Micro-scale modelling of bovine cortical bone fracture: Analysis of crack propagation and microstructure using X-FEM

Abstract

• This is the author's version of a work that was accepted for publication in Computational Materials Science.Changes resulting from the publishing process, such as peer review, editing, corrections, structural for- Micro-scale modelling of bovine cortical bone fracture: Analysis of crack propagation and microstructure using X-FEM Adel A. Abdel-Wahab, Angelo R. Maligno, and Vadim V. SilberschmidtWolfson School of Mechanical and Manufacturing Engineering, Loughborough University, Loughborough, Leicestershire, LE11 3TU, UK Abstract Bone fracture susceptibility increased by factors such as bone loss, microstructure changes, and material properties variations. Therefore, investigation of the microstructure and material properties effect on the crack propagation and the global response at macro-scale level is of great importance. A non-uniform distribution of osteons in a cortical bone tissue results in a localization of deformation processes. Such localization can affect bone performance under external load and initiate fracture or assist its propagation. Once the fracture initiates, that distribution can play an important role on the crack propagation process at micro-scale level. Subsequently, the global response at macro-scale level could also be affected. In this study, a two-dimensional numerical (finite-element) fracture model for osteonal bovine cortical bone was developed with account for its microstructure using X-FEM. The topology of a transverse-radial cross section of a bovine cortical bone was captured with optical microscopy. The mechanical properties for the microstructural features of the cross-section were obtained with a use of the nanoindentation technique. Both the topology and nanoindentation data were used as input to the model formulated with the Abaqus 6.10 finite-element software. The area, directly reflecting micro-scale information, was embedded into the region with homogenised properties of the cortical bone. The simulations provide the macro-scale global response, crack propagation paths and the distribution of maximum principal stress fields at the micro-scale level for three different microscopic topologies; homogeneous, two phase composite model and threr phase composite model under tensile loading condition. The calculated stress fields for various cases of topologies demonstrate different patterns due to implementation of microstructural features in the finite-element model. There is an important role of the microstructure on the crack propagation trajectory. The suggested approach emphasizes the importance of microstructural features, especially cement lines, in development of bone failure.

Bone‐Inspired Materials by Design: Toughness Amplification Observed Using 3D Printing and Testing

“…[38,43] We should point out that in our materials we did not replicate the same osteon/matrix stiffness ratio found in cortical bone, but we chose highly contrasting material properties to clearly see the effect of the geometry and stiffness ratio. We chose the size of the osteons to include, in future works, the cement line.…”

“…They are surrounded by the interstitial matrix, made of interstitial lamellae. Owing to their geometry and to different properties than the matrix (i.e., the osteon-matrix stiffness ratio is about 0.64), [38] they create stress delocalization, reducing the local stresses at the crack tip and resulting in crack shielding. Also, the osteon outer boundaries, called cement lines, are dense of microcracks, allowing for additional energy dissipation.…”

Effect of micromorphology of cortical bone tissue on crack propagation under dynamic loading

“…It employs a locally enriched element area to handle a numerical singularity associated with crack opening thus eliminating a need for remeshing. The authors [8,9] employed X-FEM to study the function of cement lines in bone fracture. Budyn et al [12] developed a multiple scale statistical X-FEM simulation method to evaluate crack propagation of cortical bone under uniaxial tension.…”

Modelling of bone fracture and strength at different length scales: a review

“…Several computational studies have investigated the role of osteons and cement lines in the crack propagation path and fracture toughness in bone [74,[166][167][168][169][170][171]. For example, Raeisi Najafi et al [74] studied the crack growth trajectory in cortical bone using an FEM model.…”

“…The extended finite-element method (XFEM) has also been used to study the crack growth path in a Haversian cortical bone [166][167][168][169][179][180][181][182]. Using XFEM, Budyn and co-workers performed extensive studies on cortical bone and investigated the effects of different parameters such as morphology, porosity, ageing and osteoporosis on stress and strain distributions, failure, and fracture of bone [167,168,[179][180][181][182][183][184].…”