Application of generalized complex modes to the calculation of the forced response of three-dimensional poroelastic materials

Finite element models based on Biotʹs {u,P} formulation for poroelastic materials are widely used to predict the behaviour of structures involving porous media. The numerical solution of such problems requires however important computational resources and the solution algorithms are not optimized. To improve the solution process, a modal approach based on an extension of the complex modes technique has been proposed recently and applied successfully to a simplified mono-dimensional problem. In this paper, this technique is investigated in the case of three-dimensional poroelastic problems. The technique is first recalled, then analytical proof of the stability of the model are given followed by considerations of numerical improvements of the method. An energetic interpretation of the generalized complex modes is then given and some numerical results are presented to illustrate the performance of the approach.