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

• Published in: International journal of solids and structures Vol. 202; pp. 881 - 894
• Main Authors: Lewandowski-Szewczyk, M.J., Stupkiewicz, S.
• Format: Journal Article
• Language: English
• Published: New York Elsevier Ltd 01.10.2020; Elsevier BV
• Subjects: Boundary conditions; Boundary layers; Contact problems; Cosserat continuum; Exact solutions; Kinematics; Microstructure; Size effects; Size effects; Contact problems; Cosserat continuum; Microstructure; Boundary layers
• ISSN: 0020-7683; 1879-2146
• DOI: 10.1016/j.ijsolstr.2020.07.001

•Enhanced contact model with non-standard contact conditions for a Cosserat continuum.•Contact occurs through rigid microblocks that rotate according to the Cosserat kinematics.•Consistent coupling of displacements and microrotations at the contact interface.•Analytical solution for the boundary layers induced by the non-standard contact conditions.•New qualitative features and size effects observed in a 2D Hertz-like contact problem. 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.