Modelling of some biological materials using continuum mechanics

Continuum mechanics provides a mathematical framework for modelling the physical stresses experienced by a material. Recent studies show that physical stresses play an important role in a wide variety of biological processes, including dermal wound healing, soft tissue growth and morphogenesis. Thus, continuum mechanics is a useful mathematical tool for modelling a range of biological phenomena. Unfortunately, classical continuum mechanics is of limited use in biomechanical problems. As cells refashion the �bres that make up a soft tissue, they sometimes alter the tissue's fundamental mechanical structure. Advanced mathematical techniques are needed in order to accurately describe this sort of biological `plasticity'. A number of such techniques have been proposed by previous researchers. However, models that incorporate biological plasticity tend to be very complicated. Furthermore, these models are often di�cult to apply and/or interpret, making them of limited practical use. One alternative approach is to ignore biological plasticity and use classical continuum mechanics. For example, most mechanochemical models of dermal wound healing assume that the skin behaves as a linear viscoelastic solid. Our analysis indicates that this assumption leads to physically unrealistic results. In this thesis we present a novel and practical approach to modelling biological plasticity. Our principal aim is to combine the simplicity of classical linear models with the sophistication of plasticity theory. To achieve this, we perform a careful mathematical analysis of the concept of a `zero stress state'. This leads us to a formal de�nition of strain that is appropriate for materials that undergo internal remodelling. Next, we consider the evolution of the zero stress state over time. We develop a novel theory of `morphoelasticity' that can be used to describe how the zero stress state changes in response to growth and remodelling. Importantly, our work yields an intuitive and internally consistent way of modelling anisotropic growth. Furthermore, we are able to use our theory of morphoelasticity to develop evolution equations for elastic strain. We also present some applications of our theory. For example, we show that morphoelasticity can be used to obtain a constitutive law for a Maxwell viscoelastic uid that is valid at large deformation gradients. Similarly, we analyse a morphoelastic model of the stress-dependent growth of a tumour spheroid. This work leads to the prediction that a tumour spheroid will always be in a state of radial compression and circumferential tension. Finally, we conclude by presenting a novel mechanochemical model of dermal wound healing that takes into account the plasticity of the healing skin.

Numerical simulation of axially loaded concrete columns under transverse impact and vulnerability assessment

With a view to assessing the vulnerability of columns to low elevation vehicular impacts, a non-linear explicit numerical model has been developed and validated using existing experimental results. The numerical model accounts for the effects of strain rate and confinement of the reinforced concrete, which are fundamental to the successful prediction of the impact response. The sensitivity of the material model parameters used for the validation is also scrutinised and numerical tests are performed to examine their suitability to simulate the shear failure conditions. Conflicting views on the strain gradient effects are discussed and the validation process is extended to investigate the ability of the equations developed under concentric loading conditions to simulate flexural failure events. Experimental data on impact force–time histories, mid span and residual deflections and support reactions have been verified against corresponding numerical results. A universal technique which can be applied to determine the vulnerability of the impacted columns against collisions with new generation vehicles under the most common impact modes is proposed. Additionally, the observed failure characteristics of the impacted columns are explained using extended outcomes. Based on the overall results, an analytical method is suggested to quantify the vulnerability of the columns.

The suitability of using accumulated plastic strain to assess the damage at the rail-wheel interfaces

Numerous Abaqus [1] finite element analyses have been carried out using various plasticity models to investigate the effect of friction force on the rail head in relation to both the development of the accumulated plastic strain (PEEQ) and the changes in the depth of PEEQ distribution in the wheel-rail contact. The normal force distribution on the rail head was assumed to be Hertzian. The tangential force was implemented as a fraction of the normal force in the subroutine. Each analysis was carried out for a single pass and the effect of various friction coefficient values has been observed.

Single layer lead iodide: Computational exploration of structural, electronic and optical properties, strain induced band modulation and the role of spin-orbital-coupling

Graphitic like layered materials exhibit intriguing electronic structures and thus the search for new types of two-dimensional (2D) monolayer materials is of great interest for developing novel nano-devices. By using density functional theory (DFT) method, here we for the first time investigate the structure, stability, electronic and optical properties of monolayer lead iodide (PbI2). The stability of PbI2 monolayer is first confirmed by phonon dispersion calculation. Compared to the calculation using generalized gradient approximation, screened hybrid functional and spin–orbit coupling effects can not only predicts an accurate bandgap (2.63 eV), but also the correct position of valence and conduction band edges. The biaxial strain can tune its bandgap size in a wide range from 1 eV to 3 eV, which can be understood by the strain induced uniformly change of electric field between Pb and I atomic layer. The calculated imaginary part of the dielectric function of 2D graphene/PbI2 van der Waals type hetero-structure shows significant red shift of absorption edge compared to that of a pure monolayer PbI2. Our findings highlight a new interesting 2D material with potential applications in nanoelectronics and optoelectronics.

Shaping development through mechanical strain: The transcriptional basis of diet-induced phenotypic plasticity in a cichlid fish

Adaptive phenotypic plasticity, the ability of an organism to change its phenotype to match local environments, is increasingly recognized for its contribution to evolution. However, few empirical studies have explored the molecular basis of plastic traits. The East African cichlid fish Astatoreochromis alluaudi displays adaptive phenotypic plasticity in its pharyngeal jaw apparatus, a structure that is widely seen as an evolutionary key innovation that has contributed to the remarkable diversity of cichlid fishes. It has previously been shown that in response to different diets, the pharyngeal jaws change their size, shape and dentition: hard diets induce an adaptive robust molariform tooth phenotype with short jaws and strong internal bone structures, while soft diets induce a gracile papilliform tooth phenotype with elongated jaws and slender internal bone structures. To gain insight into the molecular underpinnings of these adaptations and enable future investigations of the role that phenotypic plasticity plays during the formation of adaptive radiations, the transcriptomes of the two divergent jaw phenotypes were examined. Our study identified a total of 187 genes whose expression differs in response to hard and soft diets, including immediate early genes, extracellular matrix genes and inflammatory factors. Transcriptome results are interpreted in light of expression of candidate genesmarkers for tooth size and shape, bone cells and mechanically sensitive pathways. This study opens up new avenues of research at new levels of biological organization into the roles of phenotypic plasticity during speciation and radiation of cichlid fishes.

Application of a continuum theory to vertical vibrations of a layer of granular material

Many interesting phenomena have been observed in layers of granular materials subjected to vertical oscillations; these include the formation of a variety of standing wave patterns, and the occurrence of isolated features called oscillons, which alternately form conical heaps and craters oscillating at one-half of the forcing frequency. No continuum-based explanation of these phenomena has previously been proposed. We apply a continuum theory, termed the double-shearing theory, which has had success in analyzing various problems in the flow of granular materials, to the problem of a layer of granular material on a vertically vibrating rigid base undergoing vertical oscillations in plane strain. There exists a trivial solution in which the layer moves as a rigid body. By investigating linear perturbations of this solution, we find that at certain amplitudes and frequencies this trivial solution can bifurcate. The time dependence of the perturbed solution is governed by Mathieu’s equation, which allows stable, unstable and periodic solutions, and the observed period-doubling behaviour. Several solutions for the spatial velocity distribution are obtained; these include one in which the surface undergoes vertical velocities that have sinusoidal dependence on the horizontal space dimension, which corresponds to the formation of striped standing waves, and is one of the observed patterns. An alternative continuum theory of granular material mechanics, in which the principal axes of stress and rate-of-deformation are coincident, is shown to be incapable of giving rise to similar instabilities.

Morphologic and genomic characterisation of the koala Chlamydia pneumoniae strain

Chlamydia pneumoniae is a common human and animal pathogen associated with a wide range of upper and lower respiratory tract infections. In more recent years there has been increasing evidence to suggest a link between C. pneumoniae and chronic diseases in humans, including atherosclerosis, stroke and Alzheimer’s disease. C. pneumoniae human strains show little genetic variation, indicating that the human-derived strain originated from a common ancestor in the recent past. Despite extensive information on the genetics and morphology processes of the human strain, knowledge concerning many other hosts (including marsupials, amphibians, reptiles and equines) remains virtually unexplored. The koala (Phascolarctos cinereus) is a native Australian marsupial under threat due to habitat loss, predation and disease. Koalas are very susceptible to chlamydial infections, most commonly affecting the conjunctiva, urogenital tract and/or respiratory tract. To address this gap in the literature, the present study (i) provides a detailed description of the morphologic and genomic architecture of the C. pneumoniae koala (and human) strain, and shows that the koala strain is microscopically, developmentally and genetically distinct from the C. pneumoniae human strain, and (ii) examines the genetic relationship of geographically diverse C. pneumoniae isolates from human, marsupial, amphibian, reptilian and equine hosts, and identifies two distinct lineages that have arisen from animal-to-human cross species transmissions. Chapter One of this thesis explores the scientific problem and aims of this study, while Chapter Two provides a detailed literature review of the background in this field of work. Chapter Three, the first results chapter, describes the morphology and developmental stages of C. pneumoniae koala isolate LPCoLN, as revealed by fluorescence and transmission electron microscopy. The profile of this isolate, when cultured in HEp-2 human epithelial cells, was quite different to the human AR39 isolate. Koala LPCoLN inclusions were larger; the elementary bodies did not have the characteristic pear-shaped appearance, and the developmental cycle was completed within a shorter period of time (as confirmed by quantitative real-time PCR). These in vitro findings might reflect biological differences between koala LPCoLN and human AR39 in vivo. Chapter Four describes the complete genome sequence of the koala respiratory pathogen, C. pneumoniae LPCoLN. This is the first animal isolate of C. pneumoniae to be fully-sequenced. The genome sequence provides new insights into genomic ‘plasticity’ (organisation), evolution and biology of koala LPCoLN, relative to four complete C. pneumoniae human genomes (AR39, CWL029, J138 and TW183). Koala LPCoLN contains a plasmid that is not shared with any of the human isolates, there is evidence of gene loss in nucleotide salvage pathways, and there are 10 hot spot genomic regions of variation that were previously not identified in the C. pneumoniae human genomes. Sequence (partial-length) from a second, independent, wild koala isolate (EBB) at several gene loci confirmed that the koala LPCoLN isolate was representative of a koala C. pneumoniae strain. The combined sequence data provides evidence that the C. pneumoniae animal (koala LPCoLN) genome is ancestral to the C. pneumoniae human genomes and that human infections may have originated from zoonotic infections. Chapter Five examines key genome components of the five C. pneumoniae genomes in more detail. This analysis reveals genomic features that are shared by and/or contribute to the broad ecological adaptability and evolution of C. pneumoniae. This analysis resulted in the identification of 65 gene sequences for further analysis of intraspecific variation, and revealed some interesting differences, including fragmentation, truncation and gene decay (loss of redundant ancestral traits). This study provides valuable insights into metabolic diversity, adaptation and evolution of C. pneumoniae. Chapter Six utilises a subset of 23 target genes identified from the previous genomic comparisons and makes a significant contribution to our understanding of genetic variability among C. pneumoniae human (11) and animal (6 amphibian, 5 reptilian, 1 equine and 7 marsupial hosts) isolates. It has been shown that the animal isolates are genetically diverse, unlike the human isolates that are virtually clonal. More convincing evidence that C. pneumoniae originated in animals and recently (in the last few hundred thousand years) crossed host species to infect humans is provided in this study. It is proposed that two animal-to-human cross species events have occurred in the context of the results, one evident by the nearly clonal human genotype circulating in the world today, and the other by a more animal-like genotype apparent in Indigenous Australians. Taken together, these data indicate that the C. pneumoniae koala LPCoLN isolate has morphologic and genomic characteristics that are distinct from the human isolates. These differences may affect the survival and activity of the C. pneumoniae koala pathogen in its natural host, in vivo. This study, by utilising the genetic diversity of C. pneumoniae, identified new genetic markers for distinguishing human and animal isolates. However, not all C. pneumoniae isolates were genetically diverse; in fact, several isolates were highly conserved, if not identical in sequence (i.e. Australian marsupials) emphasising that at some stage in the evolution of this pathogen, there has been an adaptation/s to a particular host, providing some stability in the genome. The outcomes of this study by experimental and bioinformatic approaches have significantly enhanced our knowledge of the biology of this pathogen and will advance opportunities for the investigation of novel vaccine targets, antimicrobial therapy, or blocking of pathogenic pathways.

Damage assessment in reinforced concrete flexural members using modal strain energy based method

Damage assessment (damage detection, localization and quantification) in structures and appropriate retrofitting will enable the safe and efficient function of the structures. In this context, many Vibration Based Damage Identification Techniques (VBDIT) have emerged with potential for accurate damage assessment. VBDITs have achieved significant research interest in recent years, mainly due to their non-destructive nature and ability to assess inaccessible and invisible damage locations. Damage Index (DI) methods are also vibration based, but they are not based on the structural model. DI methods are fast and inexpensive compared to the model-based methods and have the ability to automate the damage detection process. DI method analyses the change in vibration response of the structure between two states so that the damage can be identified. Extensive research has been carried out to apply the DI method to assess damage in steel structures. Comparatively, there has been very little research interest in the use of DI methods to assess damage in Reinforced Concrete (RC) structures due to the complexity of simulating the predominant damage type, the flexural crack. Flexural cracks in RC beams distribute non- linearly and propagate along all directions. Secondary cracks extend more rapidly along the longitudinal and transverse directions of a RC structure than propagation of existing cracks in the depth direction due to stress distribution caused by the tensile reinforcement. Simplified damage simulation techniques (such as reductions in the modulus or section depth or use of rotational spring elements) that have been extensively used with research on steel structures, cannot be applied to simulate flexural cracks in RC elements. This highlights a big gap in knowledge and as a consequence VBDITs have not been successfully applied to damage assessment in RC structures. This research will address the above gap in knowledge and will develop and apply a modal strain energy based DI method to assess damage in RC flexural members. Firstly, this research evaluated different damage simulation techniques and recommended an appropriate technique to simulate the post cracking behaviour of RC structures. The ABAQUS finite element package was used throughout the study with properly validated material models. The damaged plasticity model was recommended as the method which can correctly simulate the post cracking behaviour of RC structures and was used in the rest of this study. Four different forms of Modal Strain Energy based Damage Indices (MSEDIs) were proposed to improve the damage assessment capability by minimising the numbers and intensities of false alarms. The developed MSEDIs were then used to automate the damage detection process by incorporating programmable algorithms. The developed algorithms have the ability to identify common issues associated with the vibration properties such as mode shifting and phase change. To minimise the effect of noise on the DI calculation process, this research proposed a sequential order of curve fitting technique. Finally, a statistical based damage assessment scheme was proposed to enhance the reliability of the damage assessment results. The proposed techniques were applied to locate damage in RC beams and slabs on girder bridge model to demonstrate their accuracy and efficiency. The outcomes of this research will make a significant contribution to the technical knowledge of VBDIT and will enhance the accuracy of damage assessment in RC structures. The application of the research findings to RC flexural members will enable their safe and efficient performance.

Ratchetting of railhead in the vicinity of the gap of the insulated rail joints

Insulated Rail Joints (IRJs) are designed to electrically isolate two rails in rail tracks to control the signalling system for safer train operations. Unfortunately the gapped section of the IRJs is structurally weak and often fails prematurely especially in heavy haul tracks, which adversely affects service reliability and efficiency. The IRJs suffer from a number of failure modes; the railhead ratchetting at the gap is, however, regarded as the root cause and attended to in this thesis. Ratchetting increases with the increase in wheel loads; in the absence of a life prediction model, effective management of the IRJs for increased wagon wheel loads has become very challenging. Therefore, the main aim of this thesis is to determine method to predict IRJs' service life. The distinct discontinuity of the railhead at the gap makes the Hertzian theory and the rolling contact shakedown map, commonly used in the continuously welded rails, not applicable to examine the metal ratchetting of the IRJs. Finite Element (FE) technique is, therefore, used to explore the railhead metal ratchetting characteristics in this thesis, the boundary conditions of which has been determined from a full scale study of the IRJ specimens under rolling contact of the loaded wheels. A special purpose test set up containing full-scale wagon wheel was used to apply rolling wheel loads on the railhead edges of the test specimens. The state of the rail end face strains was determined using a non-contact digital imaging technique and used for calibrating the FE model. The basic material parameters for this FE model were obtained through independent uniaxial, monotonic tensile tests on specimens cut from the head hardened virgin rails. The monotonic tensile test data have been used to establish a cyclic load simulation model of the railhead steel specimen; the simulated cyclic load test has provided the necessary data for the three decomposed kinematic hardening plastic strain accumulation model of Chaboche. A performance based service life prediction algorithm for the IRJs was established using the plastic strain accumulation obtained from the Chaboche model. The predicted service lives of IRJs using this algorithm have agreed well with the published data. The finite element model has been used to carry out a sensitivity study on the effects of wheel diameter to the railhead metal plasticity. This study revealed that the depth of the plastic zone at the railhead edges is independent of the wheel diameter; however, large wheel diameter is shown to increase the IRJs' service life.

Local stress-strain distribution and load transfer across cartilage matrix at micro-scale using combined microscopy-based finite element method

Articular cartilage is the load-bearing tissue that consists of proteoglycan macromolecules entrapped between collagen fibrils in a three-dimensional architecture. To date, the drudgery of searching for mathematical models to represent the biomechanics of such a system continues without providing a fitting description of its functional response to load at micro-scale level. We believe that the major complication arose when cartilage was first envisaged as a multiphasic model with distinguishable components and that quantifying those and searching for the laws that govern their interaction is inadequate. To the thesis of this paper, cartilage as a bulk is as much continuum as is the response of its components to the external stimuli. For this reason, we framed the fundamental question as to what would be the mechano-structural functionality of such a system in the total absence of one of its key constituents-proteoglycans. To answer this, hydrated normal and proteoglycan depleted samples were tested under confined compression while finite element models were reproduced, for the first time, based on the structural microarchitecture of the cross-sectional profile of the matrices. These micro-porous in silico models served as virtual transducers to produce an internal noninvasive probing mechanism beyond experimental capabilities to render the matrices micromechanics and several others properties like permeability, orientation etc. The results demonstrated that load transfer was closely related to the microarchitecture of the hyperelastic models that represent solid skeleton stress and fluid response based on the state of the collagen network with and without the swollen proteoglycans. In other words, the stress gradient during deformation was a function of the structural pattern of the network and acted in concert with the position-dependent compositional state of the matrix. This reveals that the interaction between indistinguishable components in real cartilage is superimposed by its microarchitectural state which directly influences macromechanical behavior.

Swelling induced finite strain flexure in a rectangular block of an isotropic elastic material

The deformation of a rectangular block into an annular wedge is studied with respect to the state of swelling interior to the block. Nonuniform swelling fields are shown to generate these flexure deformations in the absence of resultant forces and bending moments. Analytical expressions for the deformation fields demonstrate these effects for both incompressible and compressible generalizations of conventional hyperelastic materials. Existing results in the absence of a swelling agent are recovered as special cases.

Porohyperelastic finite element model for the kangaroo humeral head cartilage based on experimental study and the consolidation theory

Solid-extracellular fluid interaction is believed to play an important role in the strain-rate dependent mechanical behaviors of shoulder articular cartilages. It is believed that the kangaroo shoulder joint is anatomically and biomechanically similar to human shoulder joint and it is easy to get in Australia. Therefore, the kangaroo humeral head cartilage was used as the suitable tissue for the study in this paper. Indentation tests from quasi-static (10-4/sec) to moderately high strain-rate (10-2/sec) on kangaroo humeral head cartilage tissues were conduced to investigate the strain-rate dependent behaviors. A finite element (FE) model was then developed, in which cartilage was conceptualized as a porous solid matrix filled with incompressible fluids. In this model, the solid matrix was modeled as an isotropic hyperelastic material and the percolating fluid follows Darcy’s law. Using inverse FE procedure, the constitutive parameters related to stiffness, compressibility of the solid matrix and permeability were obtained from the experimental results. The effect of solid-extracellular fluid interaction and drag force (the resistance to fluid movement) on strain-rate dependent behavior was investigated by comparing the influence of constant, strain dependent and strain-rate dependent permeability on FE model prediction. The newly developed porohyperelastic cartilage model with the inclusion of strain-rate dependent permeability was found to be able to predict the strain-rate dependent behaviors of cartilages.