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

Unique strain patterns were observed in the explants specific surface curvature model
(Figure 5). Tissue deformation ranged from 0mm at the bottom of the cartilage to a
maximum of 0.185mm experienced at the central surface region, the site where initial
contact with the platen was at the beginning of loading. In addition to the depth wise
variation, deformation was also observed to vary in the transverse plane with the outer
region experiencing significantly less strain, approximately 0.03mm. Similarly,
maximum principal stress distribution in the explants specific surface curvature model
was found to vary in depth and transversely. The highest maximum principal stresses
were predicted at the immediate region adjacent to the point where initial contact with
the platen was established (Figure 5).
Figure 5 Contour plot of tissue deformation predicted for the explants specific surface curvature model:
red indicates maximum displacement of 1.85mm and black indicates the minimum 0mm (left) Contour
plot of maximum principal stress pattern predicted for the explant specific surface curvature model (right)
5. DISCUSSION
By comparing predictions for the flat and explants specific surface curvature models, it
was shown that the flat surface model, underestimated deformation at the point of initial
contact during maximum loading by 74.6% and the maximum principal stress by
87.3%. In the bulk material, it was also observed that the maximum principal stress is
generally underestimated by an order of magnitude of 10e -2 . Examination of the basic
mechanics equations show that this is to be expected, using
Equation 2
Where σ is stress, F is the force applied and A is the contact surface area. Force applied
in both models was the same. Contact surface area in the curved surface model is less
than that in the flat surface model. Therefore, stresses experience in the curved surface
models should be greater than those in the flat surface model. As the definition of
Young’s modulus for a linear elastic material is,
Equation 3
Where E is the Young’s modulus, σ stress and ε is strain. Young’s modulus was again
kept constant between the models. As a result of the deduction above, greater stress is
experienced in the curved surface model, it should therefore be expected that greater
strain should be experienced.
The explants specific surface curvature affected the stress and strain patterns
significantly. In the flat surface models, transversely uniform depth varying local strain
different to that of the bulk tissue strain was noted. This has been reported previously in
literature 12 . However, it must be noted that in the explants specific surface curvature