Derivation of a poroelastic elliptic membrane shell model

International audienceA derivation of the model for a poroelastic elliptic membrane shell is undertaken. The flow and deformation in a three-dimensional shell domain is described by the quasi-static Biot equations of linear poroelasticity. We consider the limit when the shell thickness goes to zero and look for the limit equations. Using the technique developed in the seminal articles by Ciarlet, Lods, Miara et al and the recent results on the rigorous derivation of the equations for poroelastic plates and flexural poroelastic shells by Marciniak-Czochra, Mikeli´cMikeli´c and Tambača, we present a rigorous derivation of the linear poroelastic elliptic membrane shell model. After rescaling, the corresponding velocity and the pressure field are close in the C([0, T ]; (H 1 x) 2 × (L 2 x) 2) norm and the stresses in C([0, T ]; (L 2 x) 9) norm. In the case of a spherical membrane shell we confirm the results by Taber from the literature