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.

An improved modal strain energy method for damage assessment

The modal strain energy method, which depends on the vibration characteristics of the structure, has been reasonably successful in identifying and localising damage in the structure. However, existing strain energy methods require the first few modes to be measured to provide meaningful damage detection. Use of individual modes with existing strain energy methods may indicate false alarms or may not detect the damage at or near the nodal points. This paper proposes a new modal strain energy based damage index which can detect and localize the damage using any one of the modes measured and illustrates its application for beam structures. It becomes evident that the proposed strain energy based damage index also has potential for damage quantification.

Indentation size effect and strain rate sensitivity of nanocrystalline Mg-Al alloys

Deformation Behaviour of microcrystalline (mc) and nanocrystalline (nc) Mg-5%Al alloys produced by hot extrusion of ball-milled powders were investigated using instrumented indentation tests. The hardness values of the mc and nc metals exhibited indentation size effect (ISE), with nc alloys showing weaker ISE. The highly localized dislocation activities resulted in a small activation volume, hence enhanced strain rate sensitivity. Relative higher strain rate sensitivity and the negative Hall-Petch Relationship suggested the increasingly important role of grain boundary mediated mechanisms when the grain size decreased to nanometer region.

Compressive behaviour of nanocrystallilne Mg-5%Al alloys

Magnesium alloys are attracting increasing research interests due to their low density, high specific strength and good mechineability and availability as compared to other structural materials. However, the deformation and failure mechanisms of nanocrystalline Mg alloys have not been well understood. In this work, the deformation behavior of nanocrystalline Mg-5% Al alloys was investigated using compression test, with a focus on the effects of grain size. The average grain size of the Mg-Al alloy was changed from 13 µm to 50 nm via mechanical milling. The results showed that grain size had a significant influence on the yield stress and ductility of the Mg alloys, and the materials exhibited increased strain rate sensitivity with decrease of grain size. The deformation mechanisms were also strongly dependent with the grain sizes.

The role of emotional labour and role stress on burnout and psychological strain in high contact service employees

This study examines the relationships between job demands (in the form of role stressors and emotional management) and employee burnout amongst high contact service employees. Employees in customer facing roles are frequently required to manage overwhelming, conflicting or ambiguous demands, which they may feel ill-equipped to handle. Simultaneously, they must manage the emotions they display towards customers, suppressing some, and expressing others, be they genuine or contrived. If the in-role effort required of employees exceeds their inherent capacity to cope, burnout may result. Burnout, in turn, can have serious detrimental consequences for the psychological well being of employees. We find that both emotional management and role stressors impact burnout. We also confirm that burnout predicts psychological strain. In line with the Job Demands and Resources Model, we examine the mitigating impact of perceived support on these relationships but do not find a significant mitigating impact.

Complete Nucleotide Sequence of Rice Tungro Spherical Virus Genome of a Highly Virulent Strain Vt6

The complete nucleotide sequence of rice tungro spherical virus (RTSV) strain Vt6, originally from Mindanao, the Philippines, with higher virulence to resistant rice cultivars, was determined and compared with the published sequence for the Philippine-type strain A (RTSV-A-Shen). It was reported that RTSV-A was not able to infect a rice resistant cultivar TKM 6 (10). RTSV-Vt6 and RTSV-A-Shen share 90% and 95% homology at nucleotide and amino-acid levels, respectively. The N-terminal leader sequence of RTSV-Vt6 contained a 39-amino acids-region (positions 65 to 103) which was totally different from that of RTSV-A-Shen; the difference resulted from frame shifting by nucleotide insertions and deletions. To confirm the amino-acid sequence differences of the leader polypeptide, the same region was cloned and sequenced using a newly obtained variant of RTSV-type 6, which had been collected in the field of IRRI, and seven field isolates from Mindanao, the Philippines. Since all the sequences of the target region are identical to that of the Vt6 leader polypeptide, the sequence difference in the leader region seems not to correlate with the virulence of Vt6.

Vibration characteristics of plate elements subjected in-plane loads (axial loads)

Axial deformations resulting from in-plane loads (axial forces) of plate elements impact significantly on their vibration characteristics. Although, numerous methods have been developed to quantify axial forces and hence deformations of individual plate elements with different boundary conditions based on their natural frequencies, these methods are unable to apply to the plate elements in a structural system. This is because the natural frequency is a global parameter for the entire structure. Thus, this paper proposes a comprehensive vibration based procedure to quantify axial deformations of plate elements in a structural framing system. Unique capabilities of the proposed method present through illustrative examples. Keywords- Plate Elements, Dynamic Stiffness Matrix, Finite Element Method, Vibration Characteristics, Axial Deformation

Mechanical conditions in the initial phase of bone healing

Background: Bone healing is sensitive to the initial mechanical conditions with tissue differentiation being determined within days of trauma. Whilst axial compression is regarded as stimulatory, the role of interfragmentary shear is controversial. The purpose of this study was to determine how the initial mechanical conditions produced by interfragmentary shear and torsion differ from those produced by axial compressive movements. ----- ----- Methods: The finite element method was used to estimate the strain, pressure and fluid flow in the early callus tissue produced by the different modes of interfragmentary movement found in vivo. Additionally, tissue formation was predicted according to three principally different mechanobiological theories. ----- ----- Findings: Large interfragmentary shear movements produced comparable strains and less fluid flow and pressure than moderate axial interfragmentary movements. Additionally, combined axial and shear movements did not result in overall increases in the strains and the strain magnitudes were similar to those produced by axial movements alone. Only when axial movements where applied did the non-distortional component of the pressure–deformation theory influence the initial tissue predictions. ----- ----- Interpretation: This study found that the mechanical stimuli generated by interfragmentary shear and torsion differed from those produced by axial interfragmentary movements. The initial tissue formation as predicted by the mechanobiological theories was dominated by the deformation stimulus.

A material model for flexural crack simulation in reinforced concrete elements using ABAQUS

This paper presents a material model to simulate load induced cracking in Reinforced Concrete (RC) elements in ABAQUS finite element package. Two numerical material models are used and combined to simulate complete stress-strain behaviour of concrete under compression and tension including damage properties. Both numerical techniques used in the present material model are capable of developing the stress-strain curves including strain softening regimes only using ultimate compressive strength of concrete, which is easily and practically obtainable for many of the existing RC structures or those to be built. Therefore, the method proposed in this paper is valuable in assessing existing RC structures in the absence of more detailed test results. The numerical models are slightly modified from the original versions to be comparable with the damaged plasticity model used in ABAQUS. The model is validated using different experiment results for RC beam elements presented in the literature. The results indicate a good agreement with load vs. displacement curve and observed crack patterns.

A biomechanical investigation of vertebral staples for fusionless scoliosis correction

Background: Fusionless scoliosis surgery is an early-stage treatment for idiopathic scoliosis which claims potential advantages over current fusion-based surgical procedures. Anterior vertebral stapling using a shape memory alloy staple is one such approach. Despite increasing interest in this technique, little is known about the effects on the spine following insertion, or the mechanism of action of the staple. The purpose of this study was to investigate the biomechanical consequences of staple insertion in the anterior thoracic spine, using in vitro experiments on an immature bovine model. Methods: Individual calf spine thoracic motion segments were tested in flexion, extension, lateral bending and axial rotation. Changes in motion segment rotational stiffness following staple insertion were measured on a series of 14 specimens. Strain gauges were attached to three of the staples in the series to measure forces transmitted through the staple during loading. A micro-CT scan of a single specimen was performed after loading to qualitatively examine damage to the vertebral bone caused by the staple. Findings: Small but statistically significant decreases in bending stiffness occurred in flexion,extension, lateral bending away from the staple, and axial rotation away from the staple. Each strain-gauged staple showed a baseline compressive loading following insertion which was seen to gradually decrease during testing. Post-test micro-CT showed substantial bone and growth plate damage near the staple. Interpretation: Based on our findings it is possible that growth modulation following staple insertion is due to tissue damage rather than sustained mechanical compression of the motion segment.

The measurement of applied forces during anterior single rod surgical correction of adolescent idiopathic scoliosis

INTRODUCTION. Following anterior thoracoscopic instrumentation and fusion for the treatment of thoracic AIS, implant related complications have been reported as high as 20.8%. Currently the magnitudes of the forces applied to the spine during anterior scoliosis surgery are unknown. The aim of this study was to measure the segmental compressive forces applied during anterior single rod instrumentation in a series of adolescent idiopathic scoliosis patients. METHODS. A force transducer was designed, constructed and retrofitted to a surgical cable compression tool, routinely used to apply segmental compression during anterior scoliosis correction. Transducer output was continuously logged during the compression of each spinal joint, the output at completion converted to an applied compression force using calibration data. The angle between adjacent vertebral body screws was also measured on intra-operative frontal plane fluoroscope images taken both before and after each joint compression. The difference in angle between the two images was calculated as an estimate for the achieved correction at each spinal joint. RESULTS. Force measurements were obtained for 15 scoliosis patients (Aged 11-19 years) with single thoracic curves (Cobb angles 47˚- 67˚). In total, 95 spinal joints were instrumented. The average force applied for a single joint was 540 N (± 229 N)ranging between 88 N and 1018 N. Experimental error in the force measurement, determined from transducer calibration was ± 43 N. A trend for higher forces applied at joints close to the apex of the scoliosis was observed. The average joint correction angle measured by fluoroscope imaging was 4.8˚ (±2.6˚, range 0˚-12.6˚). CONCLUSION. This study has quantified in-vivo, the intra-operative correction forces applied by the surgeon during anterior single rod instrumentation. This data provides a useful contribution towards an improved understanding of the biomechanics of scoliosis correction. In particular, this data will be used as input for developing patient-specific finite element simulations of scoliosis correction surgery.

Simulation of inplane and out of plane AE source in thin plate

In most materials, short stress waves are generated during the process of plastic deformation, phase transformation, crack formation and crack growth. These phenomena are applied in acoustic emission (AE) for the detection of material defects in a wide spectrum of areas, ranging from nondestructive testing for the detection of materials defects to monitoring of microseismical activity. AE technique is also used for defect source identification and for failure detection. AE waves consist of P waves (primary longitudinal waves), S waves (shear/transverse waves) and Rayleigh (surface) waves as well as reflected and diffracted waves. The propagation of AE waves in various modes has made the determination of source location difficult. In order to use acoustic emission technique for accurate identification of source, an understanding of wave propagation of the AE signals at various locations in a plate structure is essential. Furthermore, an understanding of wave propagation can also assist in sensor location for optimum detection of AE signals along with the characteristics of the source. In real life, as the AE signals radiate from the source it will result in stress waves. Unless the type of stress wave is known, it is very difficult to locate the source when using the classical propagation velocity equations. This paper describes the simulation of AE waves to identify the source location and its characteristics in steel plate as well as the wave modes. The finite element analysis (FEA) is used for the numerical simulation of wave propagation in thin plate. By knowing the type of wave generated, it is possible to apply the appropriate wave equations to determine the location of the source. For a single plate structure, the results show that the simulation algorithm is effective to simulate different stress waves.

Testing and simulation of extruded polystyrene foam at low to moderate strain rates

This paper presents a study into the behaviour of extruded polystyrene foam at low strain rates. The foam is being studied in order assess its potential for use as part of a new innovative design of portable road safety barrier the aim to consume less water and reduce rates of serious injury. The foam was tested at a range of low strain rates, with the stress and strain behaviour of the foam specimens being recorded. The energy absorption capabilities of the foam were assessed as well as the response of the foam to multiple loadings. The experimental data was then used to create a material model of the foam for use in the explicit finite element solver LS-DYNA. Simulations were carried out using the material model which showed excellent correlation between the numerical material model and the experimental data.