ARUP; ISBN: 978-0-9562121-5-3 - CMBBE 2012 - Cardiff University

(a)
(b)
Figure 2. Load-displacement curves (a) and NP pressure-displacement curves (b)
provided by the FE model with hexahedral (λ = 8) and tetrahedral mesh (λ = 2, 4, 6, 8).
models with a tetrahedral mesh provided different results to the hexahedral mesh.
However, a finer tetrahedral mesh reduced the errors by half, to maximum 12.6%. The
internal pressure of the NP was always underestimated by the model with a coarse mesh
(λ=2) for all loading cases (Figure 2.b). The prediction of internal pressure improved
with a finer tetrahedral mesh model (λ=4) with the exception of torsion.
5. DISCUSSION
In this study, an algorithm to compute the fibre direction in an arbitrarily aligned mesh
of the IVD was developed. Tetrahedral and hexahedral meshes of an IVD model were
tested with various loading cases to investigate the numerical outcome of the two types
of grid discretization. The numerical analyses showed that, depending on the load case,
the IVD has to be discretized with a fine enough mesh to provide a similar behaviour to
a reference hexahedral mesh when using a tetrahedral mesh. In particular, this aspect
was found to be critical when simulating torsion. Although we had expected to observe
a stiffer behaviour in the coarse tetrahedral mesh than in the hexahedral mesh, the
opposite was observed. The cause of such behaviour is suspected to be a repartitioning
of loads within the discretised model. Since one large tetrahedral element may radially
cover the entire AF area, the positions of the integration points are inadequate to
describe the intermediate layers accurately. However, such an outcome should be
verified when using alternative formulations of the constitutive equations i.e. [19, 1]
Further, to improve the accuracy of the fibre computation, the parameters ∆z, ∆y, and n
can be adjusted. However, if for instance ∆y, ∆z, are too small no nodes are detected; if
n is too high an inconsistent description of the geometry could be computed (i.e. a zigzag
line between the nodes). A check of the fibre distribution by plotting the fibre
directions, i.e. quiver3() in Matlab ® , should highlight anomalies. In summary, the
presented algorithm provides a possibility to model the IVD with arbitrary meshes
which will act as a useful tool to develop subject-specific IVD FE models.
Acknowledgements
Funding for this research project was provided by the European Union through a Marie
Curie action (FTP7-PITN-GA-2009-238690-SPINEFX)