Asymptotic Derivation of Effective Boundary Conditions for Thin Poroelastic Slabs

Abstract

This work is devoted to the asymptotic derivation of effective boundary conditions for a thin poroelas tic strip in the framework of linear elasticity with voids. We consider a three-dimensional transmission problem coupling a thick elastic body with voids and a thin bonded layer. Using asymptotic expansion techniques, we construct an approximate impedance operator that replaces the thin layer. Rigorous er ror estimates are established, showing that the error between the solution of the transmission problem and the solution of the approximate impedance problem is of order O(δ 2 ) in the H1 -norm.