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

Therefore, in order to examine the effect of microstructure of bone on the microcrack
growth trajectory in transverse direction, various models were created and the effects of
the fracture toughness and strength of the cement line and crack length were evaluated.
The models were first created, and a background mesh of 4-noded tetrahedron cells was
generated. We used just the nodes of these elements for representing the meshless
models (Fig. 1b), the problem domains and their boundaries, and then we discarded the
elements. So that, the background mesh of cells was used for integration of the system
matrices. A displacement loading was applied at the bottom edge of each model and an
initial edged microcrack was introduced into the models with orientation perpendicular
to the loading direction, as shown in figure 1b. Then EFG Cohesive Fracture Method in
LS-DYNA was implemented for fracture analysis. In current study, the extension of the
crack was assumed to be of mode I – It is a current limitation of the method formulation
in LS-DYNA. The interfaces between sub-domains of the models were perfect bounded.
4. RESULTS AND DISCUSSION
The first analysis focused on the role of cement lines in crack propagation behavior of
cortical bone. For this purpose two different mesh-less models – Model A (absence of
cement line) and Model B (presence of cement line) – were developed. In this case, the
initial crack length was 303.8 [µm]. The interstitial bone and osteon have cohesive
properties in common with each other and the cohesive properties of cement line were
assumed some one third of cortical bone’s cohesive properties. After modeling and
analysis with EFG cohesive fracture method in Ls-Dyna, the following were observed:
In model A, the microcrack entered the osteon directly. In contrast, the crack deflected
into the cement line and continued to grow within the cement line in model B (Fig. 3).
(a) (b)
Fig. 3. Simulation results of (a) osteon penetration in absence of the cement line and (b) crack
deflection in presence of the cement line.
Consistent with these observations, the cement line’s weak interface tends to deviate or
stop microcrack propagation and thereby increases bone toughness. These results are, of
course, dependent on cohesive fracture properties of cement line. The deviation is due
to low fracture toughness and strength of cement line with respect to the interstitial bone
and osteon. Meanwhile, the micro-architecture of Haversian cortical bone with changing
the distribution of stress, in its turn, influences the microcrack propagation trajectories.