Cohesive finite element modeling of age-related toughness loss in human cortical bone

Although the age-related loss of bone quality has been implicated in bone fragility, a mechanistic understanding of the relationship is necessary for developing diagnostic and treatment modalities in the elderly population at risk of fracture. In this study, a finite element based cohesive zone model is developed and applied to human cortical bone in order to capture the experimentally shown rising crack growth behavior and age-related loss of bone toughness. The cohesive model developed here is based on a traction–crack opening displacement relationship representing the fracture processes in the vicinity of a propagating crack. The traction–displacement curve, defining the cohesive model, is composed of ascending and descending branches that incorporate material softening and nonlinearity. The results obtained indicate that, in contrast to initiation toughness, the finite element simulations of crack growth in compact tension (CT) specimens successfully capture the rising R-curve (propagation toughness) behavior and the age-related loss of bone toughness. In close correspondence with the experimentally observed decrease of 14–15% per decade, the finite element simulation results show a decrease of 13% in the R-curve slope per decade. The success of the simulations is a result of the ability of cohesive models to capture and predict the parameters related to bone fracture by representing the physical processes occurring in the vicinity of a propagating crack. These results illustrate that fracture mechanisms in the process zone control bone toughness and any modification to these would cause age-related toughness loss.     

A model of tension and compression cracks with cohesive zone at a bone-cement interface

This paper gives an insight about compression and tension cracks as encountered at a bone-cement interface. Within the context of continuum theory of fracture, an analytical solution is presented for the problem of a bimaterial interface edge crack under uniaxial tension or compression, assuming no tangential slip along the crack faces since cement pedicles penetrate into the cancellous bone several millimeters. Also essential to the solution are cohesive zone effects that account for a strengthening mechanism over the crack faces. The solution provides a methodological framework for quantifying the influence of the cohesive zone on the magnitude of the stress singularity. Mode I crack tip stress intensity factors are calculated at different stages of the loading and unloading phases under uniaxial tension or compression. Finally, an inelastic mechanism is presented that gives theoretical support to explain the formation of interfacial compression cracks, a phenomenon that was not previously appreciated and that arises from the rigid cement being forced into the more compliant cancellous bone.     

Unlocalized crack initiation and propagation in staggered biomaterials

Many types of tissues in living organisms exhibit a combination of different properties to fulfil their mechanical functions in complex environments. Nacre with more than 90% brittle and hard phase and a little protein matrix, exhibits high strength and toughness, which is difficult to achieve in artificial materials. Researchers have shown that the toughness of nacre is related to the cracking process. Most of them, however, assume an obvious pre-existing crack on the model and the initiation of the microscopical pre-existing crack is not considered yet. Based on fracture mechanics with the cohesive zone model, we reveal the mechanism of the crack initiation and propagation pattern in staggered biomaterials without any pre-existing crack. The simulation result shows that there are two crack propagation modes: localized mode and unlocalized mode. A crack initiates and propagates in a small area in the localized mode, while cracks initiate at different points and propagate in various paths in the unlocalized mode. The crack initiation mechanism from the intrinsic properties of the material is clarified using energy based stability analysis. The result shows that the shear interfacial mechanism significantly delays the crack initiation.     

A crack model of a bone cement interface

This paper is concerned with the fracture mechanics of a bone-cement interface that includes a cohesive zone effect on the crack faces. This accounts for the experimentally observed strengthening mechanism due to the mechanical interlock between the crack faces. Edge crack models are developed where the cohesive zone is simulated by a continuous or a discrete distribution of linear or nonlinear springs. It is shown that the solution obtained by assuming a homogeneous material is fairly close to the exact solution for the bimaterial interface edge crack problem. On the basis of that approximation, the analysis is conducted for the problem of two interacting edge cracks, one at the interface, and the other one in the cement. The small crack that was observed to initiate in the cement, close to the bone-cement interface, does not affect much the mode I stress-intensity factor at the tip of the interface crack. However it may grow, leading to a catastrophic breakdown of the cement. The analysis and following discussion point out an interdependency between bone-cement interface strength and cement strength not previously appreciated. The suggested crack models provide a framework for quantifying the fracture mechanisms at the bone-cement interface.     

Anisotropy of age-related toughness loss in human cortical bone: a finite element study

A mechanistic understanding of the role of bone quality on fracture processes is essential for determining the underlying causes of age-related changes in the mechanical response of the human bone. In this study, a previously developed cohesive finite element model was used to investigate the effects of age-related changes and the orientation of crack growth on the toughening behavior of human cortical bone. The change in the anisotropy of toughening mechanisms with age was also studied. Finite element method (FEM) simulations showed that the initiation toughness decreased by 3% and 8%/decade for transverse and longitudinal crack growth, respectively. In contrast, fracture resistance curve slope for transverse and longitudinal crack growth decreased by 2% and 3%/decade, respectively. Initiation fracture toughness values were higher for the transverse than for the longitudinal for a given age. On the other hand, propagation fracture toughness values were higher for longitudinal than for transverse crack growth for a given age. With respect to age, the toughness ratio for crack initiation decreased by 6%/decade, but that for propagation showed almost no change (less than 1%). In light of these findings, an analytical model evaluating the crack arresting feature of cement lines, is proposed to explain the factors that determine crack penetration into osteons or its deflection by cement lines.     

Fracture-toughening mechanisms responsible for differences in work to fracture of hydrated and dehydrated dentine

This study investigates the nature of deformation and differences in the mechanisms of fracture and properties of dentine where there has been a loss of moisture, as may occur with removal of the pulp in the endodontic treatment of teeth. Controlled fracture toughness testing was conducted on bovine teeth to determine the influence of hydration on the work of fracture of dentine. Significant differences (p<0.01) were observed between the fracture toughness of hydrated (554+/-27.7J/m2) and dehydrated (113+/-17.8J/m2) dentine. Observations of the crack tip region during crack extension revealed extensive ligament formation occurred behind the crack tip. These ligaments provide considerable stability to the crack by significantly increasing the work of fracture, thereby acting as a fracture-toughening mechanism. Micro-cracking, reported as a fracture-toughening mechanism in bone, is also clearly seen. A zone of in-elastic deformation may occur as hydrated specimens revealed upon crack extension, a region about the tip that appeared to suck water into the structure and to exude water behind the crack tip. In dehydrated dentine, no in-elastic zone was observed. Micro-cracking is present though the cracks are smaller, straighter and with less opening than hydrated dentine. Only limited ligament formation just behind the crack tip was observed. These differences resulted in a significantly lower work of fracture with unstable brittle fracture characteristics. Based on these results, several fracture-toughening mechanisms were identified in dentine, with micro-cracking not considered the most important. These findings may be relevant for bone, a similar mineralised hydrated tissue.     

Failure modelling of trabecular bone using a non-linear combined damage and fracture voxel finite element approach

Trabecular bone tissue failure can be considered as consisting of two stages: damage and fracture; however, most failure analyses of 3D high-resolution trabecular bone samples are confined to damage mechanisms only, that is, without fracture. This study aims to develop a computational model of trabecular bone consisting of an explicit representation of complete failure, incorporating damage criteria, fracture criteria, cohesive forces, asymmetry and large deformation capabilities. Following parameter studies on a test specimen, and experimental testing of bone sample to complete failure, the asymmetric critical tissue damage and fracture strains of ovine vertebral trabecular bone were calibrated and validated to be compression damage ?1.16 %, tension damage 0.69 %, compression fracture ?2.91 % and tension fracture 1.98 %. Ultimate strength and post–ultimate strength softening were captured by the computational model, and the failure of individual struts in bending and shear was also predicted. This modelling approach incorporated a cohesive parameter that provided a facility to calibrate ductile–brittle behaviour of bone tissue in this non-linear geometric and non-linear constitutive property analyses tool. Finally, the full accumulation of tissue damage and tissue fracture has been monitored from range of small magnitude (normal daily loading) through to specimen yielding, ultimate strength and post–ultimate strength softening.     

Material heterogeneity,microstructure, and microcracks demonstrate differential influence on crack initiation and propagation in cortical bone

The recent studies have shown that long-term bisphosphonate use may result in a number of mechanical alterations in the bone tissue including a reduction in compositional heterogeneity and an increase in microcrack density. There are limited number of experimental and computational studies in the literature that evaluated how these modifications affect crack initiation and propagation in cortical bone. Therefore, in this study, the entire crack growth process including initiation and propagation was simulated at the microscale by using the cohesive extended finite element method. Models with homogeneous and heterogeneous material properties (represented at the microscale capturing the variability in material property values and their distribution) as well as different microcrack density and microstructure were compared. The results showed that initiation fracture resistance was higher in models with homogeneous material properties compared to heterogeneous ones, whereas an opposite trend was observed in propagation fracture resistance. The increase in material heterogeneity level up to 10 different material property sets increased the propagation fracture resistance beyond which a decrease was observed while still remaining higher than the homogeneous material distribution. The simulation results also showed that the total osteonal area influenced crack propagation and the local osteonal area near the initial crack affected the crack initiation behavior. In addition, the initiation fracture resistance was higher in models representing bisphosphonate treated bone (low material heterogeneity, high microcrack density) compared to untreated bone models (high material heterogeneity, low microcrack density), whereas an opposite trend was observed at later stages of crack growth. In summary, the results demonstrated that tissue material heterogeneity, microstructure, and microcrack density influenced crack initiation and propagation differently. The findings also elucidate how possible modifications in material heterogeneity and microcrack density due to bisphosphonate treatment may influence the initiation and propagation fracture resistance of cortical bone.     

The relative contributions of non-enzymatic glycation and cortical porosity on the fracture toughness of aging bone

The risk of fracture increases with age due to the decline of bone mass and bone quality. One of the age-related changes in bone quality occurs through the formation and accumulation of advanced glycation end-products (AGEs) due to non-enzymatic glycation (NEG). However as a number of other changes including increased porosity occur with age and affect bone fragility, the relative contribution of AGEs on the fracture resistance of aging bone is unknown. Using a high-resolution nonlinear finite element model that incorporate cohesive elements and micro-computed tomography-based 3d meshes, we investigated the contribution of AGEs and cortical porosity on the fracture toughness of human bone. The results show that NEG caused a 52% reduction in propagation fracture toughness (R-curve slope). The combined effects of porosity and AGEs resulted in an 88% reduction in propagation toughness. These findings are consistent with previous experimental results. The model captured the age-related changes in the R-curve toughening by incorporating bone quantity and bone quality changes, and these simulations demonstrate the ability of the cohesive models to account for the irreversible dynamic crack growth processes affected by the changes in post-yield material behavior. By decoupling the matrix-level effects due to NEG and intracortical porosity, we are able to directly determine the effects of NEG on fracture toughness. The outcome of this study suggests that it may be important to include the age-related changes in the material level properties by using finite element analysis towards the prediction of fracture risk.     

Effects of intracortical porosity on fracture toughness in aging human bone: a microCT-based cohesive finite element study

The extent to which increased intracortical porosity affects the fracture properties of aging and osteoporotic bone is unknown. Here, we report the development and application of a microcomputed tomography based finite element approach that allows determining the effects of intracortical porosity on bone fracture by blocking all other age-related changes in bone. Previously tested compact tension specimens from human tibiae were scanned using microcomputed tomography and converted to finite element meshes containing three-dimensional cohesive finite elements in the direction of the crack growth. Simulations were run incorporating age-related increase in intracortical porosity but keeping cohesive parameters representing other age-related effects constant. Additional simulations were performed with reduced cohesive parameters. The results showed a 6% decrease in initiation toughness and a 62% decrease in propagation toughness with a 4% increase in porosity. The reduction in toughnesses became even more pronounced when other age-related effects in addition to porosity were introduced. The initiation and propagation toughness decreased by 51% and 83%, respectively, with the combined effect of 4% increase in porosity and decrease in the cohesive properties reflecting other age-related changes in bone. These results show that intracortical porosity is a significant contributor to the fracture toughness of the cortical bone and that the combination of computational modeling with advanced imaging improves the prediction of the fracture properties of the aged and the osteoporotic cortical bone.     

Numerical Simulation of Bone Plate with Fatigue Crack and Investigation of Attraction Hole for Retarding Crack Growth

Premature fracture of the bone plate caused by fatigue crack is the main failure mode in treating femoral shaft fracture. In order to improve the durability of the plate, this study proposed a crack attraction hole (CAH) to retard the crack propagation based on the fracture mechanics. In this paper, a numerical model of the femoral fracture internal fixation system was constructed, in which the femur was developed using a validated simplified model. First, the fatigue crack initiation location was defined at the stress concentration through static analysis. Next, with the joint simulation method of Franc3D and ABAQUS, the fatigue crack path in the bone plate was predicted. Meanwhile, the Paris parameters of Ti-6Al-4V obtained through experiments were encoded into Franc3D to calculate the crack propagation life. Finally, we considered the influence of CAH designs with different relative vertical distances (2.0, 3.0, and 4.0 mm) and diameters (1.5, 2.0, and 2.5 mm) on the crack propagation path and life of the bone plate. Additionally, the effects of all CAH configurations on the biomechanical performance of the bone plate fixation system were evaluated. The results indicated that the fatigue crack growth path in the bone plate is comparable to a straight line, and the crack growth rate significantly increases when the crack tip reaches the outer boundary of the plate. The findings suggest that the addition of CAH in the bone plate will lead to the deflection of the crack path and increase the fatigue life. Equally important, the improvement of the fatigue life was positively correlated with the diameter of CAH and negatively correlated with the relative vertical distance. In addition, the biomechanical properties of the bone plate system were slightly affected by CAH, substantiating the feasibility of this method. Finally, the comparative analysis verified that a CAH with a relative vertical distance of 3 mm and a diameter of 2 mm exhibited superior improvement in the comprehensive performance on the bone plate.     

Linear and nonlinear analyses of femoral fractures: Computational/experimental study

This paper describes two new methods for computational fracture analysis of human femur using Quantitative Computed Tomography (QCT) voxel-based finite element (FE) simulation. The paper also reports comprehensive mechanical testing for validation of the methods and evaluation of the required material properties. The analyses and tests were carried out on 15 human femurs under 11 different stance-type loading orientations. Several classical forms of subcapital, transcervical, basicervical, and intertrochanteric fractures plus a specific type of subtrochanteric fracture were created and analyzed. A new procedure was developed for prediction of the strengths and the fracture initiation patterns using a FE-based linear scheme. The predicted and observed fracture patterns were in correspondence, and the FE predictions of the fracture loads were in very good agreement with the experimental results. Moreover, the crack initiation and growth behaviors of two subtrochanteric fractures were successfully simulated through a novel implementation of the cohesive zone model (CZM) within a nonlinear FE analysis scheme. The CZM parameters were obtained through a series of experimental tests on different types of specimens and determination of a variety of material properties for different anatomic regions and orientations. The presented results indicated that the locations and patterns of crack initiation, the sequences of crack growth on different paths, and the compatibility of growth increments agreed very well with the observed specifications. Also, very good agreements were achieved between the measured and simulated fracture loads.     

Bone fracture characterization under mixed-mode I+II loading using the single leg bending test

Fracture under mixed-mode I+II was induced in bovine cortical bone tissue using a developed miniaturized version of the single leg bending test (SLB). Due to the difficulty in crack length monitoring in the course of the test, an equivalent crack method based on specimen compliance and beam theory was adopted as a data reduction scheme. The method was applied to the experimental results in order to obtain the Resistance curves in each loading mode. The determined fracture energy is well described by an energetic power law whose exponent is below one, which means that the linear energetic criterion is not applicable to this material. The proposed procedure was numerically validated by means of a cohesive mixed-mode I+II damage model with bilinear softening. It was concluded that the miniaturized version of the SLB test is adequate for mixed-mode I+II fracture characterization of bone for a constant mode ratio.     

Rising crack-growth-resistance behavior in cortical bone: implications for toughness measurements

Fracture mechanics studies have characterized bone's resistance to fracture in terms of critical stress intensity factor and critical strain energy release rate measured at the onset of a fracture crack. This approach, although useful, provide a limited insight into fracture behavior of bone because, unlike classical brittle materials, bone is a microcracking solid that derives its resistance to fracture during the process of crack propagation from microfracture mechanisms occurring behind the advancing crack front. To address this shortfall, a crack propagation-based approach to measure bone toughness is described here and compared with crack initiation approach. Post hoc analyses of data from previously tested bovine and antler cortical bone compact specimens demonstrates that, in contrast to crack initiation approach, the crack propagation approach successfully identifies the superior toughness properties of red deer's antler cortical bone. Propagation-based slope of crack growth resistance curve is, therefore, a more useful parameter to evaluate cortical bone fracture toughness.     

Prediction of Colles’ fracture load in human radius using cohesive finite element modeling

Osteoporotic and age-related fractures are a significant public health problem. One of the most common osteoporotic fracture sites in the aging population is distal radius. There is evidence in the literature that distal radius fractures (Colles’ fracture) are an indicative of increased risk of future spine and hip fractures. In this study, a nonlinear fracture mechanics-based finite element method is applied to human radius to assess its fracture load as a function of cortical bone geometry and material properties. Seven three-dimensional finite element models of radius were created and the fracture loads were determined by using cohesive finite element modeling which explicitly represents the crack and the fracture process zone behavior. The fracture loads found in the simulations (731–6793 N) were in the range of experimental values reported in the literature. The fracture loads predicted by the simulations decreased by 4–5% per decade based only on material level changes and by 6–20% per decade when geometrical changes were also included. Cortical polar moment of inertia at 15% distal radius showed the highest correlation to fracture load (r²=0.97). These findings demonstrate the strength of fracture mechanics-based finite element modeling and show that combining geometrical and material properties provides a better assessment of fracture risk in human radius.     

Experimental validation of a microcracking-based toughening mechanism for cortical bone

It has been proposed that cortical bone derives its toughness by forming microcracks during the process of crack propagation (J. Biomech. 30 (1997) 763; J. Biomech. 33 (2000) 1169). The purpose of this study was to experimentally validate the previously proposed microcrack-based toughening mechanism in cortical bone. Crack initiation and propagation tests were conducted on cortical bone compact tension specimens obtained from the antlers of red deer. For these tests, the main fracture crack was either propagated to a predetermined crack length or was stopped immediately after initiating from the notch. The microcracks produced in both groups of specimens were counted in the same surface area of interest around and below the notch, and crack growth resistance and crack propagation velocity were analyzed. There were more microcracks in the surface area of interest in the propagation than in initiation specimens showing that the formation of microcracks continued after the initiation of a fracture crack. Crack growth resistance increased with crack extension, and crack propagation velocity vs. crack extension curves demonstrated the characteristic jump increase and decrease pattern associated with the formation of microcracks. The scanning electron micrographs of crack initiation and propagation displayed the formation of a frontal process zone and a wake, respectively. These results support the microcrack-based toughening mechanism in cortical bone. Bone toughness is, therefore, determined by its ability to form microcracks during fracture.     

Fracture toughness and fatigue crack propagation rate of short fiber reinforced epoxy composites for analogue cortical bone

Third-generation mechanical analogue bone models and synthetic analogue cortical bone materials manufactured by Pacific Research Laboratories, Inc. (PRL) are popular tools for use in mechanical testing of various orthopedic implants and biomaterials. A major issue with these models is that the current third-generation epoxy-short fiberglass based composite used as the cortical bone substitute is prone to crack formation and failure in fatigue or repeated quasistatic loading of the model. The purpose of the present study was to compare the tensile and fracture mechanics properties of the current baseline (established PRL "third-generation" E-glass-fiber-epoxy) composite analogue for cortical bone to a new composite material formulation proposed for use as an enhanced fourth-generation cortical bone analogue material. Standard tensile, plane strain fracture toughness, and fatigue crack propagation rate tests were performed on both the third- and fourth-generation composite material formulations using standard ASTM test techniques. Injection molding techniques were used to create random fiber orientation in all test specimens. Standard dog-bone style tensile specimens were tested to obtain ultimate tensile strength and stiffness. Compact tension fracture toughness specimens were utilized to determine plane strain fracture toughness values. Reduced thickness compact tension specimens were also used to determine fatigue crack propagation rate behavior for the two material groups. Literature values for the same parameters for human cortical bone were compared to results from the third- and fourth-generation cortical analogue bone materials. Tensile properties of the fourth-generation material were closer to that of average human cortical bone than the third-generation material. Fracture toughness was significantly increased by 48% in the fourth-generation composite as compared to the third-generation analogue bone. The threshold stress intensity to propagate the crack was much higher for the fourth-generation material than for the third-generation composite. Even at the higher stress intensity threshold, the fatigue crack propagation rate was significantly decreased in the fourth-generation composite compared to the third-generation composite. These results indicate that the bone analogue models made from the fourth-generation analogue cortical bone material may exhibit better performance in fracture and longer fatigue lives than similar models made of third-generation analogue cortical bone material. Further fatigue testing of the new composite material in clinically relevant use of bone models is still required for verification of these results. Biomechanical test models using the superior fourth-generation cortical analogue material are currently in development.     

Fracture properties of bovine tibial bone

Linear elastic fracture mechanics predicts that the fracture stress of precracked materials is dependent on the length of the initial crack tip radius of curvature, as supported by the Griffith and Inglis equations. In order to determine the applicability of these equations and the effects of other variables, tensile specimens of bovine tibia were produced with edge cracks of known dimensions and tested to fracture. Longitudinal sheet tensile specimens were taken from the midposterior diaphysis of bovine tibiae that had been kept frozen in saline soaked towels. Each specimen had a milled gauge length of 25 mm, 16 mm width and 2 mm thickness. All specimen preparation was performed under a saline drip. An edge crack, centered along the gauge length, was milled in the specimen perpendicular to its long axis. The crack lengths used were 4, 6, 8, 10 and 12 mm. The crack tip was formed with drill bits having nominal diameters of 1/32, 1/16, and 3/32 in. All the combinations of crack length and crack tip radius were repeated five times for a total of 75 specimens. The testing order was randomly selected. Each specimen was tested in tension to fracture at a constant deformation rate of 7.5 X 10(-3) mm s-1, on an Instron mechanical testing device, and the fracture stress was measured. A linear load-deflection curve to fracture was exhibited by all of the specimens. The weight percent calcium of each specimen was determined by atomic absorption spectrophotometry. Microradiographs were used to determine the fractional void area and to histologically evaluate each bone sample.(ABSTRACT TRUNCATED AT 250 WORDS)     

Contribution, development and morphology of microcracking in cortical bone during crack propagation

A fracture mechanics study of cortical bone is presented to investigate the contribution, development morphology of microcracking in cortical bone during crack propagation. Post-hoc analyses of microcrack orientation, crack propagation velocity and fracture surface roughness were conducted on previously tested human and bovine bone compact tension specimens. It was found that, consistent with its higher toughness, bovine bone formed significantly more longitudinal, transverse and inclined microcracks than human bone. However, in human bone more of the microcracks that formed were longitudinal than transverse or inclined, a feature that would optimise bone's toughness. Crack propagation velocity in human and bovine bone displayed the same characteristic pattern with crack extension, where an increase in velocity is followed by a consequent decrease and vice versa. On the basis of this pattern, a model or crack propagation has been proposed. It provides a detailed account of mocrocrack formation and contribution towards the propagation of a fracture crack. Analyses of fracture surfaces indicated that, consistent with its higher toughness, bovine bone displays a rougher surface than human bone but they both have the same basic fractured element, i.e. a mineralised collagen fibril.     

Fracture in human cortical bone: local fracture criteria and toughening mechanisms

Micromechanical models for fracture initiation that incorporate local failure criteria have been widely developed for metallic and ceramic materials; however, few such micromechanical models have been developed for the fracture of bone. In fact, although the fracture event in "hard" mineralized tissues such as bone is commonly believed to be locally strain-controlled, only recently has there been experimental evidence (using double-notched four-point bend testing) to support this widely held belief. In the present study, we seek to shed further light on the nature of the local cracking events that precede catastrophic fracture in human cortical bone, and to define their relationship to the microstructure. Specifically, numerical computations are reported that demonstrate that the stress and strain states ahead of such a notch are qualitatively similar irrespective of the deformation mechanism (pressure-insensitive plasticity vs. pressure-sensitive microcracking). Furthermore, we use the double-notched test to examine crack-microstructure interactions from a perspective of determining the salient toughening mechanisms in bone and to characterize how these may affect the anisotropy in fracture properties. Based on preliminary micromechanical models of these processes, the relative contributions of various toughening mechanisms are established. In particular, crack deflection and uncracked-ligament bridging are identified as the major mechanisms of toughening in cortical bone.