Fracture process in cortical bone: X-FEM analysis of microstructured models
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ORIGINAL PAPER
Fracture process in cortical bone: X-FEM analysis of microstructured models Simin Li · Adel Abdel-Wahab · Emrah Demirci · Vadim V. Silberschmidt
Received: 3 November 2012 / Accepted: 28 January 2013 © Springer Science+Business Media Dordrecht 2013
Abstract Bones tissues are heterogeneous materials that consist of various microstructural features at different length scales. The fracture process in cortical bone is affected significantly by the microstructural constituents and their heterogeneous distribution. Understanding mechanics of bone fracture is necessary for reduction and prevention of risks related to bone fracture. The aim of this study is to develop a finite-element approach to evaluate the fracture process in cortical bone at micro-scale. In this study, three microstructural models with various random distributions based on statistical realizations were constructed using the global model’s framework together with a submodelling technique to investigate the effect of microstructural features on macroscopic fracture toughness and microscopic crack-propagation behaviour. Analysis of processes of crack initiation and propagation utilized the extended finite-element method using energy-based cohesive-segment scheme. The S. Li · A. Abdel-Wahab · E. Demirci · V. V. Silberschmidt (B) Wolfson School of Mechanical and Manufacturing Engineering, Loughborough University, Loughborough, Leicestershire LE11 3TU, UK e-mail: [email protected] A. Abdel-Wahab e-mail: [email protected] E. Demirci e-mail: [email protected] S. Li e-mail: [email protected]
obtained results were compared with our experimental data and observations and demonstrated good agreement. Additionally, the microstructured cortical bone models adequately captured various damage and toughening mechanisms observed in experiments. The studies of crack length and fracture propagation elucidated the effect of microstructural constituents and their mechanical properties on the microscopic fracture propagation process. Keywords X-FEM · Microstructured model · Crack propagation · Fracture toughening mechanisms
1 Introduction Fracture of cortical bone can significantly affect structural integrity of a load-bearing skeletal system, and, consequently, cause injuries, mobility loss and reduced life quality. As a naturally formed composite material, a cortical bone tissue is formed by heterogeneously distributed microstructural constituents that could be categorised into several hierarchical organizations from nano-scale to macro-scale levels (Currey 2011; Ritchie et al. 2005). At the nano-scale, bone is composed of mineralized collagen fiber matrix and extrafibrillar mineral particles known as carbonated hydroxyapatite (Currey 1999; Fratzl et al. 2004). At the micro-scale, cortical bone is laid down in layers of lamellar structure (3–7 µ m in thickness) that is similar to that of plywood composite—parallel with each other within layer, but
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having a staggered arrangement between the adjacent layers (Asce
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