Impedance operator of a curved thin layer in linear elasticity with voids

Abstract

We consider a two‐dimensional transmission problem of linear elasticity with voids in a fixed domain coated by a curved thin layer . Our aim is to model the effect of the thin layer on the fixed domain by an impedance boundary condition. For that, we use the techniques of asymptotic expansion to approximate the transmission problem by an impedance problem set in the fixed domain , and we prove an error estimate for the approximate impedance problem.