The mechanics of microdamage and microfracture in trabecular bone

This thesis presents a study using mechanical testing techniques combined with advanced computational methods to examine the mechanics of bone. It contributes novel observations and analysis of how bones fail at the microscopic level, which will be valuable in furthering our understanding and the treatment of bone damage in health and disease, including osteoporosis.

Nonlinear analysis for the pre- and post-yield behaviour of a hybrid structure by a higher-order element with the refined plastic hinge approach

Efficient and accurate geometric and material nonlinear analysis of the structures under ultimate loads is a backbone to the success of integrated analysis and design, performance-based design approach and progressive collapse analysis. This paper presents the advanced computational technique of a higher-order element formulation with the refined plastic hinge approach which can evaluate the concrete and steel-concrete structure prone to the nonlinear material effects (i.e. gradual yielding, full plasticity, strain-hardening effect when subjected to the interaction between axial and bending actions, and load redistribution) as well as the nonlinear geometric effects (i.e. second-order P-d effect and P-D effect, its associate strength and stiffness degradation). Further, this paper also presents the cross-section analysis useful to formulate the refined plastic hinge approach.

Nonlinear analysis for the pre- and post-yield behaviour of a composite structure with the refined plastic hinge approach

The computational technique of the full ranges of the second-order inelastic behaviour evaluation of steel-concrete composite structure is not always sought forgivingly, and therefore it hinders the development and application of the performance-based design approach for the composite structure. To this end, this paper addresses of the advanced computational technique of the higher-order element with the refined plastic hinges to capture the all-ranges behaviour of an entire steel-concrete composite structure. Moreover, this paper presents the efficient and economical cross-section analysis to evaluate the element section capacity of the non-uniform and arbitrary composite section subjected to the axial and bending interaction. Based on the same single algorithm, it can accurately and effectively evaluate nearly continuous interaction capacity curve from decompression to pure bending technically, which is the important capacity range but highly nonlinear. Hence, this cross-section analysis provides the simple but unique algorithm for the design approach. In summary, the present nonlinear computational technique can simulate both material and geometric nonlinearities of the composite structure in the accurate, efficient and reliable fashion, including partial shear connection and gradual yielding at pre-yield stage, plasticity and strain-hardening effect due to axial and bending interaction at post-yield stage, loading redistribution, second-order P-δ and P-Δ effect, and also the stiffness and strength deterioration. And because of its reliable and accurate behavioural evaluation, the present technique can be extended for the design of the high-strength composite structure and potentially for the fibre-reinforced concrete structure.

Single-subject analysis reveals varied knee mechanics during step landing in response to isokinetic fatigue of the quadriceps

Introduction: The ability to regulate joint stiffness and coordinate movement during landing when impaired by muscle fatigue has important implications for knee function. Unfortunately, the literature examining fatigue effects on landing mechanics suffers from a lack of consensus. Inconsistent results can be attributed to variable fatigue models, as well as grouping variable responses between individuals when statistically detecting differences between conditions. There remains a need to examine fatigue effects on knee function during landing with attention to these methodological limitations. Aim: The purpose of this study therefore, was to examine the effects of isokinetic fatigue on pre-impact muscle activity and post-impact knee mechanics during landing using singlesubject analysis. Methodology: Sixteen male university students (22.6+3.2 yrs; 1.78+0.07 m; 75.7+6.3 kg) performed maximal concentric and eccentric knee extensions in a reciprocal manner on an isokinetic dynamometer and step-landing trials on 2 occasions. On the first occasion each participant performed 20 step-landing trials from a knee-high platform followed by 75 maximal contractions on the isokinetic dynamometer. The isokinetic data was used to calculate the operational definition of fatigue. On the second occasion, with a minimum rest of 14 days, participants performed 2 sets of 20 step landing trials, followed by isokinetic exercise until the operational definition of fatigue was met and a final post-fatigue set of 20 step-landing trials. Results: Single-subject analyses revealed that isokinetic fatigue of the quadriceps induced variable responses in pre impact activation of knee extensors and flexors (frequency, onset timing and amplitude) and post-impact knee mechanics(stiffness and coordination). In general however, isokinetic fatigue induced sig nificant (p<0.05) reductions in quadriceps activation frequency, delayed onset and increased amplitude. In addition, knee stiffness was significantly (p<0.05) increased in some individuals, as well as impaired sagittal coordination. Conclusions: Pre impact activation and post-impact mechanics were adjusted in patterns that were unique to the individual, which could not be identified using traditional group-based statistical analysis. The results suggested that individuals optimised knee function differently to satisfy competing demands, such as minimising energy expenditure, as well as maximising joint stability and sensory information.

The effects of muscle fatigue on knee function during landing

The human knee acts as a sophisticated shock absorber during landing movements. The ability of the knee to perform this function in the real world is remarkable given that the context of the landing movement may vary widely between performances. For this reason, humans must be capable of rapidly adjusting the mechanical properties of the knee under impact load in order to satisfy many competing demands. However, the processes involved in regulating these properties in response to changing constraints remain poorly understood. In particular, the effects of muscle fatigue on knee function during step landing are yet to be fully explored. Fatigue of the knee muscles is significant for 2 reasons. First, it is thought to have detrimental effects on the ability of the knee to act as a shock absorber and is considered a risk factor for knee injury. Second, fatigue of knee muscles provides a unique opportunity to examine the mechanisms by which healthy individuals alter knee function. A review of the literature revealed that the effect of fatigue on knee function during landing has been assessed by comparing pre and postfatigue measurements, with fatigue induced by a voluntary exercise protocol. The information is limited by inconsistent results with key measures, such as knee stiffness, showing varying results following fatigue, including increased stiffness, decreased stiffness or failure to detect any change in some experiments. Further consideration of the literature questions the validity of the models used to induce and measure fatigue, as well as the pre-post study design, which may explain the lack of consensus in the results. These limitations cast doubt on the usefulness of the available information and identify a need to investigate alternative approaches. Based on the results of this review, the aims of this thesis were to: • evaluate the methodological procedures used in validation of a fatigue model • investigate the adaptation and regulation of post-impact knee mechanics during repeated step landings • use this new information to test the effects of fatigue on knee function during a step-landing task. To address the aims of the thesis, 3 related experiments were conducted that collected kinetic, kinematic and electromyographic data from 3 separate samples of healthy male participants. The methodologies involved optoelectronic motion capture (VICON), isokinetic dynamometry (System3 Pro, BIODEX) and wireless surface electromyography (Zerowire, Aurion, Italy). Fatigue indicators and knee function measures used in each experiment were derived from the data. Study 1 compared the validity and reliability of repetitive stepping and isokinetic contractions with respect to fatigue of the quadriceps and hamstrings. Fifteen participants performed 50 repetitions of each exercise twice in randomised order, over 4 sessions. Sessions were separated by a minimum of 1 week’s rest, to ensure full recovery. Validity and reliability depended on a complex interaction between the exercise protocol, the fatigue indicator, the individual and the muscle of interest. Nevertheless, differences between exercise protocols indicated that stepping was less effective in eliciting valid and reliable changes in peak power and spectral compression, compared with isokinetic exercise. A key finding was that fatigue progressed in a biphasic pattern during both exercises. The point separating the 2 phases, known as the transition point, demonstrated superior between-test reliability during the isokinetic protocol, compared with stepping. However, a correction factor should be used to accurately apply this technique to the study of fatigue during landing. Study 2 examined alterations in knee function during repeated landings, with a different sample (N =12) performing 60 consecutive step landing trials. Each landing trial was separated by 1-minute rest periods. The results provided new information in relation to the pre-post study design in the context of detecting adjustments in knee function during landing. First, participants significantly increased or decreased pre-impact muscle activity or post-impact mechanics despite environmental and task constraints remaining unchanged. This is the 1st study to demonstrate this effect in healthy individuals without external feedback on performance. Second, single-subject analysis was more effective in detecting alterations in knee function compared to group-level analysis. Finally, repeated landing trials did not reduce inter-trial variability of knee function in some participants, contrary to assumptions underpinning previous studies. The results of studies 1 and 2 were used to modify the design of Study 3 relative to previous research. These alterations included a modified isokinetic fatigue protocol, multiple pre-fatigue measurements and singlesubject analysis to detect fatigue-related changes in knee function. The study design incorporated new analytical approaches to investigate fatiguerelated alterations in knee function during landing. Participants (N = 16) were measured during multiple pre-fatigue baseline trial blocks prior to the fatigue model. A final block of landing trials was recorded once the participant met the operational fatigue definition that was identified in Study 1. The analysis revealed that the effects of fatigue in this context are heavily dependent on the compensatory response of the individual. A continuum of responses was observed within the sample for each knee function measure. Overall, preimpact preparation and post-impact mechanics of the knee were altered with highly individualised patterns. Moreover, participants used a range of active or passive pre-impact strategies to adapt post-impact mechanics in response to quadriceps fatigue. The unique patterns identified in the data represented an optimisation of knee function based on priorities of the individual. The findings of these studies explain the lack of consensus within the literature regarding the effects of fatigue on knee function during landing. First, functional fatigue protocols lack validity in inducing fatigue-related changes in mechanical output and spectral compression of surface electromyography (sEMG) signals, compared with isokinetic exercise. Second, fatigue-related changes in knee function during landing are confounded by inter-individual variation, which limits the sensitivity of group-level analysis. By addressing these limitations, the 3rd study demonstrated the efficacies of new experimental and analytical approaches to observe fatigue-related alterations in knee function during landing. Consequently, this thesis provides new perspectives into the effects of fatigue in knee function during landing. In conclusion: • The effects of fatigue on knee function during landing depend on the response of the individual, with considerable variation present between study participants, despite similar physical characteristics. • In healthy males, adaptation of pre-impact muscle activity and postimpact knee mechanics is unique to the individual and reflects their own optimisation of demands such as energy expenditure, joint stability, sensory information and loading of knee structures. • The results of these studies should guide future exploration of adaptations in knee function to fatigue. However, research in this area should continue with reduced emphasis on the directional response of the population and a greater focus on individual adaptations of knee function.

Analysis of residual tropical cemented soil behaviour

In -situ soils in gee-material spectrum might arise due to sedimentation or could be non-sedimentary residual formations. The inherent nature and diversity of geological processes involved in the soil formation stage itself are responsible for a wide variability in the in-situ state of the soil. In this paper the possibility of analyses to arrive at engineering parameters of residual soils with varied degrees of residual or acquired cementation by the use of physical and in-situ parameters normally determined in routine investigations, are examined. An Intrinsic State Line,(ISL), with reference to an intrinsic state parameter (e/e(L)) and its variation with effective stress for reconstituted clays has been developed for residual tropical soils of non-sedimentary origin. In relation to the Intrinsic State Line (ISL), the undisturbed state, e, the potential parameter, e(L), along with the overburden pressure data has been analyzed to identify the dominance of cementation or stress history or both in controlling the compressibility and strength behaviour of natural residual soil. The location of yield stress point in relation to the ISL, pre-, and post- yield stress, compression indices along the e- log sigma(v) path provide a simple means to the analysis of the compressibility characteristics of cemented soils for analysis.

Predicting trabecular bone microdamage initiation and accumulation using a non-linear perfect damage model

Studies evaluating the mechanical behavior of the trabecular microstructure play an important role in our understanding of pathologies such as osteoporosis, and in increasing our understanding of bone fracture and bone adaptation. Understanding of such behavior in bone is important for predicting and providing early treatment of fractures. The objective of this study is to present a numerical model for studying the initiation and accumulation of trabecular bone microdamage in both the pre- and post-yield regions. A sub-region of human vertebral trabecular bone was analyzed using a uniformly loaded anatomically accurate microstructural three-dimensional finite element model. The evolution of trabecular bone microdamage was governed using a non-linear, modulus reduction, perfect damage approach derived from a generalized plasticity stress-strain law. The model introduced in this paper establishes a history of microdamage evolution in both the pre- and post-yield regions

An anisotropic elastic-viscoplastic damage model for bone tissue

A new anisotropic elastic-viscoplastic damage constitutive model for bone is proposed using an eccentric elliptical yield criterion and nonlinear isotropic hardening. A micromechanics-based multiscale homogenization scheme proposed by Reisinger et al. is used to obtain the effective elastic properties of lamellar bone. The dissipative process in bone is modeled as viscoplastic deformation coupled to damage. The model is based on an orthotropic ecuntric elliptical criterion in stress space. In order to simplify material identification, an eccentric elliptical isotropic yield surface was defined in strain space, which is transformed to a stress-based criterion by means of the damaged compliance tensor. Viscoplasticity is implemented by means of the continuous Perzyna formulation. Damage is modeled by a scalar function of the accumulated plastic strain D(κ) , reducing all element s of the stiffness matrix. A polynomial flow rule is proposed in order to capture the rate-dependent post-yield behavior of lamellar bone. A numerical algorithm to perform the back projection on the rate-dependent yield surface has been developed and implemented in the commercial finite element solver Abaqus/Standard as a user subroutine UMAT. A consistent tangent operator has been derived and implemented in order to ensure quadratic convergence. Correct implementation of the algorithm, convergence, and accuracy of the tangent operator was tested by means of strain- and stress-based single element tests. A finite element simulation of nano- indentation in lamellar bone was finally performed in order to show the abilities of the newly developed constitutive model.

Fabric-mechanical property relationships of trabecular bone allografts are altered by supercritical CO2 treatment and gamma sterilization

Tissue grafts are implanted in orthopedic surgery every day. In order to minimize infection risk, bone allografts are often delipidated with supercritical CO2 and sterilized prior to implantation. This treatment may, however, impair the mechanical behavior of the bone graft tissue. The goal of this study was to determine clinically relevant mechanical properties of treated/sterilized human trabecular bone grafts, e.g. the apparent modulus, strength, and the ability to absorb energy during compaction. They were compared with results of identical experiments performed previously on untreated/fresh frozen human trabecular bone from the same anatomical site (Charlebois, 2008). We tested the hypothesis that the morphology–mechanical property relationships of treated cancellous allografts are similar to those of fresh untreated bone. The morphology of the allografts was determined by μCT. Subsequently, cylindrical samples were tested in unconfined and confined compression. To account for various morphologies, the experimental data was fitted to phenomenological mechanical models for elasticity, strength, and dissipated energy density based on bone volume fraction (BV/TV) and the fabric tensor determined by MIL. The treatment/sterilization process does not appear to influence bone graft stiffness. However, strength and energy dissipation of the bone grafts were found to be significantly reduced by 36% to 47% and 66% to 81%, respectively, for a broad range of volume fraction (0.14 < BV/TV < 0.39) and degree of anisotropy (1.24 < DA < 2.18). Since the latter properties are strongly dominated by BV/TV, the clinical consequences of this reduction can be compensated by using grafts with lower porosity. The data of this study suggests that an increase of 5–10% in BV/TV is sufficient to compensate for the reduced post-yield mechanical properties of treated/sterilized bone in monotonic compression. In applications where graft stiffness needs to be matched and strength is not a concern, treated allograft with the same BV/TV as an appropriate fresh bone graft may be used.

Embedding of human vertebral bodies leads to higher ultimate load and altered damage localisation under axial compression

Computer tomography (CT)-based finite element (FE) models of vertebral bodies assess fracture load in vitro better than dual energy X-ray absorptiometry, but boundary conditions affect stress distribution under the endplates that may influence ultimate load and damage localisation under post-yield strains. Therefore, HRpQCT-based homogenised FE models of 12 vertebral bodies were subjected to axial compression with two distinct boundary conditions: embedding in polymethylmethalcrylate (PMMA) and bonding to a healthy intervertebral disc (IVD) with distinct hyperelastic properties for nucleus and annulus. Bone volume fraction and fabric assessed from HRpQCT data were used to determine the elastic, plastic and damage behaviour of bone. Ultimate forces obtained with PMMA were 22% higher than with IVD but correlated highly (R2 = 0.99). At ultimate force, distinct fractions of damage were computed in the endplates (PMMA: 6%, IVD: 70%), cortex and trabecular sub-regions, which confirms previous observations that in contrast to PMMA embedding, failure initiated underneath the nuclei in healthy IVDs. In conclusion, axial loading of vertebral bodies via PMMA embedding versus healthy IVD overestimates ultimate load and leads to distinct damage localisation and failure pattern.

Continuum damage interactions between tension and compression in osteonal bone

Skeletal diseases such as osteoporosis impose a severe socio-economic burden to ageing societies. Decreasing mechanical competence causes a rise in bone fracture incidence and mortality especially after the age of 65 y. The mechanisms of how bone damage is accumulated under different loading modes and its impact on bone strength are unclear. We hypothesise that damage accumulated in one loading mode increases the fracture risk in another. This study aimed at identifying continuum damage interactions between tensile and compressive loading modes. We propose and identify the material constants of a novel piecewise 1D constitutive model capable of describing the mechanical response of bone in combined tensile and compressive loading histories. We performed several sets of loading–reloading experiments to compute stiffness, plastic strains, and stress-strain curves. For tensile overloading, a stiffness reduction (damage) of 60% at 0.65% accumulated plastic strain was detectable as stiffness reduction of 20% under compression. For compressive overloading, 60% damage at 0.75% plastic strain was detectable as a stiffness reduction of 50% in tension. Plastic strain at ultimate stress was the same in tension and compression. Compression showed softening and tension exponential hardening in the post-yield regime. The hardening behaviour in compression is unaffected by a previous overload in tension but the hardening behaviour in tension is affected by a previous overload in compression as tensile reloading strength is significantly reduced. This paper demonstrates how damage accumulated under one loading mode affects the mechanical behaviour in another loading mode. To explain this and to illustrate a possible implementation we proposed a theoretical model. Including such loading mode dependent damage and plasticity behaviour in finite element models will help to improve fracture risk analysis of whole bones and bone implant structures.

Tailoring Magnetic, Mechanical and Dielectric Properties of Magnetorheological Elastomers based on Natural Rubber and Iron by Magnetic Field Assisted Curing for Possible Applications

If magnetism is universal in nature, magnetic materials are ubiquitous. A life without magnetism is unthinkable and a day without the influence of a magnetic material is unimaginable. They find innumerable applications in the form of many passive and active devices namely, compass, electric motor, generator, microphone, loud speaker, maglev train, magnetic resonance imaging, data recording and reading, hadron collider etc. The list is endless. Such is the influence of magnetism and magnetic materials in ones day to day life. With the advent of nanoscience and nanotechnology, along with the emergence of new areas/fields such as spintronics, multiferroics and magnetic refrigeration, the importance of magnetism is ever increasing and attracting the attention of researchers worldwide. The search for a fluid which exhibits magnetism has been on for quite some time. However nature has not bestowed us with a magnetic fluid and hence it has been the dream of many researchers to synthesize a magnetic fluid which is thought to revolutionize many applications based on magnetism. The discovery of a magnetic fluid by Jacob Rabinow in the year 1952 paved the way for a new branch of Physics/Engineering which later became magnetic fluids. This gave birth to a new class of material called magnetorheological materials. Magnetorheological materials are considered superior to electrorheological materials in that magnetorheology is a contactless operation and often inexpensive.Most of the studies in the past on magnetorheological materials were based on magnetic fluids. Recently the focus has been on the solid state analogue of magnetic fluids which are called Magnetorheological Elastomers (MREs). The very word magnetorheological elastomer implies that the rheological properties of these materials can be altered by the influence of an external applied magnetic field and this process is reversible. If the application of an external magnetic field modifies the viscosity of a magnetic fluid, the effect of external magnetic stimuli on a magnetorheological elastomer is in the modification of its stiffness. They are reversible too. Magnetorheological materials exhibit variable stiffness and find applications in adaptive structures of aerospace, automotive civil and electrical engineering applications. The major advantage of MRE is that the particles are not able to settle with time and hence there is no need of a vessel to hold it. The possibility of hazardous waste leakage is no more with a solid MRE. Moreover, the particles in a solid MRE will not affect the performance and durability of the equipment. Usually MR solids work only in the pre yield region while MR fluids, typically work in the post yield state. The application of an external magnetic field modifies the stiffness constant, shear modulus and loss modulus which are complex quantities. In viscoelastic materials a part of the input energy is stored and released during each cycle and a part is dissipated as heat. The storage modulus G′ represents the capacity of the material to store energy of deformation, which contribute to material stiffness. The loss modulusG′′ represents the ability of the material to dissipate the energy of deformation. Such materials can find applications in the form of adaptive vibration absorbers (ATVAs), stiffness tunable mounts and variable impedance surfaces. MREs are an important material for automobile giants and became the focus of this research for eventual automatic vibration control, sound isolation, brakes, clutches and suspension systems

Double incretin receptor knock-out (DIRKO) mice present with alterations of trabecular and cortical micromorphology and bone strength.

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Anisotropic damage mechanics as a novel approach to improve pre-and post-failure borehole stability analysis

Anisotropic damage distribution and evolution have a profound effect on borehole stress concentrations. Damage evolution is an irreversible process that is not adequately described within classical equilibrium thermodynamics. Therefore, we propose a constitutive model, based on non-equilibrium thermodynamics, that accounts for anisotropic damage distribution, anisotropic damage threshold and anisotropic damage evolution. We implemented this constitutive model numerically, using the finite element method, to calculate stress–strain curves and borehole stresses. The resulting stress–strain curves are distinctively different from linear elastic-brittle and linear elastic-ideal plastic constitutive models and realistically model experimental responses of brittle rocks. We show that the onset of damage evolution leads to an inhomogeneous redistribution of material properties and stresses along the borehole wall. The classical linear elastic-brittle approach to borehole stability analysis systematically overestimates the stress concentrations on the borehole wall, because dissipative strain-softening is underestimated. The proposed damage mechanics approach explicitly models dissipative behaviour and leads to non-conservative mud window estimations. Furthermore, anisotropic rocks with preferential planes of failure, like shales, can be addressed with our model.

Young men utilise limited neuromuscular prepartion to regulate post-impact knee mechanics during step landing

Purpose The neuromuscular mechanisms determining the mechanical behaviour of the knee during landing impact remain poorly understood. It was hypothesised that neuromuscular preparation is subject-specific and ranges along a continuum from passive to active. Methods A group of healthy men (N = 12) stepped-down from a knee-high platform for 60 consecutive trials. Surface EMG of the quadriceps and hamstrings was used to determine pre-impact onset timing, activation amplitude and cocontraction for each trial. Partial least squares regression was used to associate pre-impact preparation with post-impact knee stiffness and coordination. Results The group analysis revealed few significant changes in pre-impact preparation across trial blocks. Single-subject analyses revealed changes in muscle activity that varied in size and direction between individuals. Further, the association between pre-impact preparation and post-impact knee mechanics was subject-specific and ranged along a continuum of strategies. Conclusion The findings suggest that neuromuscular preparation during step landing is subject-specific and its association to post-impact knee mechanics occurs along a continuum, ranging from passive to active control strategies. Further work should examine the implications of these strategies on the distribution of knee forces in-vivo.