No dofs for poroelastic materials ! How to avoid the discretisation of porous thin layers
Résumé
The modelling of porous layers, especially when the solid part is elastic or when the material is excited mechanically, remains challenging. Indeed, the Biot theory needs to be considered and its Finite-Element discretisation leads to at least 4 degrees of freedom by node (u,P formulation). In this work, we will present strategies to avoid this discretisation. We will focus this presentation on problem in which the porous layer is in between two structures modelled by the Finite- Element Method. Structure is a generic term. It can correspond to elastic structures or fluid cavity. The porous domain is then linking two boundaries, one for each structure. The common idea between these strategies is to express the boundary operators of the Finite-Element operators as function of the physical dofs of the models. Surface terms are then added to the weak form. Their discretisation implies additional terms in the global matrices of the two FE domains. Several strategies are considered: Empirical laws, Transfer Matrix Method, Wave expansion method. The results show that for thin layers this method can capture most of the physical effects due to the porous material.