A hydrogel consists of a cross-linked polymer network and solvent molecules, capable of large, reversible deformation in response to a variety of external stimuli. In particular, diverse instability patterns have been observed experimentally in swelling hydrogels under mechanical constraints. The present study develops a general theoretical framework based on a variational approach, which leads to a set of governing equations coupling mechanical and chemical equilibrium conditions for swelling deformation of hydrogels, along with proper boundary conditions. A specific material model is employed for analytical and numerical studies, for which the nonlinear constitutive behavior of the hydrogel is derived from a free energy function combining rubber elasticity with a polymer solution theory. A finite element method is then developed and implemented as a user-defined material (UMAT) in the commercial package, ABAQUS. By numerical simulations, the effect of constraint on inhomogeneous swelling of substrate-attached hydrogel lines is elucidated. It is found that crease-like surface instability occurs when the width-to-height aspect ratio of the hydrogel line exceeds a critical value. Next, by considering a hydrogel layer on a rigid substrate, swell-induced surface instability is studied in details. A linear perturbation analysis is performed to predict the critical condition for onset of the surface instability. In contrast to previously suggested critical conditions, the present study predicts a range of critical swelling ratios, from about 2.5 to 3.4, depending on the material properties of the hydrogel system. A stability diagram is constructed with two distinct regions for stable and unstable hydrogels with respect to two dimensionless material parameters. Numerical simulations are presented to show the swelling process, with evolution of initial surface perturbations followed by formation of crease-like surface patterns. Furthermore, with combined swelling and mechanical compression, the stability analysis is extended to predict a general critical condition that unifies the swell-induced surface instability of hydrogels with mechanically induced surface instability of rubbers. The effect of surface tension is found to be critical in suppressing short-wavelength modes of surface instability, while the substrate confinement suppresses long-wavelength modes. With both surface tension and substrate confinement, an intermediate wavelength is selected at a critical swelling ratio for onset of surface instability. Both the critical swelling ratio and the characteristic wavelength depend on the initial thickness of the hydrogel layer as well as other material properties of the hydrogel. It is found that the hydrogel layer becomes increasingly stable as the initial layer thickness decreases. A critical thickness is predicted, below which the hydrogel layer swells homogeneously and remains stable at the equilibrium state. Finally, three-dimensional finite element models are developed to simulate swelling deformation of hydrogel lines. Depending on the aspect ratio of the cross section as well as the material properties of the hydrogel, two types of swell-induced instability patterns are envisaged, i.e., localized surface instability versus global buckling. / text

MSc Physiotherapy, Faculty of Health Sciences, University of the Witwatersrand, 2009. / INTRODUCTION Rugby is a high impact sport with many injuries reported in the literature. A high rate of ankle injury is reported with resultant recurrence of these injuries. There is however only scarce epidemiological data with minimal detail to highlight clinical findings and prevalence of ankle injuries especially in the club rugby fraternity. AIMS This study investigated the prevalence of clinical signs of ankle injuries in rugby players at club rugby level in the South Gauteng region. The data collected was used to identify the clinical signs related to ankle instability for perceived, mechanical and functional parameters and was applied to determine the difference between players with and those without previous injury. METHODOLOGY The researcher obtained ethical clearance to do the study from the Human Research Ethics Committee of the University of the Witwatersrand. Permission was obtained from the Golden Lions Gauteng Rugby Union to use players in the South Gauteng region. One hundred and eighty players from nine clubs in the region participated in the study. Informed consent was obtained from all parties concerned and players were asked to complete a battery of tests. To determine the prevalence of clinical signs of perceived instability each player was asked to complete a data questionnaire and the Olerud and Molander questionnaire. The data questionnaire also included questions pertaining to the exclusion criteria. iii Objective testing was done to determine the clinical signs of mechanical instability of both ankles of each player through mechanical tests; the talar tilt and anterior drawer tests. Balance and proprioception were assessed through the Star Excursion Balance Test (SEBT) and Balance Error Scoring System (BESS) which is used to indicate clinical signs of functional instability and these tests were used to determine the prevalence of clinical signs of functional instability and to relate the clinical signs of functional instability to the other clinical findings. RESULTS The prevalence of ankle injuries at club rugby level is discussed for the different parameters of instability. The prevalence of clinical signs of perceived instability based on the Olerud and Molander questionnaire is 47%, as reported by the player and is further described in a sub-analysis of perceived problems. The prevalence of clinical signs of mechanical ankle instability, when laterality is ignored is 38.7%. The prevalence of clinical signs of functional ankle instability depends on the surface and the visual input and is greater as the challenge or protuberance increases in difficulty. The clinical signs of perceived, mechanical and functional ankle instability are further described and related to other clinical findings for two groups, namely those with and those without previous injury to the ankle and as expected clinically significant differences were noted with the players with previous injury recording a higher prevalence for perceived and mechanical parameters. The odds ratios for the presence of certain clinical signs revealed significant p-values for the presence of pain, stiffness and swelling and the need for supports e.g. bracing or taping and the affect on activities of daily living. DISCUSSION In this study there is a high prevalence of clinical signs of ankle instability in club rugby players for perceived, mechanical and functional parameters, compared to the prevalence reported in the literature. From the study the clinical findings associated with the presentation of ankle injuries in club rugby players have been established and related to the perceived, mechanical and functional signs of instability. Differentiation between players with reported ankle injury and those without were also done and significant differences were noted between the two groups for perceived and mechanical parameters but where the functional assessment was done it supported the fact that balance and proprioception tests included the whole kinetic chain and does not view the ankle in isolation. It was evident that previously injured players were more likely to sustain future injury to the ankle and odds-ratios to support this showed an increased risk of the presence of swelling, stiffness and pain for players with previous injury and the greater need for the use of supports and influence on activities of daily life. The information gathered can be used in the future to set up a management plan for pre-season screening, assessing and addressing individual predisposing biomechanical factors, managing acute injuries successfully and rehabilitation in the post-season phase.

No description available.

An investigation is described of the instability of the horizontal free surface of a thin layer of liquid metal. The instability is due to the interaction of imposed electric and magnetic fields which are both initially horizontal. The interaction of fields produces a vertically upward magnetic force within the layer. Various two-dimensional theoretical models of the instability are described. A linear, viscous analysis of free surface instability is presented, and an analytical expression is obtained for the rate of growth of amplitude of a plane sinusoidal wave on the liquid free surface. A nonlinear model of a wave is also discussed on the assumption, later justified by experiment, that the waveform remains approximately sinusoidal providing the ratio of its amplitude and wavelength is small. An exact analysis is presented of a stationary wave in dynamical equilibrium. An experiment is described investigating the instability of a thin layer of liquid gallium. A new method for making instantaneous measurements of two-dimensional wave profiles is presented. Experimental observations are described of waves on an initially undisturbed free surface. It is confirmed that wave corrugations of the orientation predicted by linear theory to grow most quickly are observed to grow more quickly than other wave modes. Qualitative observations indicate the presence of secondary horizontal motions much larger than previous linear analyses have suggested. Quantative results indicate certain stability at non-zero amplitudes of linearly unstable waves if the Weber number is less than 0.12 and the Reynolds number is less than 75. Conversely, separation of gallium from the layer is observed invariably if the Weber number is greater than 0.31 and the Reynolds number is greater than 130.

No description available.

No description available.

No description available.

No description available.

No description available.

No description available.