Cracks in osmoelastic porous media : fluid flow and crack
growth alternate
Citation for published version (APA):
Kraaijeveld, F., Huyghe, J. M. R. J., Remmers, J. J. C., Borst, de, R., Ito, K., & Baaijens, F. P. T. (2008). Cracks in osmoelastic porous media : fluid flow and crack growth alternate. 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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Orthopaedic Biomechanics
Cracks in osmoelastic porous media.
Fluid flow and crack growth alternate.
F. Kraaijeveld, J.M. Huyghe, J.J.C. Remmers,
R. de Borst, K. Ito, F.P.T. Baaijens
/department of biomedical engineering
Introduction
During life, 60-80% of the population suffer anytime from low back pain. Low back pain is closely associated with Interverte-bral Disc (IVD) (Fig. 1a) degeneration and herniation (Fig. 1b). Degeneration is characterized by decreasing osmotic prestress in the disc as well as crack development. To prevent these patholo-gies, we investigate under which conditions a fracture propagates in the disc.
a. b.
Fig. 1 a. Schematics of IVD position. b. A herniated IVD.
Research hypotheses
• The osmotic prestressing of the disc is a determinant of crack propagation
• The fluid diffusion affects crack propagation in a saturated porous medium
Methods
Model
Crack growth is taken into account by a cohesive zone model, i.e. model for micro-damage ahead of the crack tip (Fig. 2a). Cracks are introduced by applying Partition of Unity Method (PU-FEM) to Lanir’s biphasic theory. Mass balance accounts for fluid flow across the crack. Implementation was verified for shear loading.
a. b.
Fig. 2 a. Fictitious crack is modeled by a cohesive zone. b.Compression test for shear failure.
Example
As an example a compression test is considered (Fig. 2b). The initial crack length is 0.3 mm. The piston is displaced (du) with constant velocity (v = 0.15e-3 mm/s). Different states of osmotic prestress is studied.
Results
Effect prestress
a. b. c.
Fig. 3Distribution chemical potential after same loading (dt = 15.3 s, du = 0.0230 mm). Sample is prestressed
in a. both directions b. x only c. y only
The model is able to capture mesh-independent crack growth. Crack growth depends on the prestress (Fig. 3). Higher pre-stress in x-direction deflects the crack more.
Growth and flow
0 0.005 0.01 0.015 0.02 0.025 0.03 0 -2e-4 -4e-4 displacement [mm] normal flow dx = 0.28 mm 0 -2e-4 -4e-4 dx = 0.48 mm 0 0.5 1 1.5 position tip [mm] crack length cohesive zone
Fig. 4Left: Flow over the crack versus displacement of the piston at two points: before initial crack (dx = 0.28) and after
(dx = 0.48). Right: Crack and cohesive zone growth.
The crack grows stepwise. Each growth step covers several el-ements and is mesh-independent. Crack growth causes sudden local increase of fluid flow and this is also felt along the crack. As the fluid stabilizes, stress increases and the crack grows.
Conclusion
• Crack propagation, osmotic prestress and fluid flow are strongly coupled.
• Crack grows by a length ∆x is followed by a fluid diffusion over at time ∆t satisfying
