An interface damage model that captures crack propagation at the microscale in cortical bone using XFEM

Fracture behavior of human cortical bone with high glycation content under dynamic loading

The present study simulates the fracture behavior of diabetic cortical bone with high levels of advanced glycation end-products (AGEs) under dynamic loading. We consider that the increased AGEs in diabetic cortical bone degrade the materials heterogeneity of cortical bone through a reduction in critical energy release rates of the microstructural features. To simulate the initiation and propagation of cracks, we implement a phase field fracture framework on 2D models of human tibia cortical microstructure. The simulations show that the mismatch between the fracture properties (e.g., critical energy release rate) of osteons and interstitial tissue due to high AGEs contents can change crack growth trajectories. The results show crack branching in the cortical microstructure under dynamic loading is affected by the mismatches related to AGEs. In addition, we observe cortical features such as osteons and cement lines can prevent multiple cracking under dynamic loading even with changing the mismatches due to high AGEs. Furthermore, under dynamic loading, some toughening mechanisms can be activated and deactivated with different AGEs contents. In conclusion, the current findings present that the combination of the loading type and materials heterogeneity of microstructural features can change the fracture response of diabetic cortical bone and its fragility.

Research on ultrasonic bone cutting mechanism based on extended finite element method

The research on the crack propagation mechanism of bone has important research significance and clinical medical value for the selection of cutting parameters and the development of new surgical tools. In this paper, an extended finite element method (X-FEM) model of ultrasonic bone cutting considering microstructure was developed to further study the ultrasonic bone cutting mechanism and to quantitatively analyze the effects of cutting direction, ultrasonic parameters, and cutting parameters on the mechanism of ultrasonic bone cutting crack propagation. The results show that ultrasonic bone cutting is essentially a controlled crack propagation process, in which brittle crack and fatigue crack are the main crack propagation mechanisms. In order to improve the efficiency of ultrasonic bone cutting, large amplitude and high-frequency ultrasonic vibration are preferred. Compared with the other two cutting directions, the crack propagation deflection angle in the transverse cutting direction is the largest, resulting in the worst cutting surface. Therefore, in the path planning of orthopedic surgical robots, the transverse cutting direction should be avoided as much as possible. Frequency only has a significant effect on the crack propagation rate and has a positive correlation. There is a positive correlation between the deflection angle, propagation length, propagation rate, and amplitude, which provides the possibility to control the direction and length of crack propagation by controlling the amplitude of ultrasonic. The feed speed is much lower than the ultrasonic vibration speed, which makes the influence of ultrasonic vibration speed on the crack propagation characteristics dominant. The X-FEM model of ultrasonic bone cutting provides an effective method for selecting reasonable machining parameters of orthopedic robot and optimize the design of ultrasonic osteotome.

A numerical study of dehydration induced fracture toughness degradation in human cortical bone

A 2D plane strain extended finite element method (XFEM) model was developed to simulate three-point bending fracture toughness tests for human bone conducted in hydrated and dehydrated conditions. Bone microstructures and crack paths observed by micro-CT imaging were simulated using an XFEM damage model. Critical damage strains for the osteons, matrix, and cement lines were deduced for both hydrated and dehydrated conditions and it was found that dehydration decreases the critical damage strains by about 50%. Subsequent parametric studies using the various microstructural models were performed to understand the impact of individual critical damage strain variations on the fracture behavior. The study revealed the significant impact of the cement line critical damage strains on the crack paths and fracture toughness during the early stages of crack growth. Furthermore, a significant sensitivity of crack growth resistance and crack paths on critical strain values of the cement lines was found to exist for the hydrated environments where a small change in critical strain values of the cement lines can alter the crack path to give a significant reduction in fracture resistance. In contrast, in the dehydrated state where toughness is low, the sensitivity to changes in critical strain values of the cement lines is low. Overall, our XFEM model was able to provide new insights into how dehydration affects the micromechanisms of fracture in bone and this approach could be further extended to study the effects of aging, disease, and medical therapies on bone fracture.

XFEM for Composites, Biological, and Bioinspired Materials: A Review

The eXtended finite element method (XFEM) is a powerful tool for structural mechanics, assisting engineers and designers in understanding how a material architecture responds to stresses and consequently assisting the creation of mechanically improved structures. The XFEM method has unraveled the extraordinary relationships between material topology and fracture behavior in biological and engineered materials, enhancing peculiar fracture toughening mechanisms, such as crack deflection and arrest. Despite its extensive use, a detailed revision of case studies involving XFEM with a focus on the applications rather than the method of numerical modeling is in great need. In this review, XFEM is introduced and briefly compared to other computational fracture models such as the contour integral method, virtual crack closing technique, cohesive zone model, and phase-field model, highlighting the pros and cons of the methods (e.g., numerical convergence, commercial software implementation, pre-set of crack parameters, and calculation speed). The use of XFEM in material design is demonstrated and discussed, focusing on presenting the current research on composites and biological and bioinspired materials, but also briefly introducing its application to other fields. This review concludes with a discussion of the XFEM drawbacks and provides an overview of the future perspectives of this method in applied material science research, such as the merging of XFEM and artificial intelligence techniques.

Microstructural fatigue fracture behavior of glycated cortical bone

The current study aims to simulate fatigue microdamage accumulation in glycated cortical bone with increased advanced glycation end-products (AGEs) using a phase field fatigue framework. We link the material degradation in the fracture toughness of cortical bone to the high levels of AGEs in this tissue. We simulate fatigue fracture in 2D models of cortical bone microstructure extracted from human tibias. The results present that the mismatch between the critical energy release rate of microstructural features (e.g., osteons and interstitial tissue) can alter crack initiation and propagation patterns. Moreover, the high AGEs content through the increased mismatch ratio can cause the activation or deactivation of bone toughening mechanisms under cyclic loading. The fatigue fracture simulations also show that the lifetime of diabetic cortical bone samples can be dependent on the geometry of microstructural features and the mismatch ratio between the features. Additionally, the results indicate that the trapped cracks in cement lines in the diabetic cortical microstructure can prevent further crack growth under cyclic loading. The present findings show that alterations in the materials heterogeneity of microstructural features can change the fatigue fracture response, lifetime, and fragility of cortical bone with high AGEs contents. Cortical bone models are created from microscopy images taken from the cortical cross-section of human tibias. Increased glycation contents in the cortical bone sample can change the crack growth trajectories.

Human femur fracture by mechanical compression: Towards the repeatability of bone fracture acquisition

The increase in life expectancy combined with greater bone fragility over the years is causing a rise in the bone fracture cases. Femur fractures are the most important due to their high mortality rate. This multidisciplinary work is carried out in this context and focuses on the experimental reproduction of human femur fractures by compression. We describe a sequence of steps supervised by orthopaedic surgeons for the correct arrangement of specimens on the system set up to perform the experiment. The device applies force by compression until the human bone is fractured. All tests performed have been monitored and evaluated from different knowledge perspectives. The results obtained have demonstrated the repeatability of the fracture type in a controlled environment as well as identifying the main features involved in this process. In addition, the fractured bones have been digitized to analyze the fracture zone to recreate and evaluate future simulations.

An integrated experimental-computational framework to assess the influence of microstructure and material properties on fracture toughness in clinical specimens of human femoral cortical bone

Microstructural and compositional changes that occur due to aging, pathological conditions, or pharmacological treatments alter cortical bone fracture resistance. However, the relative importance of these changes to the fracture resistance of cortical bone has not been quantified in detail. In this technical note, we developed an integrated experimental-computational framework utilizing human femoral cortical bone biopsies to advance the understanding of how fracture resistance of cortical bone is modulated due to modifications in its microstructure and material properties. Four human biopsy samples from individuals with varying fragility fracture history and osteoporosis treatment status were converted to finite element models incorporating specimen-specific material properties and were analyzed using fracture mechanics-based modeling. The results showed that cement line density and osteonal volume had a significant effect on crack volume. The removal of cement lines substantially increased the crack volume in the osteons and interstitial bone, representing straight crack growth, compared to models with cement lines due to the lack of crack deflection in the models without cement lines. Crack volume in the osteons and interstitial bone increased when mean elastic modulus and ultimate strength increased and mean fracture toughness decreased. Crack volume in the osteons and interstitial bone was reduced when material property heterogeneity was incorporated in the models. Although both the microstructure and the heterogeneity of the material properties of the cortical bone independently increased the fracture toughness, the relative contribution of the microstructure was more significant. The integrated experimental-computational framework developed here can identify the most critical microscale features of cortical bone modulated by pathological processes or pharmacological treatments that drive changes in fracture resistance and improve our understanding of the relative influence of microstructure and material properties on fracture resistance of cortical bone.

Isolating the Role of Bone Lacunar Morphology on Static and Fatigue Fracture Progression through Numerical Simulations

Currently, the onset of bone damage and the interaction of cracks with the surrounding micro-architecture are still black boxes. With the motivation to address this issue, our research targets isolating lacunar morphological and densitometric effects on crack advancement under both static and cyclic loading conditions by implementing static extended finite element models (XFEM) and fatigue analyses. The effect of lacunar pathological alterations on damage initiation and progression is evaluated; the results indicate that high lacunar density considerably reduces the mechanical strength of the specimens, resulting as the most influencing parameter among the studied ones. Lacunar size has a lower effect on mechanical strength, reducing it by 2%. Additionally, specific lacunar alignments play a key role in deviating the crack path, eventually slowing its progression. This could shed some light on evaluating the effects of lacunar alterations on fracture evolution in the presence of pathologies.

On the fracture behavior of cortical bone microstructure: The effects of morphology and material characteristics of bone structural components

Bone encompasses a complex arrangement of materials at different length scales, which endows it with a range of mechanical, chemical, and biological capabilities. Changes in the microstructure and characteristics of the material, as well as the accumulation of microcracks, affect the bone fracture properties. In this study, two-dimensional finite element models of the microstructure of cortical bone were considered. The eXtended Finite Element Method (XFEM) developed by Abaqus software was used for the analysis of the microcrack propagation in the model as well as for local sensitivity analysis. The stress-strain behavior obtained for the different introduced models was substantially different, confirming the importance of bone tissue microstructure for its failure behavior. Considering the role of interfaces, the results highlighted the effect of cement lines on the crack deflection path and global fracture behavior of the bone microstructure. Furthermore, bone micromorphology and areal fraction of cortical bone tissue components such as osteons, cement lines, and pores affected the bone fracture behavior; specifically, pores altered the crack propagation path since increasing porosity reduced the maximum stress needed to start crack propagation. Therefore, cement line structure, mineralization, and areal fraction are important parameters in bone fracture. The parameter-wise sensitivity analysis demonstrated that areal fraction and strain energy release rate had the greatest and the lowest effect on ultimate strength, respectively. Furthermore, the component-wise sensitivity analysis revealed that for the areal fraction parameter, pores had the greatest effect on ultimate strength, whereas for the other parameters such as elastic modulus and strain energy release rate, cement lines had the most important effect on the ultimate strength. In conclusion, the finding of the current study can help to predict the fracture mechanisms in bone by taking the morphological and material properties of its microstructure into account.

Bone Abrasive Machining: Influence of Tool Geometry and Cortical Bone Anisotropic Structure on Crack Propagation

The abrasive machining of cortical tissue is used in many arthroplasties and craniofacial surgery procedures. However, this method requires further research due to the processes’ complexity and the tissue’s composite structure. Therefore, studies were carried out to assess the impact of grid geometry and the anisotropic structure of bone tissue on the cutting process and crack propagation. The analysis was performed based on an orthogonal cutting in three directions. The grain shape has been simplified, and the cutting forces, crack path and surface quality were monitored. The results indicate that a depth of cut at 100−25 µm allows the most accurate cutting control. A transverse cutting direction results in the greatest surface irregularity: Iz = 17.7%, Vvc = 3.29 mL/m2 and df = 5.22 µm and generates the most uncontrolled cracks. Maximum fracture force values of FF > 80 N were generated for d = 175 µm. For d < 5 µm, no cracks or only slight penetration occurs. A positive γ provides greater repeatability and crack control. Negative γ generates penetrating cracks and uncontrolled material damage. The individual types of cracks have a characteristic course of changes in Fx. The clearance angle did not affect the crack propagation.

Influence of Porosity on Fracture Toughness and Fracture Behavior of Antibiotic-Loaded PMMA Bone Cement

Aseptic loosening is the most common reason for the long-term revision of cemented arthroplasties with fracture of the cement being a postulated cause or contributing factor. In our previous studies we showed that adding an antibiotic to a polymethylmethacrylate (PMMA) bone cement led to detrimental effects on various mechanical properties of the cement such as bending strength, compressive strength and fracture toughness (KIC). This finding implied that the mechanical failure of antibiotic-loaded PMMA bone cement was influenced by its pore volume fraction. Up to now this aspect has not been studied. Hence the purposes of this study were to determine (1) the influence of antibiotic (telavancin) loading on the KIC of a widely used PMMA bone cement brand (Palacos®R) and (2) the influence of pore size and pore distribution on the fracture behavior of the KIC specimens. For (2) both experimental and numerical methods (extended finite element method [XFEM]) were used allowing a comparison between the two sets of results. We found that: (1) KIC decreased with increased porosity with the drop (relative to the value for the control cement) being significant when the telavancin loading was 4.8 wt/wt % (2 g of telavancin added to 40 g of control cement powder); (2) there was a critical pore size above which there was a significant decrease in KIC and is 1 mm; (3) crack propagation was strongly influenced by pore size and pore locations (pore-pore interactions); and, (4) there was good agreement between the experimental and XFEM results. The implications of these findings for the use of a telavancin-loaded PMMA bone cement in cemented total joint arthroplasties are commented upon.

Computational homogenisation based extraction of transverse tensile cohesive responses of cortical bone tissue

The numerical assessment of fracture properties of cortical bone is important in providing suggestions on patient-specific clinical treatments. We present a generic finite element modelling framework incorporating computational fracture approaches and computational homogenisation techniques. Finite element computations for statistical volume elements (SVEs) at the microscale are performed for different sizes with random osteon packing with a fixed volume fraction. These SVEs are loaded in the transverse direction under tension. The minimal SVE size in terms of ensuring a representative effective cohesive law is suggested to be 0.6 mm. Since cement lines as weak interfaces play a key role in bone fracture, the effects of their fracture properties on the effective fracture strength and toughness are investigated. The extracted effective fracture properties can be used as homogenised inputs to a discrete crack simulation at macroscopic or structural scale. The extrinsic toughening mechanisms observed in the SVE models are discussed with a comparison against experimental observations from the literature, giving beneficial insights to cortical bone failure.

Fracture behavior of human cortical bone: Role of advanced glycation end-products and microstructural features

Diabetes is associated with increased fracture risk in human bone, especially in the elderly population. In the present study, we investigate how simulated advanced glycation end-products (AGEs) and materials heterogeneity affect crack growth trajectory in human cortical bone. We used a phase field fracture framework on 2D models of cortical microstructure created from human tibias to analyze crack propagation. The increased AGEs level results in a higher rate of crack formation. The simulations also indicate that the mismatch between the fracture properties (e.g., critical energy release rate) of osteons and interstitial tissue can alter the post-yielding behavior. The results show that if the critical energy release rate of cement lines is lower than that of osteons and the surrounding interstitial matrix, cracks can be arrested by cement lines. Additionally, activation of toughening mechanisms such as crack merging and branching depends on bone microstructural morphology (i.e., osteons geometrical parameters, canals, and lacunae porosities). In conclusion, the present findings suggest that materials heterogeneity of microstructural features and the crack-microstructure interactions can play important roles in bone fragility.

Finite element analysis on multi-toughening mechanism of microstructure of osteon

The toughening mechanism of cortical bone is closely related to its hierarchical microstructure. Osteon is the most important microstructure of cortical bone. Therefore, it is very important to study the toughening mechanism of the microstructure of osteon. There are three main kinds of cracks in cortical bone: external crack of osteon, internal radial cracks of osteon and microporous damage cracks. Numerical models for these three kinds of cracks are established by XFEM and the progressive damage approach, respectively. The multi-toughening mechanisms of microstructure of osteon are found. The cement line on the outside of osteon is its first toughening mechanism, which can make the crack deflection and improve the fracture resistance of osteon. The resistance of cement line to fracture increases with the decrease of the strength and the increase of the thickness. The second toughening mechanism is elliptical osteocyte lacunae, which can attract the crack into the elliptical lacunae and cause stress redistribution to prevent the crack propagation. The annularly elliptical lacuna structure is an optimized arrangement and shape of microstructure, which is the third toughening mechanism of osteon. This microstructure can determine the location of the crack initiation and make the microcracks propagate along the annular direction rather than penetrating into the haversian cannal to protect the integrity of the osteon. The study of these toughening mechanisms provides new ideas for the research and design of synthetic composite structures.

The influence of microstructure on crack propagation in cortical bone at the mesoscale

The microstructure of cortical bone is key for the tissue's high toughness and strength and efficient toughening mechanisms have been identified at the microscale, for example when propagating cracks interact with the osteonal microstructure. Finite element models have been proposed as suitable tools for analyzing the complex link between the local tissue structure and the fracture resistance of cortical bone. However, previous models that could capture realistic crack paths in cortical bone were due to the required computational effort limited to idealized osteon geometries and small (<1 mm²) model domains. The objective of this study was therefore to bridge the gap between experimental and numerical analysis of crack propagation in cortical bone by introducing image-based models at the mesoscale. Tissue orientation maps from high-resolution micro-CT images were used to define the distribution and orientation of weak interfaces in the models. Crack propagation was simulated using the extended finite element method in combination with an interface damage model, previously developed to simulate crack propagation in microstructural osteon models. The results showed that image-based mesoscale models can be used to capture interactions between cracks and microstructure. The simulated crack paths predicted the general trends seen in experiments with more irregular patterns for cracks propagating perpendicular compared to parallel to the osteon orientation. In all, the proposed method enabled an efficient description of the tissue level microstructure, which is a necessity to predict realistic crack paths in cortical bone and is an important step towards simulating crack propagation in bone models in 3D.

Advanced Modeling Methods-Applications to Bone Fracture Mechanics

PURPOSE OF REVIEW

The goal of this review is to summarize recent advances in modeling of bone fracture using fracture mechanics-based approaches at multiple length scales spanning nano- to macroscale.

RECENT FINDINGS

Despite the additional information that fracture mechanics-based models provide over strength-based ones, the application of this approach to assessing bone fracture is still somewhat limited. Macroscale fracture models of bone have demonstrated the potential of this approach in uncovering the contributions of geometry, material property variation, as well as loading mode and rate on whole bone fracture response. Cortical and cancellous microscale models of bone have advanced the understanding of individual contributions of microstructure, microarchitecture, local material properties, and material distribution on microscale fracture resistance of bone. Nano/submicroscale models have provided additional insight into the effect of specific changes in mineral, collagen, and non-collagenous proteins as well as their interaction on energy dissipation and fracture resistance at small length scales. Advanced modeling approaches based on fracture mechanics provide unique information about the underlying multiscale fracture mechanisms in bone and how these mechanisms are influenced by the structural and material constituents of bone at different length scales. Fracture mechanics-based modeling provides a powerful approach that complements experimental evaluations and advances the understanding of critical determinants of fracture risk.

Crack propagation in cortical bone is affected by the characteristics of the cement line: a parameter study using an XFEM interface damage model

Bulk properties of cortical bone have been well characterized experimentally, and potent toughening mechanisms, e.g., crack deflections, have been identified at the microscale. However, it is currently difficult to experimentally measure local damage properties and isolate their effect on the tissue fracture resistance. Instead, computer models can be used to analyze the impact of local characteristics and structures, but material parameters required in computer models are not well established. The aim of this study was therefore to identify the material parameters that are important for crack propagation in cortical bone and to elucidate what parameters need to be better defined experimentally. A comprehensive material parameter study was performed using an XFEM interface damage model in 2D to simulate crack propagation around an osteon at the microscale. The importance of 14 factors (material parameters) on four different outcome criteria (maximum force, fracture energy, crack length and crack trajectory) was evaluated using ANOVA for three different osteon orientations. The results identified factors related to the cement line to influence the crack propagation, where the interface strength was important for the ability to deflect cracks. Crack deflection was also favored by low interface stiffness. However, the cement line properties are not well determined experimentally and need to be better characterized. The matrix and osteon stiffness had no or low impact on the crack pattern. Furthermore, the results illustrated how reduced matrix toughness promoted crack penetration of the cement line. This effect is highly relevant for the understanding of the influence of aging on crack propagation and fracture resistance in cortical bone.