Inter-lamellar shear resistance confers compressive stiffness in the intervertebral disc: An image-based modelling study on the bovine caudal disc

The intervertebral disc withstands large compressive loads (up to nine times bodyweight in humans) while providing flexibility to the spinal column. At a microstructural level, the outer sheath of the disc (the annulus fibrosus) comprises 12–20 annular layers of alternately crisscrossed collagen fibres embedded in a soft ground matrix. The centre of the disc (the nucleus pulposus) consists of a hydrated gel rich in proteoglycans. The disc is the largest avascular structure in the body and is of much interest biomechanically due to the high societal burden of disc degeneration and back pain. Although the disc has been well characterized at the whole joint scale, it is not clear how the disc tissue microstructure confers its overall mechanical properties. In particular, there have been conflicting reports regarding the level of attachment between adjacent lamellae in the annulus, and the importance of these interfaces to the overall integrity of the disc is unknown. We used a polarized light micrograph of the bovine tail disc in transverse cross-section to develop an image-based finite element model incorporating sliding and separation between layers of the annulus, and subjected the model to axial compressive loading. Validation experiments were also performed on four bovine caudal discs. Interlamellar shear resistance had a strong effect on disc compressive stiffness, with a 40% drop in stiffness when the interface shear resistance was changed from fully bonded to freely sliding. By contrast, interlamellar cohesion had no appreciable effect on overall disc mechanics. We conclude that shear resistance between lamellae confers disc mechanical resistance to compression, and degradation of the interlamellar interface structure may be a precursor to macroscopic disc degeneration.

Modelling of the stiffness evolution of truss core structures damaged by plastic buckling

A finite element study based on 1D beam element model is performed in order to investigate the mechanical behavior of an elasto-plastic beam loaded in axial compression over its buckling limit. The mode of loading is related to the damage of truss-cored beams in truss-cored laminates. The analysis takes into account the effects of geometry and material properties. The results of the FEM analysis are used for developing a simple mechanical model based on the basic Euler-Bernoulli beam theory and accounts for the beam compressibility. The model uses phenomenological functions containing parameters related to the basic material and geometrical properties. The presented model is developed in the form of closed solution which does not require complex numerical methods or extensive parametric studies. Predictions of the compressive stiffness degradation of truss-cored composites are made with the proposed model and compared with the results of FEM simulations. The error of the stiffness prediction with respect to the FEM results is within 10% over a 5 fold range of stiffness.

Load-unloading response of intact and artificially degraded articular cartilage correlated with near infrared (NIR) absorption spectra

The conventional mechanical properties of articular cartilage, such as compressive stiffness, have been demonstrated to be limited in their capacity to distinguish intact (visually normal) from degraded cartilage samples. In this paper, we explore the correlation between a new mechanical parameter, namely the reswelling of articular cartilage following unloading from a given compressive load, and the near infrared (NIR) spectrum. The capacity to distinguish mechanically intact from proteoglycan-depleted tissue relative to the "reswelling" characteristic was first established, and the result was subsequently correlated with the NIR spectral data of the respective tissue samples. To achieve this, normal intact and enzymatically degraded samples were subjected to both NIR probing and mechanical compression based on a load-unload-reswelling protocol. The parameter δ(r), characteristic of the osmotic "reswelling" of the matrix after unloading to a constant small load in the order of the osmotic pressure of cartilage, was obtained for the different sample types. Multivariate statistics was employed to determine the degree of correlation between δ(r) and the NIR absorption spectrum of relevant specimens using Partial Least Squared (PLS) regression. The results show a strong relationship (R(2)=95.89%, p<0.0001) between the spectral data and δ(r). This correlation of δ(r) with NIR spectral data suggests the potential for determining the reswelling characteristics non-destructively. It was also observed that δ(r) values bear a significant relationship with the cartilage matrix integrity, indicated by its proteoglycan content, and can therefore differentiate between normal and artificially degraded proteoglycan-depleted cartilage samples. It is therefore argued that the reswelling of cartilage, which is both biochemical (osmotic) and mechanical (hydrostatic pressure) in origin, could be a strong candidate for characterizing the tissue, especially in regions surrounding focal cartilage defects in joints.

Mechanical testing and modelling of a bone-implant construct

Finite Element modelling of bone fracture fixation systems allows computational investigation of the deformation response of the bone to load. Once validated, these models can be easily adapted to explore changes in design or configuration of a fixator. The deformation of the tissue within the fracture gap determines its healing and is often summarised as the stiffness of the construct. FE models capable of reproducing this behaviour would provide valuable insight into the healing potential of different fixation systems. Current model validation techniques lack depth in 6D load and deformation measurements. Other aspects of the FE model creation such as the definition of interfaces between components have also not been explored. This project investigated the mechanical testing and FE modelling of a bone– plate construct for the determination of stiffness. In depth 6D measurement and analysis of the generated forces, moments and movements showed large out of plane behaviours which had not previously been characterised. Stiffness calculated from the interfragmentary movement was found to be an unsuitable summary parameter as the error propagation is too large. Current FE modelling techniques were applied in compression and torsion mimicking the experimental setup. Compressive stiffness was well replicated, though torsional stiffness was not. The out of plane behaviours prevalent in the experimental work were not replicated in the model. The interfaces between the components were investigated experimentally and through modification to the FE model. Incorporation of the interface modelling techniques into the full construct models had no effect in compression but did act to reduce torsional stiffness bringing it closer to that of the experiment. The interface definitions had no effect on out of plane behaviours, which were still not replicated. Neither current nor novel FE modelling techniques were able to replicate the out of plane behaviours evident in the experimental work. New techniques for modelling loads and boundary conditions need to be developed to mimic the effects of the entire experimental system.

On the biomechanical significance of inter-lamellar interfaces in the intervertebral disc

The intervertebral disc (IVD) is a unique soft tissue structure which provides structural support and flexibility in the axial skeleton of vertebrates. From a structural perspective, the disc behaves somewhat like a thick walled pressure vessel, where the walls are comprised of a series of composite annular rings (lamellae). However, a prior study (Marchand and Ahmed, 1990) found a high proportion of circumferentially discontinuous lamellae in human lumbar IVDs. The presence of these discontinuities raises important structural questions, because discontinuous lamellae cannot withstand high nucleus pressures via the generation of circumferential (hoop) stress. A possible alternative mechanism may be that inter-lamellar cohesion allows shear stress transfer between adjacent annular layers. The aim of the present study was therefore to investigate the importance of inter-lamellar shear resistance in the intervertebral disc. This work found that inter-lamellar shear resistance has a strong influence on the compressive stiffness of the intervertebral disc, with a change in interface condition from tied (no slip) to frictionless (no shear resistance) reducing disc compressive stiffness by 40%. However, it appears that substantial inter-lamellar shear resistance is present in the bovine tail disc. Decreases in inter-lamellar shear resistance due to degradation of bridging collagenous or elastic fibre structures could therefore be an important part of the process of disc degeneration.

Increased intra-cortical porosity reduces bone stiffness and strength in pediatric patients with osteogenesis imperfecta

Osteogenesis imperfecta (OI) is a heritable disease occurring in one out of every 20,000 births. Although it is known that Type I collagen mutation in OI leads to increased bone fragility, the mechanism of this increased susceptibility to fracture is not clear. The aim of this study was to assess the microstructure of cortical bone fragments from patients with osteogenesis imperfecta (OI) using polarized light microscopy, and to correlate microstructural observations with the results of previously performed mechanical compression tests on bone from the same source. Specimens of cortical bone were harvested from the lower limbs of three (3) OI patients at the time of surgery, and were divided into two groups. Group 1 had been subjected to previous micro-mechanical compression testing, while Group 2 had not been subjected to any prior testing. Polarized light microscopy revealed disorganized bone collagen architecture as has been previously observed, as well as a large increase in the areal porosity of the bone compared to typical values for healthy cortical bone, with large (several hundred micron sized), asymmetrical pores. Importantly, the areal porosity of the OI bone samples in Group 1 appears to correlate strongly with their previously measured apparent Young's modulus and compressive strength. Taken together with prior nanoindentation studies on OI bone tissue, the results of this study suggest that increased intra-cortical porosity is responsible for the reduction in macroscopic mechanical properties of OI cortical bone, and therefore that in vivo imaging modalities with resolutions of ~ 100 μm or less could potentially be used to non-invasively assess bone strength in OI patients. Although the number of subjects in this study is small, these results highlight the importance of further studies in OI bone by groups with access to human OI tissue in order to clarify the relationship between increased porosity and reduced macroscopic mechanical integrity.

Prediction of masonry compressive behaviour using a damage mechanics inspired modelling method

Masonry under compression is affected by the properties of its constituents and their interfaces. In spite of extensive investigations of the behaviour of masonry under compression, the information in the literature cannot be regarded as comprehensive due to ongoing inventions of new generation products – for example, polymer modified thin layer mortared masonry and drystack masonry. As comprehensive experimental studies are very expensive, an analytical model inspired by damage mechanics is developed and applied to the prediction of the compressive behaviour of masonry in this paper. The model incorporates a parabolic progressively softening stress-strain curve for the units and a progressively stiffening stress-strain curve until a threshold strain for the combined mortar and the unit-mortar interfaces is reached. The model simulates the mutual constraints imposed by each of these constituents through their respective tensile and compressive behaviour and volumetric changes. The advantage of the model is that it requires only the properties of the constituents and considers masonry as a continuum and computes the average properties of the composite masonry prisms/wallettes; it does not require discretisation of prism or wallette similar to the finite element methods. The capability of the model in capturing the phenomenological behaviour of masonry with appropriate elastic response, stiffness degradation and post peak softening is presented through numerical examples. The fitting of the experimental data to the model parameters is demonstrated through calibration of some selected test data on units and mortar from the literature; the calibrated model is shown to predict the responses of the experimentally determined masonry built using the corresponding units and mortar quite well. Through a series of sensitivity studies, the model is also shown to predict the masonry strength appropriately for changes to the properties of the units and mortar, the mortar joint thickness and the ratio of the height of unit to mortar joint thickness. The unit strength is shown to affect the masonry strength significantly. Although the mortar strength has only a marginal effect, reduction in mortar joint thickness is shown to have a profound effect on the masonry strength. The results obtained from the model are compared with the various provisions in the Australian Masonry Structures Standard AS3700 (2011) and Eurocode 6.

Effect of density variation and non-covalent functionalization on the compressive behavior of carbon nanotube arrays

Arrays of aligned carbon nanotubes (CNTs) have been proposed for different applications, including electrochemical energy storage and shock-absorbing materials. Understanding their mechanical response, in relation to their structural characteristics, is important for tailoring the synthesis method to the different operational conditions of the material. In this paper, we grow vertically aligned CNT arrays using a thermal chemical vapor deposition system, and we study the effects of precursor flow on the structural and mechanical properties of the CNT arrays. We show that the CNT growth process is inhomogeneous along the direction of the precursor flow, resulting in varying bulk density at different points on the growth substrate. We also study the effects of non-covalent functionalization of the CNTs after growth, using surfactant and nanoparticles, to vary the effective bulk density and structural arrangement of the arrays. We find that the stiffness and peak stress of the materials increase approximately linearly with increasing bulk density.

Compressive failure of finite size unidirectional composite laminates with a region of fibre waviness

The compressive behaviour of finite unidirectional composites with a region of misaligned reinforcement is investigated via finite element analyses. Models with and without fibre bending stiffness are compared, confirming that compressive strength is accurately predicted without modelling fibre bending stiffness for real composite components which typically have waviness defects of several millimetres wavelength. Various defect parameters are investigated. Results confirm the well-known sensitivity of compressive strength to misalignment angle, and also show that compressive strength falls rapidly with the proportion of laminate width covered by the wavy region. A simple empirical equation is proposed to model the effect of a single patch of waviness in finite specimens. Other parameters such as length and position of the wavy region are found to have a smaller effect on compressive strength. The modelling approach is finally adapted to model distributed waviness and thus determine the compressive strength of composites with realistic waviness defects. © 2011 Elsevier Ltd. All rights reserved.

Preliminary model development for predicting strength and stiffness of cement-stabilized soils using artificial neural networks

This paper presents ongoing work on data collection and collation from a large number of laboratory cement-stabilization projects worldwide. The aim is to employ Artificial Neural Networks (ANN) to establish relationships between variables, which define the properties of cement-stabilized soils, and the two parameters determined by the Unconfined Compression Test, the Unconfined Compressive Strength (UCS), and stiffness, using E50 calculated from UCS results. Bayesian predictive neural network models are developed to predict the UCS values of cement-stabilized inorganic clays/silts, as well as sands as a function of selected soil mix variables, such as grain size distribution, water content, cement content and curing time. A model which can predict the stiffness values of cement-stabilized clays/silts is also developed and compared to the UCS model. The UCS model results emulate known trends better and provide more accurate estimates than the results from the E50 stiffness model. © 2013 American Society of Civil Engineers.

Research on Ultimate Loading Carrying Capacities in Concrete Bridge Deck Slabs with Consideration of Compressive Membrane Action

In the investigation of real loading capacities in concrete bridge deck slabs,the study of this type of structure was carried out with consideration of compressive membrane action.A series of experimental test of steel-concrete bridge structures was developed with the analysis of influences from the varying of structural parameters on loading capacities,including reinforcement percentages,supporting beam sizes and concrete compressive strength.Through the study of the experimental results,it was found that the real structural loading capacities are larger than those predicted by current design methods.Therefore,based on the previous research,a prediction method for loading capacities of concrete bridge deck slabs was established with consideration of CMA,which was built based on the plastic ultimate analysis.In this method,the lateral restraint stiffness subjected by concrete bridge deck slabs was provided.The proposed theoretical model is capable of predicting the loading capacities of this type of structure accurately with comparison of results from several bridge deck experimental tests.

Thermomechanical Response of Variable Stiffness Composite Panels

Analysis of non-traditional Variable Stiffness (VS) laminates, obtained by steering the fiber orientation as a spatial function of location, have shown to improve buckling load carrying capacity of flat rectangular panels under axial compressive loads. In some cases the buckling load of simply supported panels doubled compared to the best conventional laminate with straight fibers. Two distinct cases of stiffness variation, one due to fiber orientation variation in the direction of the loading, and the other one perpendicular to the loading direction, were identified as possible contributors to the buckling load improvements. In the first case, the increase was attributed to the favorable distribution of the transverse in-plane stresses over the panel platform. In the second case, a higher degree of improvement was obtained due to the re-distribution of the applied in-plane loads. Experimental results, however, showed substantially higher levels of buckling load improvements compared with theoretical predictions. The additional improvement was determined to be due to residual stresses introduced during curing of the laminates. The present paper provides a simplified thermomechanical analysis of residual stress state of variable stiffness laminates. Systematic parametric analyses of both cases of fiber orientation variations show that, indeed much higher buckling loads could result from the residual stresses present in such laminates.

Compressive behavior of steel fiber reinforced recycled aggregate concrete after exposure to elevated temperatures

For sustainability considerations, the use of recycled aggregate in concrete has attracted many interests in the research community. One of the main concerns for using such concrete in buildings is its spalling in fire. This may be alleviated by adding steel fibers to form steel fiber reinforced recycled aggregate concrete (SFRAC). This paper presents an experimental investigation into the compressive properties of SFRAC cylinders after exposure to elevated temperatures, including the compressive strength, Young's modulus (stiffness), stress-strain curve and energy absorption capacity (toughness). The effects of two parameters, namely steel fiber volume content (0%, 0.5%, 1%, 1.5%) and temperature (room temperature, 200 °C, 400 °C and 600 °C) on the compressive mechanical properties of concrete were investigated. The test results show that both compressive strength and stiffness of the concrete are significantly reduced after exposure to high temperatures. The addition of steel fibers is helpful in preventing spalling, and significantly improves the ductility and the cracking behavior of recycled aggregate concrete (RAC) after exposure to high temperatures, which is favorable for the application of RAC in building construction.

Estimation of the small strain stiffness of glacial till using geophysical methods and barometric loading response

Stiffness values in geotechnical structures can range over many orders of magnitude for relatively small operational strains. The typical strain levels where soil stiffness changes most dramatically is in the range 0.01-0.1%, however soils do not exhibit linear stress-strain behaviour at small strains. Knowledge of the in situ stiffness at small strain is important in geotechnical numerical modelling and design. The stress-strain regime of cut slopes is complex, as we have different principle stress directions at different positions along the potential failure plane. For example, loading may be primarily in extension near the toe of the slope, while compressive loading is predominant at the crest of a slope. Cuttings in heavily overconsolidated clays are known to be susceptible to progressive failure and subsequent strain softening, in which progressive yielding propagates from the toe towards the crest of the slope over time. In order to gain a better understanding of the rate of softening it would be advantageous to measure changes in small strain stiffness in the field.

The influence of hydration on the tensile and compressive properties of avian keratinous tissues

Despite recent research exploring the elastic properties of avian keratins, data on failure properties are less common in the literature. In this paper we present data on the failure properties and moduli of both avian feather and claw keratin in tension and the modulus of claw keratin in compression. Increased water content acts to decrease stiffness and strength but to increase strain at failure. The modulus of claw did not differ significantly when tested under tension and compression.