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Title: Some basic contact problems in couple stress elasticity
Authors: Zisis, T.
Gourgiotis, P.A.
Baxevanakis, Konstantinos P.
Georgiadis, H.G.
Keywords: Contact
Indentation
Microstructure
Micromechanics
Couple-stress elasticity
Singular integral equations
Issue Date: 2014
Publisher: © Elsevier Ltd.
Citation: 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
Abstract: 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.
Description: 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
Sponsor: 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.
Version: Accepted for publication
DOI: 10.1016/j.ijsolstr.2014.02.016
URI: https://dspace.lboro.ac.uk/2134/25950
Publisher Link: http://dx.doi.org/10.1016/j.ijsolstr.2014.02.016
ISSN: 0020-7683
Appears in Collections:Published Articles (Mechanical, Electrical and Manufacturing Engineering)

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