Adel A. Abdel-Wahab

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 bones 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 bones 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 bones 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 Youngs 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.

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.

Fracture process in cortical bone: X-FEM analysis of microstructured models

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 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.

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.

Damage in woven CFRP laminates subjected to low velocity impacts

Carbon fabric-reinforced polymer (CFRP) composites used in sports products can be exposed to different in-service conditions such as large dynamic bending deformations caused by impact loading. Composite materials subjected to such loads demonstrate various damage modes such as matrix cracking, delamination and, ultimately, fabric fracture. Damage evolution in these materials affects both their in-service properties and performance that can deteriorate with time. These processes need adequate means of analysis and investigation, the major approaches being experimental characterisation and non-destructive examination of internal damage in composite laminates. This research deals with a deformation behaviour and damage in woven composite laminates due to low-velocity dynamic out-of-plane bending. Experimental tests are carried out to characterise the behaviour of such laminates under large- deflection dynamic bending in un-notched specimens in Izod tests using a Resil Impactor. A series of low-velocity impact tests is carried out at various levels of impact energy to assess the energy absorbed and force-time response of CFRP laminates. X-ray micro computed tomography (micro-CT) is used to investigate material damage modes in the impacted specimens. X-ray tomographs revealed that through-thickness matrix cracking, inter-ply delamination and intra-ply delamination, such as tow debonding and fabric fracture, were the prominent damage modes.

Dynamic simulation of stent deployment ? effects of design, material and coating

Dynamic finite-element simulations have been carried out to study the effects of cell design, material choice and drug eluting coating on the mechanical behaviour of stents during deployment. Four representative stent designs have been considered, i.e., Palmaz-Schatz, Cypher, Xience and Endeavor. The former two are made of stainless steel while the latter two made of Co-Cr alloy. Geometric model for each design was created using ProEngineer software, and then imported into Abaqus for simulation of the full process of stent deployment within a diseased artery. In all cases, the delivery system was based on the dynamic expansion of a polyurethane balloon under applied internal pressure. Results showed that the expansion is mainly governed by the design, in particular open-cell design (e.g. Endeavor) tends to have greater expansion than closed-cell design (e.g. Cypher). Dogboning effect was strong for slotted tube design (e.g. Palmaz-Schatz) but reduced significantly for sinusoidal design (e.g. Cypher). Under the same pressure, the maximum von Mises stress in the stent was higher for the open-cell designs and located mostly at the inner corners of each cell. For given deformation, stents made of Co-Cr alloys tend to experience higher stress level than those made of stainless steels, mainly due to the difference in material properties. For artery-plaque system, the maximum stress occurred on the stenosis and dogboning led to stress concentration at the ends of the plaque. The drug eluting coating affected the stent expansion by reducing the recoiling phenomenon considerably, but also raised the stress level on the stent due to property mismatch.

Modelling fracture processes in bones

This chapter discusses numerical simulations of fracture and deformation of a cortical bone tissue employing an extended finiteelement method (X-FEM). The chapter first reviews the literature on available finite-element models for both macroscopic and microscopic fracture behaviours of the cortical bone tissue. It then discusses the formulation and analysis of a number of finite-element models investigating deformation and fracture of cortical bone using X-FEM at different length scales and for various loading conditions.

A numerical study on indentation properties of cortical bone tissue: Influence of anisotropy

PURPOSE The purpose of this study is to investigate the effect of anisotropy of cortical bone tissue on measurement of properties such as direction-dependent moduli and hardness. METHODS An advanced three-dimensional finite element model of microindentation was developed. Different modelling schemes were considered to account for anisotropy of elastic or/and plastic regimes. The elastic anisotropic behaviour was modelled employing an elasticity tensor, and Hills criteria were used to represent the direction-dependent post-yield behaviour. The Oliver-Pharr method was used in the data analysis. RESULTS A decrease in the value of the transverse elasticity modulus resulted in the increased materials indentation modulus measured in the longitudinal direction and a decreased one in the transverse direction, while they were insensitive to the anisotropy in post-elastic regime. On the other hand, an increase in plastic anisotropy led to a decrease in measured hardness for both directions, but by a larger amount in the transverse one. The size effect phenomenon was found to be also sensitive to anisotropy. CONCLUSIONS The undertaken analysis suggests that the Oliver-Pharr method is a useful tool for first-order approximations in the analysis of mechanical properties of anisotropic materials similar to cortical bone, but not necessarily for the materials with low hardening reserves in the plastic regime.

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 finite-element 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.

Fracture of cortical bone tissue

In this chapter, mechanical behaviours of a unique type of composite material—cortical bone tissue—are considered for different length scales. Both experimental and computational approaches are discussed in this study to evaluate the effects of mechanical anisotropy and structural heterogeneity on the fracture process of cortical bone. First, variability and anisotropic mechanical behaviour of cortical bone tissue are characterised and analysed experimentally for different loading conditions and orientations. Then, results from the experimental studies are used to develop finite-element models across different length-scales to elucidate mechanical and structural mechanisms underpinning the anisotropic and non-linear fracture processes of cortical bone.