Publication Details

Category Text Publication
Reference Category Journals
DOI 10.1016/j.euromechsol.2011.09.009
Title (Primary) A consistent mixed finite element formulation for hydro-mechanical processes in saturated porous media at large strains based on a generalized material description
Author Görke, U.-J.; Kaiser, S.; Bucher, A.; Kreißig, R.
Source Titel European Journal of Mechanics - A/Solids
Year 2012
Department ENVINF
Volume 32
Issue March-April
Page From 88
Page To 102
Language englisch
Keywords Saturated porous media; Mixed finite element method; Large strains
Abstract

This paper presents the theoretical background of a phenomenological biphasic model at large strains based on a generalized material description of the theory of porous media, and its numerical realization within the context of a mixed finite element formulation. The study is aimed at the simulation of coupled hydro-mechanical (HM) problems with special focus on geo- and biomechanics. If, in the sense of an initial approximation, 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, the weak formulation of the balance equations of mass and linear momentum of the overall continuum are developed. Within this context, a generalized material approach is preferred assuming the initial configuration of the solid phase as reference configuration of the overall continuum. The transient problem results in a weak formulation with respect to the displacement and pore pressure fields as well as their time derivatives. Following, time discretization is performed using a generalized single step approach, and a linearization technique based on Taylor series representation is applied. After the usual 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. This algorithmic proceeding comprises some different conceptual aspects compared to the known literature, and is characterized by a consistent and comprehensive representation. The presented numerical model was implemented into a scientific in-house finite element code based on hierarchical structures, which support the straightforward use of an iterative solver with hierarchical preconditioning, local adaptive remeshing techniques, and parallelized programming features. The accuracy and the efficiency of the numerical algorithms are demonstrated on typical examples.Therewith, the importance of the consideration of large strains in a consistent and proper way is demonstrated as well as the differences compared to models based on small strains.

Persistent UFZ Identifier https://www.ufz.de/index.php?en=20939&ufzPublicationIdentifier=11606
Görke, U.-J., Kaiser, S., Bucher, A., Kreißig, R. (2012):
A consistent mixed finite element formulation for hydro-mechanical processes in saturated porous media at large strains based on a generalized material description
Eur. J. Mech. A-Solids 32 (March-April), 88 - 102 10.1016/j.euromechsol.2011.09.009