Mathematik-Gebäude, Raum M614

The problem of dynamic wave propagation in infinite porous media half-spaces is encountered in many scientific and engineering applications, especially in geomechanics and earthquake engineering. The modeling of such phenomena comprises two major steps: First, the mathematical description of the multiphasic porous continuum which leads to a system of coupled partial differential equations (PDE), and second, the implementation and solution of initial-boundary-value problems (IBVP) using some proper numerical method. The current investigation aims at modeling heterogeneous, saturated porous materials within a continuum-mechanical framework. This is accomplished by exploiting the well-established macroscopic Theory of Porous Media (TPM) together with thermodynamically consistent constitutive equations. Proceeding from a geometrically linear treatment and under the assumption of isothermal conditions and intrinsically incompressible solid and fluid constituents, the behavior of the considered biphasic solid-fluid aggregate is governed by a multi-field system of strongly coupled PDE. In particular, these are the solid and fluid momentum balances and the overall volume balance (continuity-like constraint), which can be conveniently treated numerically following an implicit monolithic strategy. To this end, the infinite domain is first discretized in space using robust mixed finite elements (FE) for the near field surrounding the source of vibration and mixed quasi-static infinite elements (IE) at the boundaries representing the far field, i.e., the extension of the domain into infinity. Then, an appropriate monolithic implicit Runge-Kutta time-stepping scheme is applied to the semi-discrete equations. To overcome apparent wave reflections at the unbounded domain boundaries, special damping boundary terms are introduced adopting the idea of the viscous damping boundary (VDB) method. In this connection, an unconditionally stable implementation of the VDB approach is presented, where the damping terms are integrated implicitly at the boundary and added to the problem residuum in a weakly imposed sense. The underlying algorithms and procedures are tested on canonical wave propagation examples using the scientific FE package PANDAS (www.get-pandas.com).

PD Dr.-Ing. Bernd Markert

Universität Stuttgart