Enhanced Biot's Finite Element Displacement Formulation for Porous Materials and Original Resolution Methods Based on Normal Modes

The use of finite element modeling for porous sound absorbing materials is often limited by the numerical cost of the resolution scheme. To overcome this limitation, an alternative finite element formulation for poroelastic materials modelled with the Biot-Allard theory is first presented. This formulation is based on the solid and total displacement fields of the porous medium. Three resolution methods (one semi-analytical and two numerical) based on normal modes are proposed secondly. These methods take benefit from the decoupling properties of normal modes. The semi-analytical method is associated with problems in which the shear wave can be neglected. The numerical methods are a direct and an iterative scheme. The direct method allows a reduction by 2 of the number of degrees without making any approximation. The iterative method provides an approximation corresponding to a controlled tolerance. The finite element formulation is validated by comparison with an analytical model in two mono-dimensional configurations corresponding to a single and a multilayered problem. The efficiency of the two numerical resolution methods is also illustrated in term of computation time in comparison with classical formulations, such as the mixed displacement-pressure formulation.