Thesis (Ph. D.)--University of Texas at Austin, 2000. / Vita. Includes bibliographical references (leaves 277-283). Available also in a digital version from Dissertation Abstracts.

Thesis (Ph. D.)--University of Hong Kong, 2001. / Includes bibliographical references (leaves 344-354).

Thin sheets and membrane structures are widely used in space applications such as solar sails, sunshields and membrane optics. Surface flatness over a large area is one of the key requirements for many applications using the flexible thin structures. However, wrinkles are commonly observed in thin sheets. It is thus important to understand the mechanics of thin sheets for practical applications that require reliable control of surface wrinkles. In this study, a model problem of stretch-induced wrinkling of thin sheets is considered. First, a two-dimensional (2-D) finite element model was developed to determine stretch-induced stress distribution patterns in hyperelastic thin sheets, assuming no wrinkles. As a prerequisite for wrinkling, development of compressive stresses in the transverse direction was found to depend on both the length-to-width aspect ratio of the sheet and the applied tensile strain. Next, an eigenvalue analysis was performed to predict the critical conditions for buckling of the elastic sheet under the prescribed boundary conditions, followed by a nonlinear post-buckling analysis to simulate evolution of stretch-induced wrinkles. Experiments were conducted to measure stretch-induced wrinkling of polyethylene thin sheets, using the three-dimensional digital image correlation (3D-DIC) technique. It was observed that the wrinkle amplitude first increased and then decreased with increasing nominal strain, in agreement with finite element simulations for a hyperelastic thin sheet. However, unlike the hyperelastic model, the stretch-induced wrinkles in the polyethylene sheet were not fully flattened at high strains (> 30%), with the residual wrinkle amplitude depending on the loading rate. The hyper-viscoelastic and the parallel network nonlinear viscoelastic material models were adopted for finite element simulations to improve the agreement with the experiments, including the wrinkle amplitude, residual wrinkles and rate dependence. Finally it is noted that wrinkling is sensitive to defects and material inhomogeneity in thin sheets. By varying the elastic stiffness in a narrow region, numerical simulations show drastically different wrinkling behavior, including the critical strain and evolution of wrinkle amplitude and wavelength. In conclusion, a comprehensive understanding of stretch-induced wrinkling is established, where geometry, material, and boundary conditions all play important roles. / text

Polymer-free viscoelastic surfactant-based (VES) fluid systems have been used to eliminate polymer-based damage and to efficiently transport proppants into the fracture. Current models and correlations neglect the important influence of fracture walls and fluid elasticity on proppant settling. This report presents an experimental study that investigates the impact of fluid elasticity and fracture width on proppant settling in VES fluid systems. Proppant settling experiments are performed in shear-thinning VES fluids. Experimental data is presented to show that fluid elasticity plays an important role in controlling the settling rate of the proppants. It is shown that elastic effects can increase as well as reduce the settling velocities depending upon the rheological properties of the fluid and properties of the proppants. Data is presented to show that the settling velocity reduces significantly as the proppant size becomes comparable to the fracture width. The reduction in settling velocity due to the presence of the fracture walls depends on the rheological properties of the fluid, ratio of particle diameter to fracture width as well as the diameter of the particle. / text

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A three-dimensional, incompressible, Rayleigh damped magnetic resonance elastography (MRE) material property reconstruction algorithm capable of reconstructing the spatial distribution of both the real and imaginary parts of the shear modulus, density and bulk modulus from full-field MR-detected harmonic motion data was developed. The algorithm uses a subzone-based implementation of motion error minimization techniques, using 27 hexahedral finite elements, and is written in FORTRAN to run on high performance distributed computing systems. The theory behind the methods used is presented in a form that is directly applicable to the code's structure, to serve as a reference for future research building on this algorithm. Globally defined Rayleigh damping parameter reconstructions using simulated data showed that it is possible to reconstruct the correct combination of Rayleigh parameters under noise levels comparable to MR measurements. The elastic wave equation is used to demonstrate that use of a one parameter damping model to fit a Rayleigh damped material can lead to artefacts in the reconstructed damping parameter images, a prediction that is verified using simulated reconstructions. Initial results using MR-detected motion data from both gelatine phantoms and in-vivo cases produced good reconstructions of real shear modulus, as well as showing promise for successful imaging of damping properties. An initial investigation into an alternative elemental basis function approach to supporting the material property distribution produced some promising results, as well as highlighting some significant issues with large variations across the elements.

It is widely recognised that the development and optimisation of industrial processes such as extrusion or injection moulding significantly benefit from accurate polymer processing simulations. Such simulations can lead to enormous cost savings, time to market and product improvements. The development of suitable constitutive models and a robust numerical algorithm are required for successful application of such tool to these processes. Appropriate material characterisation is also imperative to select the constitutive model parameters. Despite the importance and maturity of the polymer processing industry, the constitutive modelling of the rheological behaviour of long chain branched polymers presents still fascinating questions that need some answers. A breakthrough in this area was the design of a constitutive equation based on molecular arguments and known as the pom-pom model. The key feature of this model is the presence of separate relaxation times for the orientation and stretch mechanisms. The pompom model has been proved to be very accurate for the modelling of long chain branched polymers in rheometrical flows. Although very promising, this model suffers from numerical and rheological defects that hinder its use in complex flow simulations. To overcome these issues, the Double Convected pom-pom (DCPP) model is proposed. Its predictive capabilities are first analysed in various rheometrical flows including reverse multi-step shear strain and large amplitude oscillatory shear experiments. For complex flow simulation, the DCPP model is implemented in the commercial package POLYFLOW.Model predictions are compared to experimental birefringence data in planar contraction flows. In all cases, a satisfactory agreement is found between numerical simulation and experiments, demonstrating the potential of this model for the simulation of polymer processing operations. The simulations are then extended to three-dimensional geometries. The influence of non-perfectly two-dimensional flows on birefringence data is analysed. It is shown that the impact of these imperfections is strongly dependent on the flow rate. Is is commonly believed that increasing the geometry aspect ratio tends to decrease three-dimensional influence. It is demonstrated that this is verified only if the zero-order fringe does not disappear at any time during the experiment. Finally, a pragmatic approach is introduced to reformulate constitutive equations to explicitly express them in terms of orientation and stretch variables. This procedure is applied to the Phan-Thien Tanner and Giesekus models and both modelsare compared to the DCPP model. Comparing the models in this form, highlights their differences, and allows one to adopt the best features of each. This almost naturally leads to a proposal of a number of modifications to each of these models. The modified models are then assessed in rheometrical flows by comparing model predictions to experimental data. Significant improvements are demonstrated for in particular the Modified Giesekus model and the Modified DCPP: both models perform remarkably well in a range of non-linear rheometric flows, and are therefore promising candidates for predicting industrial flow problems.