### METHOD OF DIMENSIONALITY REDUCTION IN CONTACT MECHANICS AND FRICTION: A USER'S HANDBOOK. II. POWER-LAW GRADED MATERIALS

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Popov, V.L. and Hess, M., 2015, Method of dimensionality reduction in contact mechanics and friction. Berlin Heidelberg: Springer-Verlag

Popov, V.L. and Hess, M., 2014, Method of dimensionality reduction in contact mechanics and friction: a users handbook. I. Axially-symmetric contacts, Facta Universitatis, Series: Mechanical Engineering, 12(1), pp. 1-14.

Argatov, I., Hess, M., Pohrt, R., Popov, V.L., 2016, The extension of the method of dimensionality reduction to non‐compact and non‐axisymmetric contacts. ZAMM‐Journal of Applied Mathematics and Mechanics, 96(10), pp. 1144–1155, doi:10.1002/zamm.201600057

Booker, J.R., Balaam, N.P., Davis, E.H., 1985, The behaviour of an elastic non‐homogeneous half‐space. Part I–line and point loads, International Journal for Numerical and Analytical Methods in Geomechanics, 9(4), pp. 353-367.

Booker, J.R., Balaam, N.P., Davis, E.H., 1985, The behaviour of an elastic non‐homogeneous half‐space. Part II–circular and strip footings, International journal for numerical and analytical methods in geomechanics, 9(4), pp. 369-381.

Giannakopoulos, A. E., Suresh, S., 1997, Indentation of solids with gradients in elastic properties: Part II, Axisymmetric indentors, International Journal of Solids and Structures, 34(19), pp. 2393-2428.

Chen, S., Yan, C., Zhang, P., Gao, H, 2009, Mechanics of adhesive contact on a power-law graded elastic half-space, Journal of the Mechanics and Physics of Solids, 57(9), pp. 1437-1448.

Jin, F., Guo, X. and Zhang, W., 2013, A unified treatment of axisymmetric adhesive contact on a power-law graded elastic half-space, Journal of Applied Mechanics, 80(6), p. 061024.

Hess, M., 2016, Normal, tangential and adhesive contacts between power-law graded materials, Presentation at the Workshop on Tribology and Contact Mechanics in Biological and Medical Applications, TU-Berlin, 14.-17. Nov. 2016

Hess, M., Popov, V.L., 2016, Die Renaissance der Winklerschen Bettung in der Kontaktmechanik und Reibungsphysik – Eine Anwendung auf Kontaktprobleme funktioneller Gradientenwerkstoffe, Conference Paper, Tribologie-Fachtagung, 04, pp. 1-11

Ciavarella M., 1998, Tangential Loading of General Three-Dimensional Contacts. Journal of Applied Mechanics, 65, pp. 998-1003.

Jaeger, J., 1995, Axi-symmetric bodies of equal material in contact under torsion or shift, Archive of Applied Mechanics, 65, pp. 478-487.

Popov, V.L., 2014, Method of dimensionality reduction in contact mechanics and tribology. Heterogeneous media, Physical Mesomechanics, 17(1), pp. 50-57.

Hess, M., 2016, A simple but precise method for solving axisymmetric contact problems involving elas-tically graded materials, arXiv preprint arXiv:1602.04720.

Hess, M., 2016, A simple method for solving adhesive and non-adhesive axisymmetric contact problems of elastically graded materials, International Journal of Engineering Science, 104, pp. 20-33.

Holl, D.L., 1940, Stress transmission in earths, Highway Research Board Proceedings, 20, pp. 709-721.

Cattaneo, C., 1938, Sul contatto di due corpi elastici: distribuzione locale degli sforzi, Rendiconti dell'Accademia nazionale dei Lincei, 27, pp. 342-348, 434-436, 474-478.

Mindlin, R.D., 1949, Compliance of elastic bodies in contact, Journal of Applied Mechanics, 16(3), pp. 259–268.

Popov, V.L., 2014, Analytic solution for the limiting shape of profiles due to fretting wear, Sci. Rep., 4, 3749.

Li, Q., 2016, Limiting profile of axisymmetric indenter due to the initially displaced dual-motion fret-ting wear, Facta Universitatis, Series: Mechanical Engineering, 14(1), pp. 55-61.

Lyashenko, I.A., Willert, E., Popov, V.L., 2016, Adhesive impact of an elastic sphere with an elastic half space: Numerical analysis based on the method of dimensionality reduction, Mechanics of Materi-als, 92, pp. 155-163.

Willert, E., Popov, V.L., 2016, Impact of an elastic sphere with an elastic half space with a constant co-efficient of friction: Numerical analysis based on the method of dimensionality reduction, ZAMM‐Journal of Applied Mathematics and Mechanics, 96(9), pp. 1089–1095, DOI: 10.1002/zamm.201400309

Argatov, I., Li, Q., Pohrt, R., Popov, V.L., 2016, Johnson–Kendall–Roberts adhesive contact for a to-roidal indenter, Proc. R. Soc: A, 472(2919): 20160218

DOI: https://doi.org/10.22190/FUME1603251H

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