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

MESHLESS MODELING OF MICROCRACK GROWTH IN CORTICAL BONE
1. ABSTRACT
H. Hemmatian 1 , H.R. Katouzian 2
A meshless model of micro-architectural cortical bone under tension is presented and
Element-Free Galerkin Cohesive simulations are run to assess the effect of
microstructure and bone mechanical characteristics upon the microcrack propagation
paths. The results indicate that the crack trajectory is influenced by the strength and
fracture toughness of the cement line relative to the bone matrix and crack length.
2. INTRODUCTION
Bone fracture process is closely related to several factors, such as reduction of bone
mineral density, bone micro-architecture, variation in the mechanical properties of the
bone tissue, and microcarck aggregations [1]. At the microstructural level, cortical bone
is composed of distinct phases such as a fiber-reinforced composite material comprising
osteons represented by fibers, interstitial bone as the matrix, weak interface between
osteon and interstitial matrix – so called cement line – ,and bone porosity that is
primarily due to Haversian canals [1]. Micro-architecture of cortical bone has an
important effect upon its fracture resistance. The crack propagation path in cortical bone
is influenced by its microstructure such as osteons and cement lines [2]. If the
microcrack enters the osteon and tries to split it, complete failure of the bone may
happen. Whereas deviation of microcracks into the cement lines leads to slowdown of
crack growth and an increase in bone robustness [3, 4].
Although various experimental and theoretical inquiries have been developed to
investigate the effect of micro-structural components on fracture behavior of a cortical
bone, the factors influencing the crack growth trajectory in cortical bone have not yet
been entirely understood. For instance, a multi-scale X-FEM model of osteonal cortical
bone tissue was developed by Budyn and Hoc [5] to investigate multiple crack growth
in cortical bone under tension. In another essay, Najafi et al., used the LEFM theory and
FEM for the analysis and modeling of the osteonal cortical bone tissue to evaluate the
interaction between osteons and microcracks [6]. In addition, Adel A.Abdel-Wahab et
al. employed a 2D micro-structural model for probing the effect of cement lines on
fracture scenarios and the global macroscopic mechanical behavior using extended
finite element method [7]. Since the cohesive crack model takes into account the
physical processes occurring in the vicinity of the crack tip, it is appropriate to examine
the effect of microdamage on bone fracture. Mischinski and Ural expanded the
application of cohesive finite element modeling to elucidate possible mechanisms that
1
Msc student, Biomedical Engineering Department, Amirkabir University of Technology, Tehran, Iran;
E-mail address: Hemmatian@aut.ac.ir
2
Associate Professor, Biomedical Engineering Department, Amirkabir University of Technology, Tehran,
Iran; E-mail address: Katouzian@engineer.com