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

We consider a two‐dimensional transmission problem of linear elasticity with voids in a fixed domain Ω−$$ {\Omega}_{-} $$ coated by a curved thin layer Ω+δ$$ {\Omega}_{+}^{\delta } $$. Our aim is to model the effect of the thin layer Ω+δ$$ {\Omega}_{+}^{\delta } $$ on the fixed domain Ω−$$ {\Omega}_{-} $$ 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 Ω−$$ {\Omega}_{-} $$, and we prove an error estimate for the approximate impedance problem. [ABSTRACT FROM AUTHOR]