Infinite elements in a poroelastodynamic FEM

Abstract

Wave propagation phenomena in unbounded domains occur in many engineering applications, e.g., soil structure interactions. When simulating unbounded domains, infinite elements are a possible choice to describe the far field behavior, whereas the near field is described through conventional finite elements. Finite element formulations for porous materials in terms of Biot's theory [1] have been published, e.g., by Zienkiewicz [2]. For infinite elements, several approaches are described in [3,4]. Infinite elements are based on special shape functions to approximate the semi-infinite geometry as well as the Sommerfeld radiation condition, i.e., the waves decay with distance and are not reflected at infinity. If there is only one wave traveling in the media, a formulation in time-domain can be established. But in poroelastodynamics, there are three body waves and eventually also a Rayleigh wave. Unfortunately, the extension to more than one wave is not straight forward. Here, an infinite element is presented which can handle all wave types, as it is needed in poroelasticity.