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

affect crack penetration into osteons or deflection into cement lines [3].
Finite element methods have been successfully used to perform analysis of crack growth
in bone. Nevertheless, FEM may present some shortages especially in crack analysis
e.g. time consuming remeshing process in such problems. In recent time, new classes of
methods known as the meshless methods have been developed to solve fracturemechanics
problems without requiring elements. As a result, the objective of this
research is to probe the effects of bone micro-architecture on microcrack growth path
using Element-Free Galerkin Cohesive Fracture Method in LS-DYNA.
3. MATERIALS AND METHODS
A meshless model of micro-architectural cortical bone under tension was created and
Element-Free Cohesive simulations were run to assess the effect of microstructure and
bone mechanical characteristics upon the microcrack propagation paths.
Given the similarities between microstructure of osteonal cortical bone and fiberreinforced
composite material, in the following models osteon is considered as fibers
since it is approximately circular; interstitial bone is considered a matrix as it fills the
gaps between the osteons. Each osteon is surrounded by a thin layer - cement line - and
contains a canal (Fig. 1a). Figure 1b illustrates the dimensions of the entire meshless
model with details. In this study, the interstitial bone and osteons were assumed
homogeneous and isotropic elastic materials – see table 1.
Cement line
(a)
Interstitial bone
Haversian canal
Osteon
(b)
Fig. 1. (a) Cross section of osteonal bovine cortical bone tissue [9], (b) schematic of the meshless
micro-structural model; The dimensions of the entire model: 1 × 1 × 0.03 [mm 3 ], the osteon
diameter[10]: 100 [µm], the Haversian canal diameter[10]: 30 [µm], the width of the cement line[7]:
1 [µm], and crack lengths: 200-400 [µm].
As mentioned earlier, in order to analyze the crack propagation in cortical bone, we
used EFG Cohesive Fracture analysis in this study. EFG cohesive fracture method is
developed by Belytschko and his group [13, 14] and is based on a strong discontinuity
approach to model the cracks and the crack initiation and propagation are governed by
cohesive law – energy release rate. In EFG method, a visibility method is implemented
to define the cracks in the solids and a fast transformation method [15] is applied to
handle the boundary conditions in the cracked media. In this method Crack propagates
cell-by-cell in current implementation.