Yes / We have studied the tensile behaviour of polycarbonate at large strains below the glass transition temperature. Experiments have been carried out at a series of constant temperatures and also under conditions of falling temperature. The specimens neck with a natural draw ratio of ~2, and the study focuses mainly on the necked material. Isothermal experiments reveal an elastic mechanism that initiates beyond the natural draw ratio. A model consisting of an Eyring process and two Gaussian elastic mechanisms is shown to be applicable to both the isothermal and anisothermal stress relaxation and stress-strain results. The same model also produces reasonable estimates of the stresses generated during the necking process. In addition, a simple relationship between isothermal and anisothermal stress relaxation is demonstrated.

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Most of the methodologies dealing with viscoelastic damping focused exclusively on the frequency dependence behavior of the material. Only a few looked into the temperature dependence of the model, although none of them has taken a more serious investigation on the control design subjected to temperature disturbances. The general purpose of this work is to develop and investigate structures with damping modeled by means of internal variables. Thermodynamic principles are used to develop models, which are based on a generalized Maxwell element. Initially, studies are conducted to verify how the method of reduced variables can be applied to account for temperature dependence, as well as to evaluate the number of internal variables necessary for good accuracy of material properties representation. Lumped and finite element models are characterized and validated against other methods. A constrained layer damping model is experimentally validated for many temperatures. A control analysis is carried out on the models with the purpose to identify the role played by the internal variables on the control design. The results show that moving the internal poles is very expensive in terms of control energy. It is also shown that it is not always possible to eliminate the internal coordinates in the reduced order model if the system is highly damped. The problem of having the internal pole moved is solved by applying partial pole placement. This technique shows similar performance as compared to the linear quadratic Gaussian regulator. The control designs are implemented and it is shown that good regulation can be achieved for a fixed temperature. It is further shown that the controller will lose its performance when the model is subjected to temperature changes. To investigate the behavior of the model under different temperatures, a linear temperature-dependent model is developed, which clearly shows how the temperature affects the time response of the model. This model is used as a baseline to develop an adaptive and a time-varying controllers. With the aid of the shift factor, the eigenvalue variation with temperature is used as a time-varying function in the design. The results show that good track performance and regulation can be achieved with a control law that is capable of compensating for temperature variations. / Ph. D.

The main purpose of this report was to test several common viscoelastic polymers and identify key attributes of their applicability to a small aircraft landing gear system for improved damping performance. The applied viscoelastic damping treatment to the gear was of a constrained layer type, promoting increased shear deformation over free surface treatments, and therefore enhanced energy dissipation within the viscoelastic layer. A total of eight materials were tested and analyzed using cyclic loading equipment to establish approximate storage modulus and loss factor data at varying loading frequencies. The three viscoelastic polymers having the highest loss factor to shear modulus ratio were chosen and tested using a cantilever beam system. A Ross, Kerwin, and Ungar analysis was used to predict the loss factor of the cantilever beam system with applied treatment and the predictions were compared to experimental data. Customer requirements often govern the scope and intensity of design in many engineering applications. Limitations and constraints, such as cost, weight, serviceability, landing gear geometry, environmental factors, and manufacturability in regards to the addition of a viscoelastic damping treatment to a landing gear system are discussed. Based on results found from theoretical and experimental testing, application of a damping treatment to a small aircraft landing gear system is very promising. Relatively high loss factors were seen in a cantilever beam for simple single layer constrained treatments for very low strain amplitudes relative to strains seen during loading of the landing gear. With future design iterations, damping levels several times those seen in this document will be seen with a constrained treatment applied to a landing gear system. / Master of Science

In this paper consider the problem of controlling a thermoviscoelastic system. We present a semigroup setting for this system, and prove the well-posedness by applying a general theorem which is given in this paper. We also study the stability of the system. We give a finite element/averaging scheme to approximate the linear quadratic regulator problem governed by the system. We prove that yields faster convergence. We give a proof of convergence of the simulation problem for singular kernels and of the control problem for L2 kernels. We carry on the numerical computation to investigate the effect of heat transfer on damping and the closed-loop system. / Ph. D.

Viscoelastic polymer materials are being actively considered as a novel material for semiconductor packaging applications as a result of their ability to develop strong adhesive bonds at lower temperatures. Viscoelastic thermoset materials are impacted by the stresses generated during the curing process, which is also accompanied by a dissipation of thermal energy. There is a need to develop a generic modeling formulation that is applicable to any material of interest in order to enable the study of different bonding materials and develop optimized curing cycles. This study reports a numerical formulation to evaluate the stress generated and energy dissipated during the cure of viscoelastic polymers. A generalized method to define the transient variation of degree of cure was developed using a 4th order Runge Kutta approximation. The mathematical formulation was implemented using a novel evaluation methodology that helped reduce the computational power requirement. The commercially-available 3501-6 resin was simulated as a characteristic material in this study. The numerical model was validated against analytically derived solutions for both a single Maxwell model, and a Generalized Maxwell Model (GMM) for cases of constant-strain inputs, and subsequently for sinusoidal strain inputs, wherein, material properties were considered to be constant or varying linearly with degree of cure. A good agreement was obtained between the present model and analytical solutions.

This thesis focuses on the micromechanical modeling of particulate viscoelastic composite materials in the quasi-static frequency domain to approximate macroscopic damping behavior and has two main objectives. The first objective is the development of a robust frequency dependent multiscale model. For this purpose, the self-consistent (SC) mean-field micromechanical model introduced by Cherkaoui et al [J. Eng. Mater. Technol. 116, 274-278 (1994)] is extended to include frequency dependence via the viscoelastic correspondence principal. The quasi-static model is then generalized using dilute strain concentration tensor formulation and validated by comparison with complex bounds from literature, acoustic and static experimental data, and established models. The second objective is SC model implementation as a tool for the design of high loss materials. This objective is met by integrating the SC model into a Compromise Decision Support Protocol (CDSP) to explore the microstructural design space of an automobile windshield. The integrated SC-CDSP design space exploration results definitively indicate that one microstructural variable dominates structure level acoustic isolation and rigidity: negative stiffness. The work concludes with a detailed description of the fundamental mechanisms leading to negative stiffness behavior and proposes two negative stiffness inclusion designs.

No description available.

The polymers are integral part of vast number of products used in day to day life due to their anomalous viscoelastic behaviour. The remarkable flow behaviour exhibited by the polymeric fluids including rod climbing, extrudate swell, tube-less siphon, viscoelastic jet, elastic recoil and sharkskin instability is attributed to the complex microstructures in the polymeric liquids that arise due to the interactions of long chain polymer molecules with each other and with the surrounding fluid particles. The significance of polymer in transportation, packaging, pharmaceutical, chemical, biomedical, textiles, food and polymer processing industries highlights the requirement to comprehend the complex rheology of polymeric fluids. First, we investigate the flow features exhibited by different shear thinning vis-coelastic fluids in rectangular cavities over a wide range of depth to width ratio. We have developed a viscoelastic flow solver in order to perform numerical simulations of highly elastic flow of viscoelastic fluids. In particular, we discuss the simulations of flows of constant viscosity Boger and shear thinning viscoelastic fluids in the complex flow problems using different constitutive equations. The effects of elasticity and inertia on the flow behaviour of two shear thinning vis-coelastic fluids modeled using Giesekus and linear PTT constitutive equations in rectangular cavities is studied. The size of the primary eddies and critical aspect ratio over which the corner eddies merge to yield a second primary eddy in deep cavities is discussed. We demonstrate that the flow in the shallow and deep cavities can be characterized using Weissenberg number, defined based on the shear rate, and Deborah number, specified based on the convective time scale, respectively. The study of flow in driven cavities is important in understanding of the mixing process during synthesis of blends and composites. Next, we study two phase polymeric flow in confined geometries. Nowadays, polymer processing industries prefer to develop newer polymer with the desired material properties mechanically by mixing and blending of different polymer components instead of chemically synthesizing fresh polymer. The microstructure of blends and emulsions following drop deformation, breakup and coalescence during mixing determines its macroscopic interfacial rheology. We developed a two phase viscoelastic flow solver using volume conserving sharp interface volume-of-fluid (VOF) method for studying the dynamics of single droplet subjected to the complex flow fields. We investigated the effects of drop and matrix viscoelasticity on the motion and deformation of a droplet suspended in a fully developed channel flow. The flow behaviour exhibited by Newtonian-Newtonian, viscoelastic-Newtonian, Newtonian-viscoelastic and viscoelastic-viscoelastic drop-matrix systems is presented. The difference in the drop dynamics due to presence of constant viscosity Boger fluid and shear thinning viscoelastic fluid is represented using FENE-CR and linear PTT constitutive equations, respectively. The presence of shear thinning viscoelastic fluid either in the drop or the matrix phase suppresses the drop deformation due to stronger influence of matrix viscoelasticity as compared to the drop elasticity. The shear thinning viscoelastic drop-matrix system further restricts the drop deformation and it displays non-monotonic de-formation. The constant viscosity Boger fluid droplet curbs the drop deformation and exhibits flow dynamics identical to the shear thinning viscoelastic droplet, thus indicating that the nature of the drop viscoelasticity has little influence on the flow behaviour. The matrix viscoelasticity due to Boger fluid increases drop deformation and displays non-monotonic deformation. The drop deformation is further enhanced in the case of Boger fluid in viscoelastic drop-matrix system. Interestingly, the pressure drop due to the presence of viscoelastic drop in a Newtonian matrix is lower than the single phase flow of Newtonian fluid. We also discuss the effects of inertia, surface tension, drop to matrix viscosity ratio and the drop size on these drop-matrix systems. Finally, we investigate the emulsion rheology by studying the motion of a droplet in the square lid driven cavity flow. The viscoelastic effects due to constant viscosity Boger fluid and shear thinning viscoelastic fluid are illustrated using FENECR and Giesekus rheological relations, respectively. The presence of viscoelasticity either in drop or matrix phase boosts the drop deformation with the drop viscoelasticity displaying intense deformation. The drop dynamics due to the droplet viscoelasticity is observed to be independent of the nature of vis-coelastic fluid. The shear thinning viscoelastic matrix has a stronger influence on the drop deformation and orientation compared to the Boger fluid matrix. The different blood components, cells and many materials of industrial importance are viscoelastic in nature. Thus, the present study has significant applications in medical diagnostics, drug delivery, manufacturing and processing industries, study of biological flows, pharmaceutical research and development of lab-on-chip devices.

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