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Homogenization results for micro-contact elasticity problems.pdf
J. Math. Anal. Appl. 441 (2016) 462–474 Contents lists available at ScienceDirect
Journal of Mathematical Analysis and Applications
/locate/jmaa
Homogenization results for micro-contact elasticity problems
Anca Capatina a, Claudia Timofte b,?
a Institute of Mathematics of the Romanian Academy, P.O. Box 1-764, RO-70700 Bucharest, Romania b University of Bucharest, Faculty of Physics, Bucharest-Magurele, P.O. Box MG-11, Romania
article info
Article history: Received 5 December 2014 Available online 12 April 2016 Submitted by D.M. Ambrose
Keywords: Homogenization Frictional contact The periodic unfolding method
abstract
The asymptotic behavior of some elasticity problems, in a perforated domain, is analyzed. We address here the case of an -periodic perforated structure, with rigid inclusions of the same size as the period. The body occupying this domain is considered to be clamped along a part of its outer boundary and subjected to given tractions on the rest of the exterior boundary. Several nonlinear conditions on the boundary of the rigid inclusions are considered. The approach we follow is based on the periodic unfolding method, which allows us to deal with general materials.
? 2016 Elsevier Inc. All rights reserved.
1. Introduction
The behavior of heterogeneous materials, with inhomogeneities at a length scale which is much smaller than the characteristic dimensions of the system, is of huge interest in the theory of composite materials. The homogenization theory was successfully applied for modeling the behavior of such materials, leading to appropriate macroscopic continuum models, obtained by averaging the rapid oscillations of the material properties. Besides, such e?ective models have the advantage of avoiding extensive numerical computations arising when dealing with the small scale behavior of the system.
This paper deals with the derivation of macroscopic models for some elasticity problems in periodically perforated domains with rigid inclusions of the sa
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