Ein Beitrag zur gemischten Finite-Elemente-Formulierung der Theorie gesättigter poröser Medien bei großen Verzerrungen

• Main Authors: Görke, Uwe-Jens, Kaiser, Sonja, Bucher, Anke, Kreißig, Reiner
• Language: German
• Published: Technische Universität Chemnitz 2009
• Subjects: info:eu-repo/classification/ddc/510; ddc:510; info:eu-repo/classification/ddc/620; ddc:620; Finite-Elemente-Methode; Poröser Stoff; Large Strains; Mixed formulation; Poroelasticity; Porous media
• Online Access: http://nbn-resolving.de/urn:nbn:de:bsz:ch1-200900691; https://monarch.qucosa.de/id/qucosa%3A19117; https://monarch.qucosa.de/api/qucosa%3A19117/attachment/ATT-0/; https://monarch.qucosa.de/api/qucosa%3A19117/attachment/ATT-1/

This paper presents the theoretical background of a phenomenological biphasic material approach at large strains based on the theory of porous media as well as its numerical realization within the context of an adaptive mixed finite element formulation. The study is aimed at the simulation of coupled multiphysics problems with special focus on biomechanics. As the materials of interest can be considered as a mixture of two immiscible components (solid and fluid phases), they can be modeled as saturated porous media. For the numerical treatment of according problems within a finite element approach, weak formulations of the balance equations of momentum and volume of the mixture are developed. Within this context, a generalized Lagrangean approach is preferred assuming the initial configuration of the solid phase as reference configuration of the mixture. The transient problem results in weak formulations with respect to the displacement and pore pressure fields as well as their time derivatives. Therefore special linearization techniques are applied, and after spatial discretization a global system for the incremental solution of the initial boundary value problem within the framework of a stable mixed U/p-c finite element approach is defined. The global system is solved using an iterative solver with hierarchical preconditioning. Adaptive mesh evolution is controlled by a residual a posteriori error estimator. The accuracy and the efficiency of the numerical algorithms are demonstrated on a typical example.