K. L. Non-Hertzian contact of elastic spheres. In The mechanics of the contact between deformable bodies, Edited by de Pater Kalker , Delft Univ. Press, 1975.

Johnson K. L. Kendall K. Roberts A. D. Surface energy and the contact of elastic solids. Proc. R. Soc. A, 1971, 324, 301.

Gladwell G. M. L. Contact problems in the classical theory of elasticity, Sijthoff and Noordhoff, 1980.

Pinnock P. K. Ward I. M. Wolfe J. M. The compression of anisotropic fibre filaments. Proc. R. Soc. A, 1966, 291, 267.

Willis J. R. Hertzian contact of anisotropic bodies. J. Mech. Phys. Solids, 1966, 14, 163.

Gibson R. E. Some results concerning displacements and stresses in a non-homogeneous elastic half-space. Z.A.M.P., 1967, 17, 58 and 1969, 19, 160.

Fredriksson B. On elastostatic contact problems with friction. Doctoral dissertation No. 6, Univ. of Linköping, 1976.

Dundurs J. Properties of elastic bodies in contact. In Mechanics of contact between deformable bodies, edited by de Pater Kalker , Delft Univ. Press, 1975.

Barber J. R. Thermoelastic contact problems. In Mechanics of contact between deformable bodies, edited by de Pater Kalker , Delft Univ. Press, 1975.

Dowson D. Higginson G. R. Whitaker A. V. Stress distribution in lubricated rolling contacts. Proc. Instn. Mech. Engrs., Symp. on Rolling Contact Fatigue, London, 1963.

Johnson K. L. Inelastic contact, plastic flow and shakedown. Proc. Int. Symp. on Contact Mech. and Wear of Wheel/rail Systems, Waterloo Univ. Press, 1982.