Adrian Kraft, Roman Pohrt

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We investigate the tangential contact problem of a spherical indenter at constant normal force. When the indenter is subjected to tangential movement, frictional shear stresses arise at the interface and do not vanish when it is moved backwards. We study the evolution of shear stress when the indenter is moved back and forth at falling amplitude. The method of dimensionality reduction (MDR) is employed for obtaining the distribution of stick and slip zones as well as external forces and the final stress distribution. We find that the shear stress decreases. For the special case of linearly falling amplitude of the movement, we observe uniform peaks in the shear stress. The absolute value of the shear stress peaks is reduced best for a high number of back-and-forth-movements with slowly decreasing amplitude.


Coulomb Friction, Residual Stress, Contact Mechanics, Stick, Slip

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Hertz, H., 1881, Über die Berührung fester elastischer Körper, Journal für die reine und angewandte Mathematik , 92, pp. 156-171.

Popov, V.L., Heß, M., 2015, Method of Dimensionality Reduction in Contact Mechanics and Friction, Springer.

Mindlin, R., Mason, W., Osmer, J., Deresiewicz, H., 1952, Effects of an oscillating tangential force on the contact surfaces of elastic spheres, Proc. 1st. US Nat'l. Congr. Appl. Mech. ASME New York, pp. 203-208.

Borri-Brunetto, M., Carpinteri, A., Invernizzi, S. & Paggi, M., 2005, Micro-slip of rough surfaces under cyclic tangential loading, Proceedings of the 4th Contact Mechanics International Symposium, pp. 333-340.

Ciavarella, M., 2013, Frictional energy dissipation in Hertzian contact under biaxial tangential harmonically varying loads, J Strain Analysis, 49(1), pp. 27-32.

E. Madelung, 1905, Über Magnetisierung durch schnell verlaufende Ströme und die Wirkungsweise des Rutherford-Marconischen Magnetdetektors, Ann. Phys. , 322(10), pp. 861-890.

Pohrt, R., Li, Q., 2014, Complete boundary element formulation for normal and tangential contact problems, Physical Mesomechanics, 17/4, pp. 334-340.

Popov, V. L., 2014, Analytic solution for the limiting shape of profiles due to fretting wear, Scientific reports, 4, doi:10.1038/srep03749

Aleshin, V., Abeele, K. V. D., 2012, Hertz–Mindlin problem for arbitrary oblique 2D loading: General solution by memory diagrams, Journal of the Mechanics and Physics of Solids, 60/1, pp. 14-36.

Aleshin, V., Abeele, K. V. D., 2009, Preisach analysis of the Hertz–Mindlin system, Journal of the Mechanics and Physics of Solids, 57, pp. 657-672.

Popov, V., Gray, J., 2012, Prandtl-Tomlinson model: History and applications in friction, plasticity, and nanotechnologies, Z. Angew. Math. Mech., 92/9, pp. 683-708.

Prandtl, L., 1928, Ein Gedankenmodell zur kinetischen Theorie der festen Körper, Z. Angew. Math. Mech., 8, pp. 85-106.



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ISSN: 0354-2025 (Print)

ISSN: 2335-0164 (Online)

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