The Hertz contact problem in couple-stress elasticity

The classical three-dimensional Hertz contact problem is re-examined in the present work within the context of couple-stress elasticity. This theory introduces characteristic material length scales that emerge from the underlying microstructure and has proved to be very effective yet rather simple f...

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Bibliographic Details
Published in:International journal of solids and structures 2019-08, Vol.168, p.228-237
Main Authors: Gourgiotis, P.A., Zisis, Th, Giannakopoulos, A.E., Georgiadis, H.G.
Format: Article
Language:English
Subjects:
Cosserat elasticity
Microstructure
Polymers
Size-effects
Spherical indentation
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Summary:The classical three-dimensional Hertz contact problem is re-examined in the present work within the context of couple-stress elasticity. This theory introduces characteristic material length scales that emerge from the underlying microstructure and has proved to be very effective yet rather simple for modeling complex microstructured materials. An exact solution of the axisymmetric contact problem is obtained through Hankel integral transforms and singular integral equations. The goal is to examine to what extend this gradient theory captures the experimentally observed indentation response and the related size effects in materials with microstructure. Furthermore, the present work extends the classical Hertz contact solution in the framework of a generalized continuum theory providing thus a useful theoretical background for the interpretation of spherical indentation tests of microstructured materials. The results obtained in the present work can be used in order to model nano/micro indentation experiments of several materials, such as polymers, ceramics, composites, cellular materials, foams, masonry, and bone tissues, of which their macroscopic response is influenced by the microstructural characteristic lengths.
ISSN:0020-7683
1879-2146
DOI:10.1016/j.ijsolstr.2019.03.032