A COUPLED MULTI–FIELD DYNAMIC MODEL FOR ANISOTROPIC POROUS MATERIALS

A fully coupled multi–field model for the dynamic simulation of anisotropic porous materials is here presented. Starting from the mixture theory and the definition of the effective stress for anisotropic poro-elasticity, the multi-field formulation of the dynamic partial differential equations was developed. Numerical solution of the initial-boundary value coupled problem in space was obtained by using the well-known Finite Element Method (FEM) with inf-sup stable discretizations, while the standard θ-Method was adopted in time. The multi-field discrete problem is addressed in a fully-implicit way. The Bi-Conjugate Gradient Stabilized (Bi-CGStab) algorithm was used to solve the time-sequence of large sparse non-symmetric linear systems, with the convergence accelerated by an ad-hoc Multi-Physics Reduction (MPR) preconditioning technique. Such enhancements have been implemented in the three-dimensional finite element research code, GeoMatFEM, and a series of dynamic analyses has been performed, in order to test the potential and computational efficiency of the developed numerical tool.