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Some basic contact problems in couple stress elasticity

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journal contribution
posted on 03.08.2017, 09:07 by T. Zisis, P.A. Gourgiotis, Konstantinos Baxevanakis, H.G. Georgiadis
Indentation tests have long been a standard method for material characterization due to the fact that they provide an easy, inexpensive, non-destructive and objective method of evaluating basic properties from small volumes of materials. As the contact scales in such experiments reduce progressively (micro to nano-scales) the internal material lengths become important and their effect upon the macroscopic response cannot be ignored. In the present study, we derive general solutions for three basic two-dimensional (2D) plane-strain contact problems within the framework of the generalized continuum theory of couple-stress elasticity. This theory introduces characteristic material lengths in order to describe the pertinent scale effects that emerge from the underlying microstructure and has proved to be very effective for modeling microstructured materials. By using this theory, we initially study the problem of the indentation of a deformable elastic half-plane by a flat punch, then by a cylindrical indentor, and finally by a shallow wedge indentor. Our approach is based on singular integral equations which have resulted from a treatment of the mixed boundary value problems via integral transforms and generalized functions. The results show significant departure from the predictions of classical elasticity revealing that it is inadequate to analyze indentation problems in microstructured materials employing only classical contact mechanics.


Panos A. Gourgiotis gratefully acknowledges support from the European Union FP7 project “Modeling and optimal design of ceramic structures with defects and imperfect interfaces” under contract number PIAP-GA-2011-286110.



  • Mechanical, Electrical and Manufacturing Engineering

Published in

International Journal of Solids and Structures






2084 - 2095


ZISIS, T. ... et al., 2014. Some basic contact problems in couple stress elasticity. International Journal of Solids and Structures, 51 (11-12), pp. 2084 - 2095


© Elsevier Ltd.


AM (Accepted Manuscript)

Publisher statement

This work is made available according to the conditions of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) licence. Full details of this licence are available at: https://creativecommons.org/licenses/by-nc-nd/4.0/

Publication date



This article was published in the International Journal of Solids and Structures [© Elsevier Ltd.] and the definitive version is available at: https://doi.org/10.1016/j.ijsolstr.2014.02.016