Caputo Derivatives in Viscoelasticity: A Non-Linear Finite-Deformation Theory for Tissue

Mathematics Subject Classification: 26A33, 74B20, 74D10, 74L15

Predictions of angle dependent tortuosity and elasticity effects on sound propagation in cancellous bone

The anisotropic pore structure and elasticity of cancellous bone cause wave speeds and attenuation in cancellous bone to vary with angle. Previously published predictions of the variation in wave speed with angle are reviewed. Predictions that allow tortuosity to be angle dependent but assume isotropic elasticity compare well with available data on wave speeds at large angles but less well for small angles near the normal to the trabeculae. Claims for predictions that only include angle-dependence in elasticity are found to be misleading. Audio-frequency data obtained at audio-frequencies in air-filled bone replicas are used to derive an empirical expression for the angle-and porosity-dependence of tortuosity. Predictions that allow for either angle dependent tortuosity or angle dependent elasticity or both are compared with existing data for all angles and porosities.

A node-based smoothed conforming point interpolation method (NS-CPIM) for elasticity problems

This paper formulates a node-based smoothed conforming point interpolation method (NS-CPIM) for solid mechanics. In the proposed NS-CPIM, the higher order conforming PIM shape functions (CPIM) have been constructed to produce a continuous and piecewise quadratic displacement field over the whole problem domain, whereby the smoothed strain field was obtained through smoothing operation over each smoothing domain associated with domain nodes. The smoothed Galerkin weak form was then developed to create the discretized system equations. Numerical studies have demonstrated the following good properties: NS-CPIM (1) can pass both standard and quadratic patch test; (2) provides an upper bound of strain energy; (3) avoid the volumetric locking; (4) provides the higher accuracy than those in the node-based smoothed schemes of the original PIMs.

Evaluation cortical bone elasticity in response to pulse power excitation using ultrasonic technique

This paper presents the ultrasonic velocity measurement method which investigates the possible effects of high voltage high frequency pulsed power on cortical bone material elasticity. Before applying a pulsed power signal on a live bone, it is essential to determine the safe parameters of pulsed power applied on bone non-destructively. Therefore, the possible changes in cortical bone material elasticity due to a specified pulsed power excitation have been investigated. A controllable positive buck-boost converter with adjustable output voltage and frequency has been used to generate high voltage pulses (500V magnitude at 10 KHz frequency). To determine bone elasticity, an ultrasonic velocity measurement has been conducted on two groups of control (unexposed to pulse power but in the same environmental condition) and cortical bone samples exposed to pulsed power. Young’s modulus of cortical bone samples have been determined and compared before and after applying the pulsed power signal. After applying the high voltage pulses, no significant variation in elastic property of cortical bone specimens was found compared to the control. The result shows that pulsed power with nominated parameters can be applied on cortical bone tissue without any considerable negative effect on elasticity of bone material.

A novel quadratic Edge-based Smoothed Conforming Point Interpolation Method (ES-CPIM) for elasticity problems

his paper formulates an edge-based smoothed conforming point interpolation method (ES-CPIM) for solid mechanics using the triangular background cells. In the ES-CPIM, a technique for obtaining conforming PIM shape functions (CPIM) is used to create a continuous and piecewise quadratic displacement field over the whole problem domain. The smoothed strain field is then obtained through smoothing operation over each smoothing domain associated with edges of the triangular background cells. The generalized smoothed Galerkin weak form is then used to create the discretized system equations. Numerical studies have demonstrated that the ES-CPIM possesses the following good properties: (1) ES-CPIM creates conforming quadratic PIM shape functions, and can always pass the standard patch test; (2) ES-CPIM produces a quadratic displacement field without introducing any additional degrees of freedom; (3) The results of ES-CPIM are generally of very high accuracy.

The modulus of elasticity of steel - is it 200 GPa?

In cold-formed steel construction, the use of a range of thin, high strength steels (0.35 mm thickness and 550 MPa yield stress) has increased significantly in recent times. A good knowledge of the basic mechanical properties of these steels is needed for a satisfactory use of them. In relation to the modulus of elasticity, the current practice is to assume it to be about 200 GPa for all steel grades. However, tensile tests of these steels have consistently shown that the modulus of elasticity varies with grade of steel and thickness. It was found that it increases to values as high as 240 GPa for smaller thicknesses and higher grades of steel. This paper discusses this topic, presents the tensile test results for a number of steel grades and thicknesses, and attempts to develop a relationship between modulus of elasticity, yield stress and thickness for the steel grades considered in this investigation.

Fine tuning of elasticity via crosslinking collagen-based materials to mediate mechanotransduction and stability using corona treatment

The common goal of tissue engineering is to develop substitutes that can closely mimic the structure of extracellular matrix (ECM). However, similarly important is the intensive material properties which have often been overlooked, in particular, for soft tissues that are not to bear load assumingly. The mechanostructural properties determine not only the structural stability of biomaterials but also their physiological functionality by directing cellular activity and regulating cell fate decision. The aim here is to emphasize that cells could sense intensive material properties like elasticity and reside, proliferate, migrate and differentiate accordinglyno matter if the construct is from a natural source like cartilage, skin etc. or of synthetic one. Meanwhile, the very objective of this work is to provide a tunable scheme for manipulating the elasticity of collagen-based constructs to be used to demonstrate how to engineer cell behavior and regulate mechanotransduction. Articular cartilage was chosen as it represents one of the most complex hierarchical arrangements of collagen meshwork in both connective tissues and ECM-like biomaterials. Corona discharge treatment was used to produce constructs with varying density of crosslinked collagen and stiffness accordingly. The results demonstrated that elastic modulus increased up to 33% for samples treated up to one minute as crosslink density was found to increase with exposure time. According to the thermal analysis, longer exposure to corona increased crosslink density as the denaturation enthalpy increased. However the spectroscopy results suggested that despite the stabilization of the collagen structure the integrity of the triple helical structure remained intact. The in vitro superficial culture of heterologous chondrocytes also determined that the corona treatment can modulate migration with increased focal adhesion of cells due to enhanced stiffness, without cytotoxicity effects, and providing the basis for reinforcing three-dimensional collagen-based biomaterials in order to direct cell function and mediate mechanotransduction.

High-throughput indentational elasticity measurements of hydrogel extracellular matrix substrates

Much interest surrounds the effect of extracellular matrix (ECM) elasticity on cell behavior. Here we present a rapid method for measuring the elasticity of synthetic ECM substrates based on indentation of the substrate with a ferromagnetic sphere and optical tracking of the resulting deformation. We find that this method yields order-of-magnitude agreement with atomic force microscopy elasticity measurements, but that the degree of this agreement depends strongly on sphere density and gel elasticity. In its regime of greatest accuracy, we envision that this method may be used for high-throughput characterization of ECM substrates in cell biological studies.

Understanding classroom trouble through regulative gravity and instructional elasticity

This paper aims to develop a more nuanced analytic vocabulary to typify how and where classroom trouble can manifest in pedagogic discourse. It draws on classroom ethnographies conducted in non-academic secondary school pathways and alternative programs in Australian communities with high youth unemployment, where the policy of ‘earning or learning’ till age 17 has effectively extended compulsory schooling. Three concepts are developed and exemplified: ‘regulative flares’, being moments when teachers resort to explicitly reasserting the lesson’s social order; ‘moral gravity’ to describe the degree to which the moral order underpinning the regulative discourse is tied to the immediate context or beyond; and ‘instructional elasticity’ to account for trouble originating in the instructional register.

Size-dependent elasticity of nanocrystalline titania

Synchrotron-based high-pressure x-ray diffraction measurements indicate that compressibility, a fundamental materials property, can have a size-specific minimum value. The bulk modulus of nanocrystalline titania has a maximum at particle size of 15 nm. This can be explained by dislocation behavior because very high dislocation contents can be achieved when shear stress induced within nanoparticles counters the repulsion between dislocations. As particle size decreases, compression increasingly generates dislocation networks hardened by overlap of strain fields that shield intervening regions from external pressure. However, when particles become too small to sustain high dislocation concentrations, elastic stiffening declines. The compressibility has a minimum at intermediate sizes.

Subsurface deformation in dry sliding of hypo-eutectic Al-Si alloys

The subsurface deformation during dry sliding of Al-Si alloys is studied by fragmentation of silicon particles. The size of the fragmented particles does not vary with load. The depth of deformation is found to increase with increase in normal load. This experimental observation agrees with load-deformation depth characteristics obtained by a slip line field model.

Chronic and acute stress in atherosclerosis : the role of endothelial function and arterial elasticity

Atherosclerosis is the main underlying pathology of coronary heart disease. Coronary heart disease is a serious health problem in Finland, and it is the leading cause of morbidity and mortality in industrialized countries. Psychological stress correlates with coronary heart disease events – myocardial infarction and sudden death, which are the most common clinical syndromes of atherosclerotic narrowing of arteries. The present series of studies examines the interaction between stress and endothelial function in relation to atherosclerosis. The study also aims to give new information on the mechanisms through which stress has its effect on atherosclerosis progression, focusing on possible relations between psychological stress and the functioning of the endothelium. Our project is based on data from one of the largest national epidemiological studies, the Cardiovascular Risk in Young Finns study, which has monitored the development of risk factors for coronary heart disease in 3596 young adults since 1980. The present study combines experimental stress research with epidemiology and uses an advanced method for examining atherosclerosis development in healthy subjects (intima-media thickness ultrasound measurement). The physiological parameters used were heart rate, respiratory sinus arrhythmia and pre-ejection period. Chronic stress was assessed by vital exhaustion. The ultrasound measurements that served as the indexes of preclinical atherosclerosis were carotid intima-media thickness, brachial flow-mediated dilatation and carotid artery compliance. The effects of cardiovascular risk factors found to be important were taken into account: serum cholesterols level, triglyceride level, serum insulin level and systolic and diastolic blood pressure. There were 69, 1596, 81 and 1721 participants in studies I-IV, respectively. The results showed that both chronic and acute stress may exert an effect on atherosclerosis in subjects with impaired endothelial responses. The findings are consistent with the idea that risk factors are more harmful if the endothelium is not working properly. Chronic stress was found to be a risk if it has resulted in ineffective cardiac stress reactivity or delayed recovery. Men were shown to be at increased risk for atherosclerotic progression in early life, which suggests men’s decreased stress coping ability in relation to stressful psychosocial coronary risk factors. Autonomic imbalance may be the common mechanism of the stress influence on atherosclerosis development. The results of the present study contain background information for the identification the first stages of atherosclerosis, and they may be useful for preventive medicine programs for young adults and could help to improve cardiovascular health in Finland as well as in other countries.

Comparison of Elasticity, Shell Core, and Sandwich Shell Theories

The problem of an infinite circular sandwich shell subjected to an a\isymmetric radial line load is investigated using three-dimensional elasticity theory, shell core method, and sandwich shell theory due to Fulton and Schmidt. A comparison of the stresses and displacements with an exact elasticity solution is carried out for various shell parameters in order to clearly bring out the limitations of sandwich shell theories of Fulton and Schmidt as well as the shell core solution.