A mixed hybrid mixture formulation for 2D porous media
Citation for published version (APA):
Pizzocolo, F., Huyghe, J. M. R. J., Ito, K., & Remmers, J. J. C. (2008). A mixed hybrid mixture formulation for 2D porous media. Poster session presented at Mate Poster Award 2008 : 13th Annual Poster Contest.
Document status and date: Published: 01/01/2008 Document Version:
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A mixed hybrid mixture formulation
for 2D porous media
F. Pizzocolo, J.M. Huyghe, K. Ito, J.J.C. Remmers
/ Department of Biomedical Engineering
Introduction
The intervertebral disc (Fig.1) is a ionised porous medium. As measurements in living humans are complex, finite element (FE) models have become an important tool to study load distribution in healthy and degenerated disc. A model with these features has been used to explore the biomedical implications of disc degeneration on its function and integrity [3]. In this code the local mass balance is only fulfilled globally. At crack tip the local flow is underestima-ted influencing the global behavior and structural integrity. A hybrid mixed formulation [4] should alleviate this problem.
Objective
Development of a mixed hybrid finite element (MHFE) formulation in 2D to study crack evolution in porous media as a result of shear loading.
Figure 1: Structure of the intervertebral disc
Method
To numerically simulate the interaction of the solid skeleton with the pore fluid, the media are modeled by Lanir’s biphasic theory [2]. A representative element volume around any mathematical point in the media is always assumed to contain the ionised solid phase and ionised fluid phase (Fig.2). For the simulation of strong discontinui-ties, the PU-FEM combined with cohesive zone approach [1] is used (Fig.3). The governing equations consist of equations for the bulk and for the discontinuity, dominated by mass balance, momentum balance and constitutive behavior.
Figure 3: Schematic representation of the cohesive surface approach to fracture
Figure 4: A mixed hybrid element takes the flow into account
Future work
First Partition of Unity formulation is integrated with Mixed Hybrid FE to deal with mode II of fracture mechanics. In later phases extending to mode I is considered as well as the development of a micro model of the crack tip.
This research is funded by MuST-STW program (POROMULT 10112).
References
1 J.J.C. Remmers, Comp. Mech., 31, 2003 2 Y. Lanir, Biorheology, 24, 1987
3 F. Kraaijeveld et al., Engng. Frac. Mech., accepted 4 K. Malakpoor, ESAIM, 41(4), 2007
Flows computed by MHFE are guaranteed to be continuous across the inter-element boundaries because normal flux fields are taken into account as degree of freedom inside the formulation (Fig.4).
