Cosserat micromechanics of human bone: strain redistribution by a hydration sensitive constituent

Analysis of micropolar elastic multi-laminated composite and its application to bioceramic materials for bone reconstruction

The asymptotic homogenization method is applied to characterize the effective behaviour of periodic multi-laminated micropolar elastic heterogeneous composites under perfect contact conditions. The local problem formulations and the analytical expressions for the effective stiffness and torque coefficients are derived for the centrosymmetric case. One of the main findings in this work is the analysis of the rotations effect of the layers' constitutive properties on the mechanical response of bi-laminated composites. The effects of microstructure and interfacial interactions on the composite's mechanical behaviour are captured through the independent effective moduli. Comparisons with the classical elastic case show the approach validation. Some numerical examples are shown. Furthermore, considering the micropolar media's prevalence in bio-inspired systems, the model's applicability is evaluated for reconstructing bone fractures using multi-laminated biocomposites. An important finding in this bio-inspired simulation is related to the analysis of a periodic bi-laminated micropolar composite whose isotropic constituents are a bioceramic material and a compact bone. This artificial bio-inspired material should integrate with host tissue to support cell growth and be stable and compatible. These characteristics are crucial in the enhancement of the fractured bone.

An orthotropic continuum model with substructure evolution for describing bone remodeling: an interpretation of the primary mechanism behind Wolff's law

We propose a variational approach that employs a generalized principle of virtual work to estimate both the mechanical response and the changes in living bone tissue during the remodeling process. This approach provides an explanation for the adaptive regulation of the bone substructure in the context of orthotropic material symmetry. We specifically focus upon the crucial gradual adjustment of bone tissue as a structural material that adapts its mechanical features, such as materials stiffnesses and microstructure, in response to the evolving loading conditions. We postulate that the evolution process relies on a feedback mechanism involving multiple stimulus signals. The mechanical and remodeling behavior of bone tissue is clearly a complex process that is difficult to describe within the framework of classical continuum theories. For this reason, a generalized continuum elastic theory is employed as a proper mathematical context for an adequate description of the examined phenomenon. To simplify the investigation, we considered a two-dimensional problem. Numerical simulations have been performed to illustrate bone evolution in a few significant cases: the bending of a rectangular cantilever plate and a three-point flexure test. The results are encouraging because they can replicate the optimization process observed in bone remodeling. The proposed model provides a likely distribution of stiffnesses and accurately represents the arrangement of trabeculae macroscopically described by the orthotropic symmetry directions, as supported by experimental evidence from the trajectorial theory.

Numerical analysis of hip fracture due to a sideways fall

The primary purpose of this paper is to outline a methodology for evaluating the likelihood of cortical bone fracture in the proximal femur in the event of a sideways fall. The approach includes conducting finite element (FE) analysis in which the cortical bone is treated as an anisotropic material, and the admissibility of the stress field is validated both in tension and compression regime. In assessing the onset of fracture, two methodologies are used, namely the Critical Plane approach and the Microstructure Tensor approach. The former is employed in the tension regime, while the latter governs the conditions at failure in compression. The propagation of localized damage is modeled using a constitutive law with embedded discontinuity (CLED). In this approach, the localized deformation is described by a homogenization procedure in which the average properties of cortical tissue intercepted by a macrocrack are established. The key material properties governing the conditions at failure are specified from a series of independent material tests conducted on cortical bone samples tested at different orientations relative to the loading direction. The numerical analysis deals with simulations of experiments involving the sideways fall, and the results are compared with the experimental data. This includes both the evolution of fracture pattern and the local load-displacement characteristics. The proposed approach is numerically efficient, and the results do not display a pathological mesh-dependency. Also, in contrast to the XFEM approach, the analysis does not require any extra degrees of freedom.

On Dynamic Extension of a Local Material Symmetry Group for Micropolar Media

For micropolar media we present a new definition of the local material symmetry group considering invariant properties of the both kinetic energy and strain energy density under changes of a reference placement. Unlike simple (Cauchy) materials, micropolar media can be characterized through two kinematically independent fields, that are translation vector and orthogonal microrotation tensor. In other words, in micropolar continua we have six degrees of freedom (DOF) that are three DOFs for translations and three DOFs for rotations. So the corresponding kinetic energy density nontrivially depends on linear and angular velocity. Here we define the local material symmetry group as a set of ordered triples of tensors which keep both kinetic energy density and strain energy density unchanged during the related change of a reference placement. The triples were obtained using transformation rules of strain measures and microinertia tensors under replacement of a reference placement. From the physical point of view, the local material symmetry group consists of such density-preserving transformations of a reference placement, that cannot be experimentally detected. So the constitutive relations become invariant under such transformations. Knowing a priori a material’s symmetry, one can establish a simplified form of constitutive relations. In particular, the number of independent arguments in constitutive relations could be significantly reduced.

THEORETICAL ANALYSIS OF THE LEAKAGE THROUGH THE CEMENT LINE OF A SINGLE OSTEON

This work focuses on the Lacunar–Canalicular Porosity (PLC) of cortical bone which includes the osteons. Osteons are semicylindrical porous structures saturated with fluid within the bone and are approximately 250[Formula: see text][Formula: see text]m in diameter. The outer boundary of the osteon is called the cement line. Some studies suggested that the cement line is less highly mineralized and produced evidence that it has less calcium and phosphorus and more sulfur than the neighboring bone lamellae. Most authors assume that the cement line is impermeable, while others assume that some canaliculi are crossing the cement line which will make it permeable to certain degree. The objective of this work is to develop a theoretical analysis to study the leakage through the cement line and its relationship with the pore pressure distribution. The theoretical analysis is developed using our previous analysis for osteon under harmonic loading with addition of leakage parameter. The leakage parameter varies from 0 to 1, where a value of 0 indicates free flow through the cement line and a value of 1 indicates no flow through the cement line. Experimental results could be compared to this developed theoretical solution to get in depth understanding of the effect of leakage on osteon poroelastic properties. Additionally, the developed theoretical solution will give insight into sensitivity of osteon pore pressure to leakage through the cement line.

A review of recent developments in mathematical modeling of bone remodeling

In this article, we summarize the developments in the mathematical modeling of the mechanics of bone and related biological phenomena. We will devote special attention to the results of the last 10–15 years, although we will cover some relevant classical work to better frame the more recent researches. We will propose a division of the literature based on the main aim of the model (mechanical/biomathematical) and the type of biological phenomena considered (stimulus, growth, cell population dynamics). Finally, we will suggest some possible directions for future investigations.

Effect of athletic fatigue damage and the associated bone targeted remodeling in the rat ulna

Background

Fatigue damage of the long bones is prevalent in running athletes and military recruits due to vigorous mid- and long-term physical activity. The current study attempted to know the features of bony athletic fatigue damage and to explore the mechanism of fatigue damage repair through bone targeted remodeling process.

Methods

Right ulnae of the Wistar rats were fatigue loaded on an INSTRON 5865 to construct the athletic fatigue damage model, and several time points (i.e. experimental days: 0, 7, 13 and 19) were selected to simulate physiological status, preliminary, mid-term and perennial stage during continuous high-intensive training, respectively. The multi-level responses of rat ulnae under the athletic fatigue loading, including cellular protein expression, micro damage or micro-crack and macro mechanical properties, were tested and statistically analyzed.

Results

Wistar rats, subjected to the athletic fatigue loading protocol, experienced a decrease of ulna fatigue mechanical properties and an active bone resorption of the loaded ulnae in the early stage, whereafter, a hyperactive bone formation and significant improvements of ulnae fatigue mechanical properties were detected. However, a deterioration of quasi-static mechanical properties in the subsequent period implied limitations of bone remodeling to maintain the bearing capacity of bone during long-term strenuous exercise.

Conclusions

In summary, after athletic fatigue loading, bone targeted remodeling is activated and proceeds to repair fatigue damage, but only to a certain extent.

Compressive rib fracture: peri-mortem and post-mortem trauma patterns in a pig model

Despite numerous studies on high impact fractures of ribs, little is known about compressive rib injuries. We studied rib fractures from a biomechanical and morphological perspective using 15, 5th ribs of domestic pigs Sus scrofa, divided into two groups, desiccated (representing post-mortem trauma) and fresh ribs with intact periosteum (representing peri-mortem trauma). Ribs were axially compressed and subjected to four-point bending in an Instron 3339 fitted with custom jigs. Morphoscopic analysis of resultant fractures consisted of standard optical methods, micro-CT (μCT) and scanning electron microscopy (SEM). During axial compression, fresh ribs had slightly higher strength because of energy absorption capabilities of their soft and fluidic components. In flexure tests, dry ribs showed typical elastic-brittle behaviour with long linear load-extension curves, followed by relatively short non-linear elastic (hyperelastic) behaviour and brittle fracture. Fresh ribs showed initial linear-elastic behaviour, followed by strain softening, visco-plastic responses. During the course of loading, dry bone showed minimal observable damage prior to the onset of unstable fracture. In contrast, fresh bone showed buckling-like damage features on the compressive surface and cracking parallel to the axis of the bone. Morphologically, all dry ribs fractured precipitously, whereas all but one of the fresh ribs showed incomplete fracture. The mode of fracture, however, was remarkably similar for both groups, with butterfly fractures predominating (7/15, 46.6% dry and wet). Our study highlights the fact that under controlled loading, despite seemingly similar butterfly fracture morphology, fresh ribs (representing perimortem trauma) show a non-catastrophic response. While extensive strain softening observed for the fresh bone does show some additional micro-cracking damage, it appears that the periosteum may play a key role in imparting the observed pseudo-ductility to the ribs. The presence of fibrous pull-out and grooving of the outer tensile surface associated with periosteal stretching suggests that the periosteum under tension is able to sustain very high strain and bridge the mouth of the extending butterfly crack, thereby contributing to the observed strain-softening behaviour.

Micromechanical model of a surrogate for collagenous soft tissues: development, validation and analysis of mesoscale size effects

Aligned, collagenous tissues such as tendons and ligaments are composed primarily of water and type I collagen, organized hierarchically into nanoscale fibrils, microscale fibers and mesoscale fascicles. Force transfer across scales is complex and poorly understood. Since innervation, the vasculature, damage mechanisms and mechanotransduction occur at the microscale and mesoscale, understanding multiscale interactions is of high importance. This study used a physical model in combination with a computational model to isolate and examine the mechanisms of force transfer between scales. A collagen-based surrogate served as the physical model. The surrogate consisted of extruded collagen fibers embedded within a collagen gel matrix. A micromechanical finite element model of the surrogate was validated using tensile test data that were recorded using a custom tensile testing device mounted on a confocal microscope. Results demonstrated that the experimentally measured macroscale strain was not representative of the microscale strain, which was highly inhomogeneous. The micromechanical model, in combination with a macroscopic continuum model, revealed that the microscale inhomogeneity resulted from size effects in the presence of a constrained boundary. A sensitivity study indicated that significant scale effects would be present over a range of physiologically relevant inter-fiber spacing values and matrix material properties. The results indicate that the traditional continuum assumption is not valid for describing the macroscale behavior of the surrogate and that boundary-induced size effects are present.

NEW MECHANICS OF GENERIC MUSCULO-SKELETAL INJURY

Prediction and prevention of musculo-skeletal injuries is an important aspect of preventive health science. Using as an example a human knee joint, this paper proposes a new coupled-loading-rate hypothesis, which states that a generic cause of any musculo-skeletal injury is a Euclidean jolt, or SE(3)-jolt, an impulsive loading that hits a joint in several coupled degrees-of-freedom simultaneously. Informally, it is a rate-of-change of joint acceleration in all six-degrees-of-freedom simultaneously, times the corresponding portion of the body mass. In the case of a human knee, this happens when most of the body mass is on one leg with a semi-flexed knee — and then, caused by some external shock, the knee suddenly "jerks"; this can happen in running, skiing, sports games (e.g., soccer, rugby) and various crashes/impacts. To show this formally, based on the previously defined covariant force law and its application to traumatic brain injury (Ref. 52), we formulate the coupled Newton–Euler dynamics of human joint motions and derive from it the corresponding coupled SE(3)-jolt dynamics of the joint in case. The SE(3)-jolt is the main cause of two forms of discontinuous joint injury: (i) mild rotational disclinations and (ii) severe translational dislocations. Both the joint disclinations and dislocations, as caused by the SE(3)-jolt, are described using the Cosserat multipolar viscoelastic continuum joint model.

Scale and boundary conditions effects on the apparent elastic moduli of trabecular bone modeled as a periodic cellular solid

We study apparent elastic moduli of trabecular bone, which is represented, for simplicity, by a two- or three-dimensional periodic cellular network. The term "apparent" refers to the case when the region used in calculations (or specimen size) is smaller than a representative volume element and the moduli depend on the size of that region and boundary conditions. Both the bone tissue forming the network and the pores (represented by a very soft material) are assumed, for simplicity, as homogeneous, linear elastic, and isotropic. In order to investigate the effects of scale and boundary conditions on the moduli of these networks we vary the specimen size and apply four different boundary conditions: displacement, traction, mixed, and periodic. The analysis using periodic boundary conditions gives the effective moduli, while the displacement, traction, and mixed boundary conditions give apparent moduli. The apparent moduli calculated using displacement and traction boundary conditions bound the effective moduli from above and below, respectively. The larger is the size of the region used in our calculations, the closer are the bounds. Our choice of mixed boundary conditions gives results that are very close to those obtained using periodic boundary conditions. We conduct this analysis computationally using a finite element method. We also investigate the effect of mismatch in elastic moduli of bone tissue and soft fill, trabecular bone structure geometry, and bone tissue volume fraction on the apparent elastic moduli of idealized periodic models of trabecular bone. This study gives guidance on how the size of the specimen and boundary conditions (used in experiments or simulations) influence elastic moduli of cellular materials. This approach is applicable to heterogeneous materials in general.

New mechanics of traumatic brain injury

The prediction and prevention of traumatic brain injury is a very important aspect of preventive medical science. This paper proposes a new coupled loading-rate hypothesis for the traumatic brain injury (TBI), which states that the main cause of the TBI is an external Euclidean jolt, or SE(3)-jolt, an impulsive loading that strikes the head in several coupled degrees-of-freedom simultaneously. To show this, based on the previously defined covariant force law, we formulate the coupled Newton-Euler dynamics of brain's micro-motions within the cerebrospinal fluid and derive from it the coupled SE(3)-jolt dynamics. The SE(3)-jolt is a cause of the TBI in two forms of brain's rapid discontinuous deformations: translational dislocations and rotational disclinations. Brain's dislocations and disclinations, caused by the SE(3)-jolt, are described using the Cosserat multipolar viscoelastic continuum brain model.

Velocity dispersion of guided waves propagating in a free gradient elastic plate: application to cortical bone

The classical linear theory of elasticity has been largely used for the ultrasonic characterization of bone. However, linear elasticity cannot adequately describe the mechanical behavior of materials with microstructure in which the stress state has to be defined in a non-local manner. In this study, the simplest form of gradient theory (Mindlin Form-II) is used to theoretically determine the velocity dispersion curves of guided modes propagating in isotropic bone-mimicking plates. Two additional terms are included in the constitutive equations representing the characteristic length in bone: (a) the gradient coefficient g, introduced in the strain energy, and (b) the micro-inertia term h, in the kinetic energy. The plate was assumed free of stresses and of double stresses. Two cases were studied for the characteristic length: h=10(-4) m and h=10(-5) m. For each case, three subcases for g were assumed, namely, g>h, g<h, and g=h. The values of g and h were of the order of the osteons size. The velocity dispersion curves of guided waves were numerically obtained and compared with the Lamb modes. The results indicate that when g was not equal to h (i.e., g not equal h), microstructure affects mode dispersion by inducing both material and geometrical dispersion. In conclusion, gradient elasticity can provide supplementary information to better understand guided waves in bones.

Couple-stress moduli of a trabecular bone idealized as a 3D periodic cellular network

Trabecular bone is modeled as a cellular material with an idealized periodic structure made of open cubic cells, which is effectively orthotropic. We evaluate apparent couple-stress moduli of such a periodic material; apparent moduli refer to the moduli obtained using a domain smaller than a Representative Volume Element and they depend on boundary conditions. We conduct this analysis computationally (using ANSYS) by subjecting a unit cell of this periodic cellular material to either displacement or traction boundary conditions. Cell walls, representing bone tissue, and void space, representing bone marrow, are both modeled and they are assumed to be linear elastic. The applied loadings include a uniaxial extension (or uniaxial stress), a hydrostatic deformation (or hydrostatic stress) and a shear deformation (or shear stress) to evaluate the first stiffness (or compliance) tensor, and an applied curvature (or bending moment), a uniaxial twist (or torsion), and a triaxial twist (or triaxial torsion) to evaluate the second couple-stress stiffness (or compliance) tensor. Apparent couple-stress moduli are computed by equating the total strain energy stored in the unit cell with the energy of an equivalent homogeneous orthotropic couple-stress material for each applied loading. The moduli computed using displacement boundary conditions give upper bound, while those obtained using traction boundary conditions give lower bound on effective couple-stress moduli. These bounds are very wide due to a large mismatch in elastic moduli of bone tissue and bone marrow. These results are in agreement with our studies on composite materials with very stiff or very compliant inclusions.

Experimental investigation on the role of water in the mechanical behavior of structural dentine

Dentine is a porous hydrated composite structure that forms the major bulk of the human tooth. The aim of this study was to investigate the role of free water on the in-plane, mechanical strain response in dentine structure. A digital moire interferometry was used for this purpose. It was observed from this experiment that structural dentine demonstrated distinct strain gradients in the axial (perpendicular to the dentinal tubules) and lateral (parallel to the dentinal tubules) directions. The hydrated dentine displayed significant increase in strain with stress in the direction perpendicular to the dentinal tubules, and this response was characteristic of a tough material. On the contrary, the dehydrated dentine, which was dehydrated at 24 degrees C, 55% relative humidity for 72 h showed a strain response characteristic of a brittle material. The strains formed in the direction parallel to the dentinal tubules for hydrated dentine were consistent and did not vary much with increase in applied loads. Upon dehydration, the outer dentine experienced higher strains, and the difference between the outer and inner dentine became more conspicuous with increase in loads. This experiment highlights hydration-induced, distinct in-plane strain gradients in the directions perpendicular and parallel to the dentinal tubules in the dentine structure.

Cement lines of secondary osteons in human bone are not mineral-deficient: New data in a historical perspective

Using qualitative backscattered electron (BSE) imaging and quantitative energy dispersive X-ray (EDX) spectroscopy, some investigators have concluded that cement (reversal) lines located at the periphery of secondary osteons are poorly mineralized viscous interfaces with respect to surrounding bone. This conclusion contradicts historical observations of apparent highly mineralized (or collagen-deficient) cement lines in microradiographs. Such conclusions, however, may stem from unrecognized artifacts that can occur during scanning electron microscopy. These include specimen degradation due to high-energy beams and the sampling of electron interaction volumes that extend beyond target locations during EDX analysis. This study used quantitative BSE imaging and EDX analysis, each with relatively lower-energy beams, to test the hypothesis that cement lines are poorly mineralized. Undemineralized adult human femoral diaphyses (n = 8) and radial diaphyses (n = 5) were sectioned transversely, embedded in polymethyl methacrylate, and imaged in a scanning electron microscope for BSE and EDX analyses. Unembedded samples were also evaluated. Additional thin embedded samples were stained and evaluated with light microscopy and correlated BSE imaging. BSE analyses showed the consistent presence of a bright line (higher atomic number) coincident with the classical location and description of the cement line. This may represent relative hypermineralization or, alternatively, collagen deficiency with respect to surrounding bone. EDX analyses of cement lines showed either higher Ca content or equivalent Ca content when compared to distant osteonal and interstitial bone. These data reject the hypothesis that cement lines of secondary osteons are poorly mineralized.

Microcrack accumulation at different intervals during fatigue testing of compact bone

Fatigue damage in bone occurs in the form of microcracks. This microdamage contributes to the formation of stress fractures and acts as a stimulus for bone remodelling. A technique has been developed, which allows microcrack growth to be monitored during the course of a fatigue test by the application of a series of fluorescent chelating agents. Specimens were taken from bovine tibiae and fatigue tested in cyclic compression at a stress range of 80MPa. The specimens were stained before testing with alizarin and up to three other chelating agents were applied during testing to label microcracks formed at different times. Microcracks initiated in interstitial bone in the early part of a specimen's life. Further accumulation of microcracks is then suppressed until the period late in the specimen's life. Microcracks were found to be longer in the longitudinal than in the transverse direction. Only a small proportion of cracks are actively propagating; these are longer than non-propagating cracks. These results support the concept of a microstructural barrier effect existing in bone, whereby cracks initiate easily but slow down or stop at barriers such as cement lines.

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.

Fracture toughness of bovine bone: influence of orientation and storage media

Using the single-edge notched bending (SENB) test, two fracture toughness parameters of longitudinal and transverse bovine bone specimens were evaluated: the critical stress intensity factor, Kc, determined from the peak load to initiate fracture, and the energy or work of fracture, Wf, the energy required to extend a crack through a notched specimen. It was found that preservation of bone in alcohol resulted in a 25-45% higher Kc value compared to control specimens stored in physiological saline; whereas the work of fracture, Wf, demonstrated the opposite behaviour, with the alcohol stored specimens having a 28-56% lower value than the saline control specimens. It was established that the effect of alcohol is reversible upon the bone being restored in saline. Consistent with previous studies, it was found that cracks oriented in the longitudinal direction resulted in both a significantly lower fracture toughness and lower work of fracture than those cracks directed transversely. The results are discussed in terms of the proposed deformation and fracture mechanisms known to occur in bone.

Quantitative assessment of in vivo bone regeneration consolidation in distraction osteogenesis

We present a new method for quantitatively assessing the consolidation of bone regeneration by performing distraction osteogenesis in micropigs. We measured in vivo stiffness using a newly developed, revolving, bone-healing meter. After the micropigs were killed, we obtained maximum torsional moment data for the regenerated bones by destructive mechanical testing, and we then correlated these data with the data for stiffness. We found a highly significant regression between in vivo stiffness and maximum torsional moment (r2 = 0.80), suggesting that monitoring stiffness may be useful for the prediction of bone regeneration in distraction osteogenesis. Therefore, our method may be a reliable tool for future quantitative monitoring of healing progress in patients with healing bones or in animal studies addressing treatments to increase bone formation in long-bone defects.

Calculation of porosity and osteonal cement line effects on the effective fracture toughness of cortical bone in longitudinal crack growth

Based on the microscopic analyses of cracks and correlational studies demonstrating evidence for a relationship between fracture toughness and microstructure of cortical bone, an equation was derived for bone fracture toughness in longitudinal crack growth, using debonding at osteonal cement lines and weakening effect of pores as main crack mechanisms. The correlation between the measured and predicted values of fracture toughness was highly significant but weak for a single optimal value of matrix to cement line fracture toughness ratio. Using fracture toughness values and histomorphometrical parameters from an available data set, matrix to cement line fracture toughness ratio was calculated for human femoral bone. Based on these calculations it is suggested that the effect of an osteon on fracture toughness will depend on the cement line's ability to compensate for the pore in an osteon. Matrix to cement line fracture toughness ratio significantly increased with increasing age, suggesting that the effectiveness of osteons in energy absorption may be reduced in the elderly due to a change in cement line properties.

Viscoelastic dissipation in compact bone: implications for stress-induced fluid flow in bone

Viscoelastic properties of wet and dry human compact bone were studied in torsion and in bending for both the longitudinal and transverse directions at frequencies from 5 mHz to 5 kHz in bending to more than 50 kHz in torsion. Two series of tests were done for different longitudinal and transverse specimens from a human tibia. Wet bone exhibited a larger viscoelastic damping tan delta (phase between stress and strain sinusoids) than dry bone over a broad range of frequency. All the results had in common a relative minimum in tan delta over a frequency range, 1 to 100 Hz, which is predominantly contained in normal activities. This behavior is inconsistent with an optimal "design" for bone as a shock absorber. There was no definitive damping peak in the range of frequencies explored, which could be attributed to fluid flow in the porosity of bone.

Results from demineralized bone creep tests suggest that collagen is responsible for the creep behavior of bone

Cortical and trabecular bone have similar creep behaviors that have been described by power-law relationships, with increases in temperature resulting in faster creep damage accumulation according to the usual Arrhenius (damage rate approximately exp (-Temp.-1)) relationship. In an attempt to determine the phase (collagen or hydroxyapatite) responsible for these similar creep behaviors, we investigated the creep behavior of demineralized cortical bone, recognizing that the organic (i.e., demineralized) matrix of both cortical and trabecular bone is composed primarily of type I collagen. We prepared waisted specimens of bovine cortical bone and demineralized them according to an established protocol. Creep tests were conducted on 18 specimens at various normalized stresses sigma/E0 and temperatures using a noninvasive optical technique to measure strain. Denaturation tests were also conducted to investigate the effect of temperature on the structure of demineralized bone. The creep behavior was characterized by the three classical stages of decreasing, constant, and increasing creep rates at all applied normalized stresses and temperatures. Strong (r2 > 0.79) and significant (p < 0.01) power-law relationships were found between the damage accumulation parameters (steady-state creep rate d epsilon/dt and time-to-failure tf) and the applied normalized stress sigma/E0. The creep behavior was also a function of temperature, following an Arrhenius creep relationship with an activation energy Q = 113 kJ/mole, within the range of activation energies for cortical (44 kJ/mole) and trabecular (136 kJ/mole) bone. The denaturation behavior was characterized by axial shrinkage at temperatures greater than approximately 56 degrees C. Lastly an analysis of covariance (ANCOVA) of our demineralized cortical bone regressions with those found in the literature for cortical and trabecular bone indicates than all three tissues creep with the same power-law exponents. These similar creep activation energies and exponents suggest that collagen is the phase responsible for creep in bone.

The effects of dehydration and rehydration on some mechanical properties of human dentine

This study was designed to investigate the effect of dehydration and rehydration on the brittleness and toughness of human dentine. Tensile and three-point bend tests were carried out on hydrated, dehydrated and rehydrated dentine bars, sectioned from sound extracted, human third molar teeth. The stress, strain and fracture energy (toughness) were calculated and the results were analysed using ANOVA and Duncan's multiple range test at p = 0.01. Stress at fracture did not differ significantly between hydrated, dehydrated or rehydrated dentine in bending or tensile tests. Strain at fracture and fracture energy were significantly greater for hydrated and rehydrated than for dehydrated dentine. In bending, the elastic energy (resilience) of dehydrated dentine was significantly greater than that of hydrated or rehydrated dentine, but dehydrated dentine showed no plastic energy (deformation) in contrast with the high values for hydrated and rehydrated dentine. Dehydration of human dentine resulted in decreased strain at fracture and demonstrated a brittle behaviour. The absence of plastic energy of deformation and the significantly reduced energy required to induce fracture were indicative of decreased toughness by dehydration. These changes were abolished after rehydration.

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.

Bone creep-fatigue damage accumulation

Creep and fatigue tests were performed on human femoral cortical bone and the results were compared to a cumulative damage model for bone fracture. Fatigue tests in tension, compression, and reversed loading with a tensile mean stress were conducted at 2 Hz and 0.02 Hz. Load frequency had a strong influence on the number of cycles to failure but did not influence the total time to failure. Bone displayed poor creep-fracture properties in both tension and compression. The fracture surfaces of the tensile creep specimens are distinctly different than those of the compressive specimens. The results suggest that tensile cyclic loading creates primarily time-dependent damage and compressive cyclic loading creates primarily cycle-dependent damage. However, data for load histories involving both tensile and compressive loading indicate lower time to failure than predicted by a simple summation of time-dependent and cycle-dependent damage.

Composition of the cement line and its possible mechanical role as a local interface in human compact bone

Human compact bone may be viewed as a fiber reinforced composite material in which the secondary osteons act as the fiber reinforcements. The cement line, which is the interface between the 'fibers' (osteons) and extraosteonal bone matrix, may impart important mechanical properties to compact bone. The nature of these properties is not known partly because the composition of the cement line is unknown. This analysis examines the constituents of the osteon cement line using scanning electron microscopy and X-ray microprobe analysis to address its biomechanical functions as a local interface. The analysis suggests that the cement line is a region of reduced mineralization which may contain sulfated mucosubstances. This composition is consistent with the hypothesis that the cement line provides a relatively ductile interface with surrounding bone matrix, and that it provides the point specific stiffness differences, poor 'fiber'-matrix bonding and energy transfer qualities required to promote crack initiation but slow crack growth in compact bone.