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On delaminated thin Timoshenko inclusions inside elastic bodies
Author(s) -
Itou H.,
Khludnev A. M.
Publication year - 2014
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.3279
Subject(s) - differential inclusion , mathematics , nonlinear system , mathematical analysis , anisotropy , rigidity (electromagnetism) , timoshenko beam theory , boundary value problem , inertia , limit (mathematics) , delamination (geology) , classical mechanics , beam (structure) , physics , materials science , composite material , geology , paleontology , subduction , quantum mechanics , optics , tectonics
In the paper, we consider equilibrium problems for 2D elastic bodies with thin inclusions modeled in the frame of Timoshenko beam theory. It is assumed that a delamination of the inclusion takes place thus providing a presence of cracks between the inclusion and the elastic body. Nonlinear boundary conditions at the crack faces are imposed to prevent a mutual penetration between the faces. Different problem formulations are analyzed: variational and differential. Dependence on physical parameters characterizing the mechanical properties of the inclusion is investigated. The paper provides a rigorous asymptotic analysis of the model with respect to such parameters. It is proved that in the limit cases corresponding to infinite and zero rigidity, we obtain rigid inclusions and cracks with the non‐penetration conditions, respectively. Also anisotropic inclusions with parameters are analyzed when parameters tend to zero and infinity. In particular, in the limit, we obtain the so called semi‐rigid inclusions. Copyright © 2014 John Wiley & Sons, Ltd.