Fracture mechanics of bone with short cracks

Tensile fracture experiments were performed upon specimens of wet mature bovine Haversian bone, with short, controlled notches. Stress concentration factors were found to be significantly less than values predicted using a maximum stress criterion in the theory of elasticity. Results were also modeled with the aid of linear elastic fracture mechanics. Agreement of experiment with theory was better in this case, however deviations were seen for short notches. Two mechanisms were evaluated for the behavior: plasticity near the crack tip, and effects of the Haversian microstructure, modelled by Cosserat elasticity, a generalized continuum theory. Plastic zone effects were found to be insignificant. Cosserat elasticity, by contrast, predicted stress concentration factors which better approximated observed values. To explore strain redistribution processes, further experiments were conducted upon notched specimens in torsion at small strain. They disclosed a strain redistribution effect consistent with Cosserat elasticity. These microelastic effects were attributed to the Haversian architecture of bone. The implications of the results are that bone resists the effect of stress raisers such as fatigue microcracks and surgical sawcuts to a much greater extent than anticipated on the basis of its elastic or elastoplastic properties.     

Anisotropic yield behavior of bone under combined axial force and torque

In this study the yield behavior of cortical bone was determined under combined loading conditions involving tension, compression and torsion. The axis of each test sample coincided with the long bone axis. To minimize viscoelastic behavior, tests were conducted using an effective strain rate in the range of 0.01-0.06 s-1. Experimental yield loci for bovine and human cortical bone were determined using a strain offset technique to determine the 'common yield point' for combined loading. Several failure criteria which have been used for composite materials were examined for applicability to the experimental results. Data were obtained for bovine and human tibial and femoral bone. The Tsai-Wu criterion was in best agreement to the test data, although Hill's criterion could describe the individual compression-torsion or tension-torsion regimes with good accuracy.     

Mechanical properties of single bovine trabeculae are unaffected by strain rate

For a better understanding of traumatic bone fractures, knowledge of the mechanical behavior of bone at high strain rates is required. Importantly, it needs to be clarified how quasistatic mechanical testing experiments relate to real bone fracture. This merits investigating the mechanical behavior of bone with an increase in strain rate. Various studies examined how cortical and trabecular bone behave at varying strain rates, but no one has yet looked at this question using individual trabeculae. In this study, three-point bending tests were carried out on bovine single trabeculae excised from a proximal femur to test the trabecular material's strain rate sensitivity. An experimental setup was designed, capable of measuring local strains at the surface of such small specimens, using digital image correlation. Microdamage was detected using the bone whitening effect. Samples were tested through two orders of magnitude, at strain rates varying between 0.01 and 3.39 s(-1). No linear relationship was observed between the strain rate and the Young's modulus (1.13-16.46 GPa), the amount of microdamage, the maximum tensile strain at failure (14.22-61.65%) and at microdamage initiation (1.95-12.29%). The results obtained in this study conflict with previous studies reporting various trends for macroscopic cortical and trabecular bone samples with an increase in strain rate. This discrepancy might be explained by the bone type, the small sample geometry, the limited range of strain rates tested here, the type of loading and the method of microdamage detection. Based on the results of this study, the strain rate can be ignored when modeling trabecular bone.     

The effect of strain rate on the mechanical properties of human cortical bone

Bone mechanical properties are typically evaluated at relatively low strain rates. However, the strain rate related to traumatic failure is likely to be orders of magnitude higher and this higher strain rate is likely to affect the mechanical properties. Previous work reporting on the effect of strain rate on the mechanical properties of bone predominantly used nonhuman bone. In the work reported here, the effect of strain rate on the tensile and compressive properties of human bone was investigated. Human femoral cortical bone was tested longitudinally at strain rates ranging between 0.14-29.1 s(-1) in compression and 0.08-17 s(-1) in tension. Young's modulus generally increased, across this strain rate range, for both tension and compression. Strength and strain (at maximum load) increased slightly in compression and decreased (for strain rates beyond 1 s(-1)) in tension. Stress and strain at yield decreased (for strain rates beyond 1 s(-1)) for both tension and compression. In general, there seemed to be a relatively simple linear relationship between yield properties and strain rate, but the relationships between postyield properties and strain rate were more complicated and indicated that strain rate has a stronger effect on postyield deformation than on initiation of yielding. The behavior seen in compression is broadly in agreement with past literature, while the behavior observed in tension may be explained by a ductile to brittle transition of bone at moderate to high strain rates.     

Design considerations for ceramic resurfaced femoral head: effect of interface characteristics on failure mechanisms

Ceramic hip resurfacing may offer improved wear resistance compared to metallic components. The study is aimed at investigating the effects of stiffer ceramic components on the stress/strain-related failure mechanisms in the resurfaced femur, using three-dimensional finite element models of intact and resurfaced femurs with varying stem–bone interface conditions. Tensile stresses in the cement varied between 1 and 5 MPa. Postoperatively, 20–85% strain shielding was observed inside the resurfaced head. The variability in stem–bone interface condition strongly influenced the stresses and strains generated within the resurfaced femoral head. For full stem–bone contact, high tensile (151–158 MPa) stresses were generated at the cup–stem junction, indicating risk of fracture. Moreover, there was risk of femoral neck fracture due to elevated bone strains (0.60–0.80% strain) in the proximal femoral neck region. Stresses in the ceramic component are reduced if a frictionless gap condition exists at the stem–bone interface. High stresses, coupled with increased strain shielding in the ceramic resurfaced femur, appear to be major concerns regarding its use as an alternative material.     

Evaluation of the influence of strain rate on Colles' fracture load

Colles' fracture, a transverse fracture of the distal radius bone, is one of the most frequently observed osteoporotic fractures resulting from low energy or traumatic events, associated with low and high strain rates, respectively. Although experimental studies on Colles' fracture were carried out at various loading rates ranging from static to impact loadings, there is no systematic study in the literature that isolates the influence of strain rate on Colles' fracture load. In order to provide a better understanding of fracture risk, the current study combines experimental material property measurements under varying strain rates with computational modeling and presents new information on the effect of strain rate on Colles' fracture. The simulation results showed that Colles' fracture load decreased with increasing strain rate with a steeper change in lower strain rates. Specifically, strain rate values (0.29s(-1)) associated with controlled falling without fracture corresponded to a 3.7% reduction in the fracture load. On the other hand, the reduction in the fracture load was 34% for strain rate of 3.7s(-1) reported in fracture inducing impact cadaver experiments. Further increase in the strain rate up to 18s(-1) led to an additional 22% reduction. The most drastic reduction in fracture load occurs at strain rates corresponding to the transition from controlled to impact falling. These results are particularly important for the improvement of fracture risk assessment in the elderly because they identify a critical range of loading rates (10-50mm/s) that can dramatically increase the risk of Colles' fracture.     

Inelastic strain accumulation in cortical bone during rapid transient tensile loading

An experimental study examined the tensile stress-strain behavior of cortical bone during rapid load cycles to high strain amplitudes. Machined bovine and human cortical bone samples were subjected to loading cycles at a nominal load/unload rate of +/- 420 MPa/s. Loads were reversed at pre selected strain levels such that load cycles were typically completed in 0.5-0.7 seconds. Axial strain behavior demonstrated considerable nonlinearity in the first load cycle, while transverse strain behavior was essentially linear. For the human bone 29.1 percent (S.D. = 4.7 percent), and for the bovine bone 35.1 percent (S.D. = 10.8 percent) of the maximum nonlinear strain accumulated after load reversal, where nonlinear strain was defined as the difference between total strain and strain corresponding to linear elastic behavior. Average residual axial strain on unloading was 35.4 percent (S.D. = 1.2 percent) for human bone and 35.1 percent (S.D. = 2.9 percent) of maximum nonlinear strain. Corresponding significant volumetric strains and residual volumetric strains were found. The results support the conclusions that the nonlinear stress-strain behavior observed during creep loading also occurs during transient loading at physiological rates. The volume increases suggest that damage accumulation, i.e., new internal surfaces and voids, plays a major role in this behavior. The residual volume increases and associated disruptions in the internal structure of bone provide a potential stimulus for a biological repair response.     

Time-dependent circumferential deformation of cortical bone upon internal radial loading

Short and long duration tests were conducted on hollow femoral bone cylinders to study the circumferential (hoop) creep response of cortical bone subjected to an intramedullary radial load. It was hypothesized that there is a stress threshold above which nonlinear creep effects dominate the mechanical response and below which the response is primarily determined by linear viscoelastic material properties. The results indicate that a hoop stress threshold exists for cortical bone, where creep strain, creep strain rate and residual strain exhibited linear behavior at low hoop stress and nonlinear behavior above the hoop stress threshold. A power-law relationship was used to describe creep strain as a function of hoop stress and time and damage morphology was assessed.     

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.     

Creep fracture in bones with different stiffnesses.

Creep fracture experiments were used to examine the differences in time to fracture of bones with very different Young's moduli (bovine bone and red deer antler) and the implications of these differences for the 'cumulative-damage' model of Caler and Carter [J. Biomechanics 22, 625-635 (1989)] for bone fracture. Using normalised stress as the explanatory variable, the slopes of the distributions agreed quite well with that of Caler and Carter for human bone. However, antler took far longer to fracture at any given normalised stress than did bovine bone. Using stress alone as the explanatory variable, the relationships within each bone type almost disappeared. Within any bone type strain is the important determinant of time to fracture, but less mineralised bone takes much longer to fracture at any given strain, or normalised stress, which seems not to be in accord with the cumulative-damage model. The rate of damage accumulation in lightly mineralised bone at high strains (greater than 1%) is much less than that occurring in more heavily mineralised bone.     

Understanding site-specific residual strain and architecture in bovine cortical bone

Living bone is considered as adaptive material to the mechanical functions, which continually undergoes change in its histological arrangement with respect to external prolonged loading. Such remodeling phenomena within bone depend on the degree of stimuli caused by the mechanical loading being experienced, and therefore, are specific to the sites. In the attempts of understanding strain adaptive phenomena within bones, different theoretical models have been proposed. Also, the existing literatures mostly follow the measurement of surface strains using strain gauges to experimentally quantify the strains experienced in the functional environment. In this work, we propose a novel idea of understanding site-specific functional adaptation to the prolonged load in bone on the basis of inherited residual strains and structural organization. We quantified the residual strains and amount of apatite crystals distribution, i.e., the degree of orientation, using X-ray diffraction procedures. The sites of naturally existing hole in bone, called foramen, are considered from bovine femur and metacarpal samples. Significant values of residual strains are found to exist in the specimens. Trends of residual strains noted in the specimens are mostly consistent with the degree of orientation of the crystallites. These features explain the response behavior of bone to the mechanical loading history near the foramen sites. Preferential orientation of crystals mapped around a femoral foramen specimen showed furnished tailored arrangement of the crystals around the hole. Effect of external loading at the femoral foramen site is also explained by the tensile loading experiment.     

A phenomenological model for predicting fatigue life in bovine trabecular bone

Cyclic loading of bone during daily activities can lead to fatigue degradation and increased risk of fracture in both the young and elderly population. Damage processes under cyclic loading in trabecular bone result in the reduction of the elastic modulus and accumulation of residual strain. These effects increase with increasing stress levels, leading to a progressive reduction in fatigue life. The present work analyzes the effect of stress and strain variation on the above damage processes in bovine trabecular bone, and develops a phenomenological model relating fatigue life to the imposed stress level. The elastic modulus reduction of the bone specimens was observed to depend on the maximum compressive strain, while the rate of residual strain accumulation was a function of the stress level. A model was developed for the upper and lower bounds of bone elastic modulus reduction with increasing number of cycles, at each stress range. The experimental observations were described well by the model. The model predicted the bounds of the fatigue life with change in fatigue stress. The decrease in the fatigue life with increasing stress was related to corresponding increases in the residual strain accumulation rates at the elevated stress levels. The model shows the validity of fatigue predictions from relatively few cyclic experiments, by combining trends observed in the monotonic and the cyclic tests. The model also presents a relatively simple procedure for predicting the endurance limit for bovine trabecular bone specimens.     

Analysis of the effect of using two different strain rates on the acoustic emission in bone

To study the effect of strain rate on the acoustic emission amplitude signature of bone, bovine cortical bone was milled into standard tensile specimens which were tested at two different strain rates while being monitored with acoustic emission equipment. It was demonstrated that the amplitude distribution of the acoustic events in bone is dependent on strain rate. Greater numbers of events occurred with the slower strain rate (0.0001 s-1), but these events were of lower amplitude than those emitted during the more rapid strain rate (0.01 s-1). The plot of the cumulative event amplitude distribution followed the power-law model, and the slope of this output, the b-value, represented a signature of the amplitude distribution. The mechanical test results were consistent with the behavior of a viscoelastic multi-phase composite material.     

Impact loading history modulates hip fracture load and location: A finite element simulation study of the proximal femur in female athletes

Sideways falls impose high stress on the thin superolateral cortical bone of the femoral neck, the region regarded as a fracture-prone region of the hip. Exercise training is a natural mode of mechanical loading to make bone more robust. Exercise-induced adaptation of cortical bone along the femoral neck has been previously demonstrated. However, it is unknown whether this adaption modulates hip fracture behavior. The purpose of this study was to investigate the influence of specific exercise loading history on fall-induced hip fracture behavior by estimating fracture load and location with proximal femur finite element (FE) models created from magnetic resonance images (MRI) of 111 women with distinct exercise histories: 91 athletes (aged 24.7 ± 6.1 years, >8 years competitive career) and 20 women as controls (aged 23.7 ± 3.8 years). The athletes were divided into five groups based on typical loading patterns of their sports: high-impact (H-I: 9 triple-jumpers and 10 high jumpers), odd-impact (O-I: 9 soccer and 10 squash players), high-magnitude (H-M: 17 power-lifters), repetitive-impact (R-I: 18 endurance runners), and repetitive non-impact (R-NI: 18 swimmers). Compared to the controls, the H-I, O-I, and R-I groups had significantly higher (11–26%, p < 0.05) fracture loads. Also, the fracture location in the H-I and O-I groups was significantly more proximal (7–10%) compared to the controls. These results suggest that an exercise loading history of high impacts, impacts from unusual directions, or repetitive impacts increases the fracture load and may lower the risk of fall-induced hip fracture.     

Fatigue of bovine trabecular bone

Fatigue loading of bone, from the activities of daily living in the elderly, or from prolonged exercise in the young, can lead to increased risk of fracture. Elderly patients with osteoporosis are particularly prone to fragility fractures of the vertebrae, where load is carried primarily by trabecular bone. In this study, specimens of bovine trabecular bone were loaded in compressive fatigue at four different normalized stresses to one of six maximum strains. The resulting change in modulus and residual strain accumulation were measured over the life of the fatigue test. The number of cycles to reach a given maximum compressive strain increased with decreasing normalized stress. Modulus reduction and specimen residual strain increased with increasing maximum compressive strain, but few differences were observed between specimens loaded to the same maximum strain at different normalized stresses.     

Mechanical behaviour of femoral bones in bending loading

A series of 33 human femoral bones have been subjected to a four point bending test at high strain rates. Two different failure modes were recognized. A Y shaped fracture at the middle region induced by a pure bending moment yielded a zone of non-linearity at the load vs deformation curve and a higher bending force, more deformation of the structure and higher strain energy to fracture compared with the less frequently occurring oblique fracture at the distal third of the structure resulting in a failure without a 'plastic' portion at the load-deformation curve. Estimated values of bending modulus and maximum bending moment based upon a simple uniform beam model showed high correlation coefficients with the experimentally determined values. Scanning electron microscopic examination of the Y fracture showed distortion and void formation of the material at the structural level. This could explain the extensive non-elastic deformation prior to failure.     

Biomechanical studies and finite element analysis of a bone-implant interface]

In the present study, the fixation system of a femoral medullary nail connection was investigated. In surgical treatment of fractured femurs, the fracture is bridged by a medullary nail that is fixed by interlocking screws in the bone. Bone failure around these screws is the most common complication associated with the treatment of fractures of osteoporotic bone. The present study analyses the stresses present in the region of the implant/bone system. Three-dimensional finite element models were generated, a nonlinear structure analysis performed, and the stresses at material interfaces investigated. The highest concentration of stresses is to be found in the middle of the interlocking screws and the holes drilled in the bone. This is in agreement with the results of experimental investigations.     

Finite element modeling for strain rate dependency of fracture resistance in compact bone

Crack growths in compact bones driven by various strain rate levels were studied using finite element modeling. The energy resistance curves in bovine femur cortical bones were characterized, whereas the orthotropic viscoelasticity in bone materials was accounted for to assess the effect of strain rate on the energy resistance curve. The models were also used to justify the anticipated plane strain response as a result of rather thick specimens used in experiments. Similarities were found between the experimental and model results when crack resistance ability exhibited in bones with slow loading rates, while unstable crack growth existed in bones with rapid loading rates. The critical energy release rates slightly decreased with the increase in strain rates. The hybrid experimental and computational method introduced in this study could be beneficial for application in fracture study in which standard experiments cannot be validly performed.     

Predictions of Birmingham hip resurfacing implant offset - In vitro and numerical models

The number of hip resurfacing arthroplasty procedures has declined dramatically in recent years, for reasons related to the survival rate. Some studies suggest that metal particles are the main critical problem, but do not specify the effect of femoral position on the failure rate. The present study aims to analyze whether the positioning of the resurfacing head implant is important in the distribution of bone strains and in the risk of fracture of the femur.

Three in vitro experimental models received the Birmingham hip resurfacing implant to replicate the total hip joint. The resurfacing head of the implanted models was placed in three different offset positions: in a positive offset, with the same femoral head center and in a negative offset.

The numerical models were validated by correlating numerical and experimental results. Comparing experimental results from the implanted and intact femurs highlights a strain increase of up to 48% in the proximal medial femur region for positive offset and up to 18% in the neutral position. A reduction of 72% for negative offset (valgus position) was also measured experimentally.

A significant change in strain distributions was observed with a resurfacing hip system and increased risk of neck fracture was found using the resurfacing head in positive offset. The iliac bone presents a high decrease in strains that will induce bone loss in the long term. Among the offset positions tested, results suggest that the negative offset (valgus position) and the natural position are the best equilibrated for better long-term results.     

Dynamic, regional mechanical properties of the porcine brain: indentation in the coronal plane

Stress relaxation tests using a custom designed microindentation device were performed on ten anatomic regions of fresh porcine brain (postmortem time <3 h). Using linear viscoelastic theory, a Prony series representation was used to describe the shear relaxation modulus for each anatomic region tested. Prony series parameters fit to load data from indentations performed to ～10% strain differed significantly by anatomic region. The gray and white matter of the cerebellum along with corpus callosum and brainstem were the softest regions measured. The cortex and hippocampal CA1/CA3 were found to be the stiffest. To examine the large strain behavior of the tissue, multistep indentations were performed in the corona radiata to strains of 10%, 20%, and 30%. Reduced relaxation functions were not significantly different for each step, suggesting that quasi-linear viscoelastic theory may be appropriate for representing the nonlinear behavior of this anatomic region of porcine brain tissue. These data, for the first time, describe the dynamic and short time scale behavior of multiple anatomic regions of the porcine brain which will be useful for understanding porcine brain injury biomechanics at a finer spatial resolution than previously possible.