The effect of a thin inclusion of high rigidity in an elastic body

摘要

AbstractWe study an elastic body comprising an inclusion whose thickness is 2ϵ and for which Lamé's constants are λϵand μ. We are interested in the limit behaviour of the inclusion, when ϵ → 0 and μϵ→ ϵ; that is when the inclusion becomes thiner and more rigid. Different behaviours are possible, according to the rate at which μϵconverges to infinity; the limit inclusion may “vanish” if it is not very rigid, but also it may