No description available.

In this thesis we examine some of the interesting aspects of stability for some convection problems. Specifically, the first part of the thesis deals with the Bénard problem for various Non-Newtonian fluids, whereas the second part develops a stability analysis for convection in a porous medium. The work on stability for viscoelastic fluids includes nonlinear stability analyses for the second grade fluid, the generalised second grade fluid, the fluid of dipolar type and the fluid of third grade. It is worth remarking that throughout the work the viscosity is supposed to be any given function of temperature, with the first derivative bounded above by a positive constant. The connection between the two parts of the thesis is made through the method used to approach the nonlinear stability analysis, namely the energy method. It is shown in the introductory chapter how this method works and what are its advantages over the linear analysis. Nonlinear stability results established in both Part I and Part II are the best one can get for the considered physical situations. Different choices of energy have been considered in order to achieve conditional or unconditional nonlinear stability results.

Sandwich composites with polymer foam core are currently used in load-bearing components in buildings and naval structures due to their high strength to weight and stiffness to weight ratios, excellent thermal insulation, and ease of manufacturing. During their service time, sandwich composites are exposed to various external mechanical and hygro-thermal stimuli. It is known that the constituent properties of the sandwich composites are greatly influenced by the temperature and moisture fields. For example extreme temperature changes and humid environmental conditions can significantly degrade the stiffness and strength of the polymer foam core. This study analyzes the effect of moisture diffusion on the deformation of viscoelastic sandwich composites, which are composed of orthotropic fiber-reinforced laminated skins and viscoelastic polymeric foam core. It is assumed that the elastic and time-dependent (transient) moduli at any particular location in the foam core depend on the moisture concentration at that location. Sequentially coupled analyses of moisture diffusion and deformation are performed to predict overall performance of the studied viscoelastic sandwich systems. A time and moisture dependent constitutive model is used for the polymer foam core. A time-integration algorithm is developed to link this constitutive model to finite element (FE) analyses framework. The overall time-dependent responses of the sandwich composites subject to moisture diffusion are analyzed using 2D plane strain and 3D continuum elements. A 23% increase in the transverse deformation of the viscoelastic sandwich beam is observed due to the moisture degradation. Experimental data and analytical models available in the literature are used to verify the results obtained from the FE code. Parametric studies on the effects of different diffusivity ratios of skin and core materials on stress, strain and displacement fields have been analyzed. At the initial times the effect of moisture on the field variables is found to be most pronounced in the case with the highest diffusivity ratio. Contributions of moisture dependent elastic and the time-dependent moduli to the overall stress, strain and displacement field have been studied. The structural analysis of the sandwich composite under combined moisture diffusion and mechanical loading for two kinds of problems using FE method is performed to complete the study.

This study analyzes the thermo-mechanical response of a composite cylinder made up of two layers of linear isotropic viscoelastic materials that belong to the class of non-Thermorheologically Simple Material. The effect of time-varying temperature field due to unsteady heat conduction phenomenon is analyzed on the short term and long term material response in terms of stress, strain and displacement fields. The material properties of the two layers of the composite cylinder at any given location and time are assumed to depend on the temperature at that location at that given instant of time. Sequentially coupled analyses of heat conduction and deformation of viscoelastic composite cylinder is carried out to obtain the overall response. The stress and strain field developed in the composite cylinder is evaluated as the discontinuity in hoop stress and radial strain at the interface of the two layers caused due to mismatch in material properties may lead to delamination if it exceeds critical value. Analytical solution for the stress, strain and displacement fields of the viscoelastic composite cylinder is developed from the corresponding solution of linear elasticity problem by using the Correspondence Principle. The analytical solution for determining the temperature dependent stress, strain and displacement fields is further developed by incorporating the temperature dependence on the material properties and modeling the material as non-TSM. To analyze more complex geometry with general loading and boundary conditions, Finite Element(FE) analysis of the composite cylinder is performed and the results of analytical and FE method are found to be in good agreement. Parametric studies are carried out to understand the effect of change in material parameters namely the Prony coefficients in the transient creep compliance, characteristic of creep time in transient creep compliance and the instantaneous elastic compliance, on the overall response of the composite cylinder. The effect of different temperature dependent functions of the material properties, namely linear temperature variation and quadratic polynomial variation on the overall material response is also analyzed. It is observed that the effect of change in elastic properties significantly increases the jump in hoop stress and radial strain. It is also observed that when the materials are highly dependent on temperature the jump in radial strain and hoop stress increases significantly. The radial displacement also increases by a significant amount in both the cases.

Three kinds of propagating waves physically admissible in a tubular section are derived to establish their dispersion characteristics in response to the presence of multi-layered viscoelastic coatings. One is the longitudinal wave that propagates in the axial direction. The other two are shear and longitudinal waves along the circumferential direction. To characterize the hollow cylinder with coating layers, wave dispersion and attenuation are studied using the “global matrix” technique. Since each layer is considered to be perfectly bonded to each other, displacement and strain continuity are imposed as the interfacial boundary conditions. Viscoelastic coating materials such as bitumen and epoxy serve to improve pipeline reliability, but they also dampen and dissipate wave energy. The viscoelastic materials are studied as well. By replacing the real material constants with complex material constants in the characteristic equation, the impact of the viscoelastic coatings on wave dispersion is established. Bisection method is followed to find the real and complex roots of the three characteristic equations derived. Roots thus obtained are manipulated to allow the phase velocity and attenuation dispersion to be plotted against frequency. The dispersion of phase velocity and wave attenuation for coated pipes are evaluated against a baseline model which is the bare, uncoated tubing to establish the propagation characteristics of the guided shear and longitudinal waves in the presence of multiple coating layers. The effects of increasing attenuation parameter and coating thickness are also investigated.

Sandwich composites with polymer foam core are currently used in load-bearing components in buildings and naval structures due to their high strength to weight and stiffness to weight ratios, excellent thermal insulation, and ease of manufacturing. During their service time, sandwich composites are exposed to various external mechanical and hygro-thermal stimuli. It is known that the constituent properties of the sandwich composites are greatly influenced by the temperature and moisture fields. For example extreme temperature changes and humid environmental conditions can significantly degrade the stiffness and strength of the polymer foam core. This study analyzes the effect of moisture diffusion on the deformation of viscoelastic sandwich composites, which are composed of orthotropic fiber-reinforced laminated skins and viscoelastic polymeric foam core. It is assumed that the elastic and time-dependent (transient) moduli at any particular location in the foam core depend on the moisture concentration at that location. Sequentially coupled analyses of moisture diffusion and deformation are performed to predict overall performance of the studied viscoelastic sandwich systems. A time and moisture dependent constitutive model is used for the polymer foam core. A time-integration algorithm is developed to link this constitutive model to finite element (FE) analyses framework. The overall time-dependent responses of the sandwich composites subject to moisture diffusion are analyzed using 2D plane strain and 3D continuum elements. A 23% increase in the transverse deformation of the viscoelastic sandwich beam is observed due to the moisture degradation. Experimental data and analytical models available in the literature are used to verify the results obtained from the FE code. Parametric studies on the effects of different diffusivity ratios of skin and core materials on stress, strain and displacement fields have been analyzed. At the initial times the effect of moisture on the field variables is found to be most pronounced in the case with the highest diffusivity ratio. Contributions of moisture dependent elastic and the time-dependent moduli to the overall stress, strain and displacement field have been studied. The structural analysis of the sandwich composite under combined moisture diffusion and mechanical loading for two kinds of problems using FE method is performed to complete the study.

This study analyzes the thermo-mechanical response of a composite cylinder made up of two layers of linear isotropic viscoelastic materials that belong to the class of non-Thermorheologically Simple Material. The effect of time-varying temperature field due to unsteady heat conduction phenomenon is analyzed on the short term and long term material response in terms of stress, strain and displacement fields. The material properties of the two layers of the composite cylinder at any given location and time are assumed to depend on the temperature at that location at that given instant of time. Sequentially coupled analyses of heat conduction and deformation of viscoelastic composite cylinder is carried out to obtain the overall response. The stress and strain field developed in the composite cylinder is evaluated as the discontinuity in hoop stress and radial strain at the interface of the two layers caused due to mismatch in material properties may lead to delamination if it exceeds critical value. Analytical solution for the stress, strain and displacement fields of the viscoelastic composite cylinder is developed from the corresponding solution of linear elasticity problem by using the Correspondence Principle. The analytical solution for determining the temperature dependent stress, strain and displacement fields is further developed by incorporating the temperature dependence on the material properties and modeling the material as non-TSM. To analyze more complex geometry with general loading and boundary conditions, Finite Element(FE) analysis of the composite cylinder is performed and the results of analytical and FE method are found to be in good agreement. Parametric studies are carried out to understand the effect of change in material parameters namely the Prony coefficients in the transient creep compliance, characteristic of creep time in transient creep compliance and the instantaneous elastic compliance, on the overall response of the composite cylinder. The effect of different temperature dependent functions of the material properties, namely linear temperature variation and quadratic polynomial variation on the overall material response is also analyzed. It is observed that the effect of change in elastic properties significantly increases the jump in hoop stress and radial strain. It is also observed that when the materials are highly dependent on temperature the jump in radial strain and hoop stress increases significantly. The radial displacement also increases by a significant amount in both the cases.

This dissertation presents the integration of a damage viscoelastic constitutive relationship with a viscoplastic relationship in order to develop a comprehensive anisotropic damage viscoelastic-viscoplastic model that is capable of capturing hot mix asphalt (HMA) response and performance under a wide range of temperatures, loading rates, and stress states. The damage viscoelasticity model developed by Schapery (1969) is employed to present the recoverable response, and the viscoplasticity model developed at the Texas Transportation Institute (TTI) is improved and used to model the irrecoverable strain component. The influence of the anisotropic aggregate distribution is accounted for in both the viscoelastic and viscoplastic responses. A comprehensive material identification experimental program is developed in this study. The experimental program is designed such that the quantification and decomposition of the response into viscoelastic and viscoplastic components can be achieved. The developed experimental program and theoretical framework are used to analyze repeated creep tests conducted on three mixes that include aggregates with different characteristics. An experiment was conducted to capture and characterize the three-dimensional distribution of aggregate orientation and air voids in HMA specimens. X-ray computed tomography (CT) and image analysis techniques were used to analyze the microstructure in specimens before and after being subjected to triaxial repeated creep and recovery tests as well as monotonic constant strain rate tests. The results indicate that the different loading conditions and stress states induce different microstructure distributions at the same macroscopic strain level. Also, stress-induced anisotropy is shown to develop in HMA specimens.

The objective of this research was to determine whether the use of polymer compounds with elastic properties can reduce residual oil saturation in porous media below that of brine or inelastic polymerized solutions. One hypothesis is that long-chain polymer molecules experience stress and a resulting strain when they flow through pore throat constrictions. If the fluid residence time in larger pore spaces is insufficient to allow full relaxation, then strain can accumulate. Sufficient strain results in normal forces which can impinge on oil interfaces and potentially mobilize them. A second hypothesis suggests that polymerized solutions can temporarily protect flowing oil filaments from snap off, allowing them to flow longer and de-saturate further than they would otherwise. The approach taken in this thesis was to conduct a series of core floods in several different sandstones using displacement fluids with elasticity ranging from none to those with extremely high relaxation times. Accelerated flow rate was also employed to reduce residence time and maximize the accumulation of elastic strain and normal force potential. Experiments were designed to provide direct comparisons between both non-elastic and elastic floods but also multiple floods with increasing elasticity. The results were inconclusive with some experiments showing additional oil recovery that could be attributed to elastic mechanisms. Most experiments, however, showed no significant difference between elastic and non-elastic floods when experimental parameters were controlled within narrow limits. This research did refine the experimental context in which elastic effects are most likely to be observed. As such, it can serve as a precursor to additional core flooding in oil-wet systems, experiments conducted at reservoir temperature, and those where the pressure gradient of the flood is held constant and the flow rate allowed to vary. Computer aided tomography could also be employed to visualize the mobilization of oil with different displacement fluids, identify where bypassed oil occurs with unstable floods, and determine how oil is subsequently mobilized with better conformance and or elasticity. / text

No description available.