Non-standard contact conditions in generalized continua: microblock contact model for a Cosserat body

Maciej Lewandowski-Szewczyk; S. Stupkiewicz

doi:10.1016/j.ijsolstr.2020.07.001

Non-standard contact conditions in generalized continua: microblock contact model for a Cosserat body

Abstract

Generalized continuum theories involve non-standard boundary conditions that are associated with the additional kinematic variables introduced in those theories, e.g., higher gradients of the displacement field or additional kinematic degrees of freedom. Accordingly, formulation of a contact problem for such a continuum necessarily requires that adequate contact conditions are formulated for the additional kinematic variables and/or for the respective generalized tractions. In this paper, we address several related open problems, namely, how to enhance the classic contact conditions to include the effects of the additional kinematic variables, how to link the enhanced contact model to the underlying microstructure of the solid, and how to do it in a consistent manner. As a first step towards a new class of contact models for generalized continua, a microblock contact model is derived for a Cosserat solid based on simple micromechanical considerations. To illustrate the non-trivial effects introduced by the non-standard boundary conditions, the problem of compression of an infinite strip with nonaligned microblocks is considered, and the analytical solution is derived for the corresponding boundary layers. A Hertz-like contact problem is also solved numerically with the focus on non-standard features of the solution and on the related size effects.

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Authors (2)

Maciej Lewandowski-Szewczyk dr inż.
S. Stupkiewicz

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Keywords

MICROSTRUCTURE CONTACT PROBLEMS SIZE EFFECTS BOUNDARY LAYERS COSSERAT CONTINUUM

Details

Category:: Articles
Type:: artykuły w czasopismach
Published in:: INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES no. 202, pages 881 - 894,
ISSN: 0020-7683
Language:: English
Publication year:: 2020
Bibliographic description:: Lewandowski-Szewczyk M., Stupkiewicz S.: Non-standard contact conditions in generalized continua: microblock contact model for a Cosserat body// INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES -Vol. 202, (2020), s.881-894
DOI:: Digital Object Identifier (open in new tab) 10.1016/j.ijsolstr.2020.07.001
Verified by:: Gdańsk University of Technology