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The effect of a thin inclusion of high rigidity in an elastic body
Author(s) -
Caillerie D.,
Nedelec J. C.
Publication year - 1980
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.1670020302
Subject(s) - inclusion (mineral) , mathematics , rigidity (electromagnetism) , infinity , limit (mathematics) , mathematical analysis , composite material , physics , thermodynamics , materials science
We study an elastic body comprising an inclusion whose thickness is 2ϵ and for which Lamé's constants are λ ϵ and μ. We are interested in the limit behaviour of the inclusion, when ϵ → 0 and μ ϵ → ϵ; that is when the inclusion becomes thiner and more rigid. Different behaviours are possible, according to the rate at which μ ϵ converges to infinity; the limit inclusion may “vanish” if it is not very rigid, but also it may be entirely solid.