An equivalent solid (u) formulation for poroelastic materials

Abstract

Finite element formulations based on Biot’s poroelasticity equations have been used extensively throughout recent years. The most common are Biot’s displacement (u_,U_) and mixed displacement-pressure (u_,p) formulations. They are used to predict the structural and acoustical behavior of poroelastic mediums within multilayered structures. These models, while accurate, lead to the resolution of large linear systems: they need, respectively, six and four degrees of freedom per node in order to efficiently describe the poroelastic medium’s vibroacoustic behavior in 3-D problems. In this paper, a simplified displacement (u_) formulation is presented. It is also based on Biot’s equations, but requires only three degrees of freedom per node, related to the solid phase displacement field, to describe the behavior of poroelastic mediums in 3-D problems. The development of the governing (u_) equations for the equivalent solid poroelastic formulation is detailed. The limitations of this approach are also discussed. Numerical and experimental validations are presented in order to show the accuracy and effectiveness of the formulation within its prescribed field of application.