Experimental and numerical analysis of deformation and fracture of cortical bone tissue

Bones are the principal structural components of a skeleton; they provide the body with unique roles, such as its shape maintenance, protection of internal organs and transmission of muscle forces among body segments. Their structural integrity is vital for the quality of life. Unfortunately, bones can only sustain loads until a certain limit, beyond which it fails. Usually, the reasons for bone fracture are traumatic falls, sports injuries, and engagement in transport or industrial accidents. The stresses imposed on a bone in such activities can be far higher than those produced during normal daily activities and lead to fracture. Understanding deformation and fracture behaviours of bone is necessary for prevention and diagnosis of traumas. Even though, in principle, studying bone’s deformation and fracture behaviour is of immense benefit, it is not possible to engage volunteers in in-vivo investigations. Therefore, by developing adequate numerical models to predict and describe its deformation and fracture behaviours, a detailed study of reasons for, and ways to prevent or treat bone fracture could be implemented. Those models cannot be formulated without a set of experimental material data. To date, a full set of bone’s material data is not implemented in the material data-base of commercial finiteelement (FE) software. Additionally, no complete set of data for the same bone can be found in the literature. Hence, a set of cortical bone’s material data was experimentally measured, and then introduced into the finite-element software. A programme of experiments was conducted to characterise mechanical properties of the cortical bone tissue and to gain a basic understanding of the spatial variability of those properties and their link to the underlying microstructure. So, several types of experiments were performed in order to quantify mechanical properties of the studied bone tissue at macro- and microscales under quasi-static and dynamic loading regimes for different cortex positions called anterior, posterior, medial and lateral. Those experiments included: (1) uniaxial tension and creep tests to obtain its elastic, plastic and viscoelastic properties; (2) nanoindentation tests to characterise its microstructural elastic-plastic properties; (3) Izod tests to investigate its fracture properties under impact bending loading; (4) tensile-impact tests to characterise its impact strength and fracture force when exposed to a longitudinal loading regime. All the experiments were performed for different cortex positions and different directions (along the bone axis and perpendicular to it) when possible. Based on the results of those experiments, a number of finite-element models were developed in order to analyse its deformation and fracture using the extended finiteelement method (X-FEM) at different length scales and under various loading conditions. Those models included: (1) two-dimensional (2D) FE models to simulate its fracture and deformation at microscale level under quasi-static tensile loading. Additionally, the effect of the underlying microstructure on crack propagation paths was investigated; (2) 2D and three-dimensional (3D) FE models to simulate its fracture and deformation at macroscale level for the Izod impact test setup. In addition, the applicability of different constitutive material models was examined; (3) 3D FE models to simulate its fracture and deformation at macroscale level for tensile-impact loading conditions. The developed models provided high-quality results, and most importantly, they adequately reflected the experimental data. The main outcome of this thesis is a comprehensive experimental analysis and numerical simulations of the deformation and fracture of the cortical bone tissue at different length scales in response to quasi-static and dynamic loading. Recommendations on further research developments are also suggested

Plastic behaviour of microstructural constituents of cortical bone tissue: a nanoindentation study

A mechanical behaviour of bone tissues is defined by mechanical properties of its microstructural constituents. Also, those properties are important as an input for finiteelement models of cortical bone to simulate its deformation and fracture behaviours at the microstructural level. The aim of this study was to investigate a post-yield behaviour of osteonal cortical bone’s microstructural constituents at different loading rates, maximum load levels and dwell times; nanoindentation with a spherical-diamond-tip indenter was employed to determine it. The nanoindentation results revealed significant difference in stiffness values of cortical bone’s microstructural features − interstitial matrix and osteons. Similarly, interstitial matrix exhibited a stiffer post-yield behaviour compared to that of osteons that reflects the relationship between the post-yield behaviour and collagen maturity. In addition, both osteons and interstitial matrix demonstrated a time-dependent behaviour. However, in order to assess elastic-plastic behaviour accurately, an effect of viscosity on nanoindentation results was reduced by using a time-delay method

Dynamic properties of cortical bone tissue: impact tests and numerical study

Bone is the principal structural component of a skeleton: it assists the load-bearing framework of a living body. Structural integrity of this component is important; understanding of its mechanical behaviour up to failure is necessary for prevention and diagnostic of trauma. Bone fractures occur in both low-energy trauma, such as falls and sports injury, and high-energy trauma, such as car crash and cycling accidents. By developing adequate numerical models to predict and describe the deformation and fracture behaviour up to fracture of a cortical bone tissue, a detailed study of reasons for, and ways to prevent or treatment methods of, bone fracture could be implemented. This study deals with both experimental analysis and numerical simulations of this tissue and its response to impact dynamic loading. Two areas are covered: Izod tests for quantifying a bone’s behaviour under impact loading, and a 3D finite-element model simulating these tests. In the first part, properties of cortical bone tissue were investigated under impact loading condition. In the second part, a 3D numerical model for the Izod test was developed using the Abaqus/Explicit finite-element software. Bone has time-dependent properties – viscoelastic – that were assigned to the specimen to simulate the short term event, impact. The developed numerical model was capable of capturing the behaviour of the hammer-specimen interaction correctly. A good agreement between the experimental and numerical data was found

Numerical modelling of impact fracture of cortical bone tissue using X-FEM

A cortical bone tissue is susceptible to fracture that can be caused by events, such as traumatic falls, sports injuries and traffic accidents. A proper treatment of bones and prevention of their fracture can be supported by in-depth understanding of deformation and fracture behaviour of this tissue in such dynamic events. Parameters such as damage initiation under impact, damage progression and impact strength can help to achieve this goal. In this paper, Extended Finite-Element Method (X-FEM) implemented into the commercial finite-element software Abaqus is used to simulate the actual crack initiation and growth in a cantilever beam of cortical bone exposed to quasi-static and impact loading using the Izod loading scheme. Izod tests were performed on notched bone specimens of bovine femur to measure its impact strength and to validate simulations. The simulation results show a good agreement with the experimental data

Temperature-dependent mechanical behaviour of PMMA: Experimental analysis and modelling

© 2016 Elsevier LtdAn experimental study of temperature-dependent mechanical behaviour of Poly-methyl methacrylate (PMMA) was performed at a range of temperatures (20 °C, 40 °C, 60 °C and 80 °C) below its glass transition point (108 °C) under uniaxial tension and three-point bending loading conditions. This study was accompanied by simulations aimed at identification of material parameters for two different constitutive material models. Experimental flow curves obtained for PMMA were used in elasto-plastic analysis, while a sim-flow optimization tool was employed for a two-layer viscoplasticity model. The temperature increase significantly affected mechanical behaviour of PMMA, with quasi-brittle fracture at room temperature and super-plastic behaviour (ε>110%) at 80 °C. The two-layer viscoplasticity material model was found to agree better with the experimental data obtained for uniaxial tension than the elasto-plastic description

Effects of material, coating, design and plaque composition on stent deployment inside a stenotic artery-finite element simulation

Finite-element simulations have been carried out to study the effects of material choice, drug eluting coating and cell design on the mechanical behaviour of stents during deployment inside a stenotic artery. Metallic stents made of materials with lower yield stress and weaker strain hardening tend to experience higher deformation and stronger dogboning and recoiling, but less residual stresses. Drug eluting coatings have limited effect on stent expansion, recoiling, dogboning and residual stresses. Stent expansion is mainly controlled by the radial stiffness of the stent which is closely associated with the stent design. In particular, open-cell design tends to have easier expansion and higher recoiling than closed-cell design. Dogboning is stronger for slotted tube design and open-cell sinusoidal design, but reduced significantly for designs strengthened with longitudinal connective struts. After deployment, the maximum von Mises stress appears to locate at the U-bends of stent cell struts, with varying magnitude that depends on the materials and severity of plastic deformation. For the artery–plaque system, the stresses, especially in the plaque which is in direct contact with the stent, appear to be distinctly different for different stent designs and materials in terms of both distribution and magnitude. The plaque composition also strongly affects the expansion behaviour of the stent–artery system and modifies the stresses on the plaque

Analysis of fracture processes in cortical bone tissue

Bones are the principal structural components of a skeleton; they play unique roles in the body providing its shape maintenance, protection of internal organs and transmission of forces. Ultimately, their structural integrity is vital for the quality of life. Unfortunately, bones can only sustain loads until a certain limit, beyond which they fail. Understanding a fracture behaviour of bone is necessary for prevention and diagnosis of trauma; this can be achieved by studying mechanical properties of bone, such as its fracture toughness. Generally, most of bone fractures occur in long bones consisting mostly of cortical bone tissue. Therefore, in this paper, an experimental study and numerical simulations of fracture processes in a bovine femoral cortical bone tissue were considered. A set of experiments was conducted to characterise fracture toughness of the bone tissue in order to gain basic understanding of spatial variability and anisotropy of its resistance to fracture and its link to an underlying microstructure. The data was obtained using single-edge-notch-bending specimens of cortical bone tested in a three-point bending setup; fracture surfaces of specimens were studied using scanning electron microscopy. Based on the results of those experiments, a number of finite-element models were developed in order to analyse its deformation and fracture using the extended finite-element method (X-FEM). Experimental results of this study demonstrate both variability and anisotropy of fracture toughness of the cortical bone tissue; the developed models adequately reflected the experimental data

Analysis of anisotropic viscoelastoplastic properties of cortical bone tissues

Bone fractures affect the health of many people and have a significant social and economic effect. Often, bones fracture due to impacts, sudden falls or trauma. In order to numerically model the fracture of a cortical bone tissue caused by an impact it is important to know parameters characterising its viscoelastoplastic behaviour. These parameters should be measured for various orientations in a bone tissue to assess bone’s anisotropy linked to its microstructure. So, the first part of this study was focused on quantification of elastic–plastic behaviour of cortical bone using specimens cut along different directions with regard to the bone axis—longitudinal (axial) and transverse. Due to pronounced non-linearity of the elastic–plastic behaviour of the tissue, cyclic loading–unloading uniaxial tension tests were performed to obtain the magnitudes of elastic moduli not only from the initial loading part of the cycle but also from its unloading part. Additional tests were performed with different deformation rates to study the bone’s strain-rate sensitivity. The second part of this study covered creep and relaxation properties of cortical bone for two directions and four different anatomical positions–anterior, posterior, medial and lateral–to study the variability of bone’s properties. Since viscoelastoplasticity of cortical bone affects its damping properties due to energy dissipation, the Dynamic Mechanical Analysis (DMA) technique was used in the last part of our study to obtain magnitudes of storage and loss moduli for various frequencies. Based on analysis of elastic–plastic behaviour of the bovine cortical bone tissue, it was found that magnitudes of the longitudinal Young’s modulus for four cortical positions were in the range of 15–24 GPa, while the transversal modulus was lower — between 10 and 15 GPa. Axial strength for various anatomical positions was also higher than transversal strength with significant differences in magnitudes for those positions. Quantitative data obtained in creep and relaxation tests exhibited no significant position-specific differences. DMA results demonstrated relatively low energy-loss capability due to viscosity of bovine cortical bone that has a loss factor in the range of 0.035–0.1

Variability and anisotropy of fracture toughness of cortical bone tissue

Bones form protective and load-bearing framework of the body. Therefore, their structural integrity is vital for the quality of life. Unfortunately, bones can only sustain a load until a certain limit, beyond which they fail. Therefore, it is essential to study their mechanical and fracture behaviours in order to get an in-depth understanding of the origins of its fracture resistance that, in turn, can assist diagnosis and prevention of bone’s trauma. This can be achieved by studying mechanical properties of bone, such as its fracture toughness. Generally, most of bone fractures occur for long bones that consist mostly of cortical bone. Therefore, in this study, only a cortical bone tissue was studied. Since this tissue has an anisotropic behaviour and possesses hierarchical and complex structure, in this paper, an experimental analysis for the fracture toughness of cortical bone tissue is presented in terms of J-integral. The data was obtained using single-edge-notch bending (SENB) cortical specimens of bone tested in a three-point bending setup. Variability of values of fracture toughness was investigated by testing specimens cut from different cortex positions of bovine femur called anterior, posterior, medial, and lateral. In addition, anisotropy ratios of fracture toughness were considered by examining specimens cut from three different orientations: longitudinal, transverse and radial. Moreover, in order to link cortical bone fracture mechanisms with its underlying microstructure, fracture surfaces of specimens from different cortices and along different orientations were studied. Experimental results of this study provide a clear understanding of both variability and anisotropy of cortical bone tissue with regard to its fracture toughness

Penetration of cutting tool into cortical bone: experimental and numerical investigation of anisotropic mechanical behaviour

An anisotropic mechanical behaviour of cortical bone and its intrinsic hierarchical microstructure act as protective mechanisms to prevent catastrophic failure due to natural loading conditions; however, they increase the extent of complexity of a penetration process in the case of orthopaedic surgery. Experimental results available in literature provide only limited information about processes in the vicinity of a tool-bone interaction zone. Also, available numerical models the bone-cutting process do not account for material anisotropy or the effect of damage mechanisms. In this study, both experimental and numerical studies were conducted to address these issues and to elucidate the effect of anisotropic mechanical behaviour of cortical bone tissue on penetration of a sharp cutting tool. First, a set of tool-penetration experiments was performed in directions parallel and perpendicular to bone axis. Also, these experiments included bone samples cut from four different cortices to evaluate the effect of spatial variability and material anisotropy on the penetration processes. Distinct deformation and damage mechanisms linked to different microstructure orientations were captured using a micro-lens high-speed camera. Then, a novel hybrid FE model employing a smoothed-particle-hydrodynamic domain embedded into a continuum FE one was developed based on the experimental configuration to characterise the anisotropic deformation and damage behaviour of cortical bone under a penetration process. The results of our study revealed a clear anisotropic material behaviour of the studied cortical bone tissue and the influence of the underlying microstructure. The proposed FE model reflected adequately the experimental results and demonstrated the need for the use of the anisotropic and damage material model to analyse cutting of the cortical-bone tissue. © 2014 The authors