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.
| Identifer | oai:union.ndltd.org:DRESDEN/oai:qucosa:de:qucosa:19117 |
| Date | 24 April 2009 |
| Creators | Görke, Uwe-Jens, Kaiser, Sonja, Bucher, Anke, Kreißig, Reiner |
| Publisher | Technische Universität Chemnitz |
| Source Sets | Hochschulschriftenserver (HSSS) der SLUB Dresden |
| Language | German |
| Detected Language | English |
| Type | doc-type:preprint, info:eu-repo/semantics/preprint, doc-type:Text |
| Source | Chemnitz Scientific Computing Preprints, 09-02 |
| Rights | info:eu-repo/semantics/openAccess |
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