Severe stenosis may cause critical flow conditions related to artery collapse, plaque cap rupture which leads directly to stroke and heart attack. In this paper, a nonlinear viscoelastic model and a numerical method are introduced to study dynamic behaviors of the tube wall and viscous flow through a viscoelastic tube with a stenosis simulating blood flow in human carotid arteries. The Mooney-Rivlin material model is used to derive a nonlinear viscoelastic thin-wall model for the stenotic viscoelastic tube wall. The mechanical parameters in the Mooney-Rivlin model are calculated from experimental measurements. Incompressible Navier-Stokes equations in the Arbitrary Lagrangian-Eulerian formulation are used as the governing equation for the fluid flow. Interactions between fluid flow and the viscoelastic axisymmetric tube wall are handled by an incremental boundary iteration method. A Generalized Finite Differences Method (GFD) is used to solve the fluid model. The Fourth-Order Runge-Kutta method is used to deal with the viscoelastic wall model where the viscoelastic parameter is adjusted to match experimental measurements. Our result shows that viscoelasticity of tube wall causes considerable phase lag between the tube radius and input pressure. Severe stenosis causes cyclic pressure changes at the throat of the stenosis, cyclic tube compression and expansions, and shear stress change directions in the region just distal to stenosis under unsteady conditions. Results from our nonlinear viscoelastic wall model are compared with results from previous elastic wall model and experimental data. Clear improvements of our viscoelastic model over previous elastic model were found in simulating the phase lag between the pressure and wall motion as observed in experiments. Numerical solutions are compared with both stationary and dynamic experimental results. Mooney-Rivlin model with proper parameters fits the non-linear experimental stress-strain relationship of wall very well. The phase lags of tube wall motion, flow rate variations with respect to the imposed pulsating pressure are simulated well by choosing the viscoelastic parameter properly. Agreement between numerical results and experimental results is improved over the previous elastic model.

We analyze a pair of nonlinear PDEs describing viscoelastic fluid flow in one dimension. We give a summary of the physical derivation and nondimensionlize the PDE system. Based on the boundary conditions and parameters, we are able to classify three different categories of traveling wave solutions, consistent with the results in [?]. We extend this work by analyzing the stability of the traveling waves. We thoroughly describe the numerical schemes and software program, VISCO, that were designed specifically to analyze the model we study in this paper. Our simulations lead us to conjecture that the traveling wave solutions found in [?] are globally stable for all sets of initial conditions with the appropriate asymptotic boundary conditions. We are able give some analytical evidence in support of this hypothesis but are unsuccessful in providing a complete proof.

We study the dynamics of an elastic fiber in a viscoelastic fluid driven by a four-roll mill. The viscoelasticity is modeled by the FENE-P model and the coupling between the fiber and the fluid is resolved by the immersed boundary method. Numerically, we follow Peskin's formally second order method to solve the fiber-fluid equations and square root method to solve the viscoelasticity equations. We examine the effect of Weissenberg number (Wi) and fiber rigidity on fiber motion and the evolution of polymer stress. We also investigate the ability of the fiber to escape closed streamlines in Newtonian fluids and viscoelastic fluids. We find that large polymer stresses occur near the ends of the fiber when it is compressed. In addition, we find that viscoelasticity hinders a fiber's ability to traverse multiple cells in the domain. / 1 / Qiang Yang

This study aims to investigate the effect of elastic properties of viscoelastic polymer solutions on the microscopic sweep efficiency in enhanced oil recovery (EOR) operations. The effect of elasticity was studied as isolated from the shear viscosity effect using polymer blends with identical shear viscosity behavior but different elastic characteristics. Oil displacement results were compared and the individual effect of elasticity on the sweep efficiency was investigated. A detailed rheological characterization of the polymer solutions was done to measure their viscoelastic properties. A series of polymer flooding experiments were performed using a radial core holder. Results of the experiments indicated that the sweep efficiency of a polymeric fluid could be effectively improved by adjusting the molecular weight distribution (MWD) of the solution at constant shear viscosity and polymer concentration. An attempt was made to find a rheological parameter of polymer solutions that correlates better with the resultant oil recovery. / Petroleum Engineering

Modeling of the time-dependent behavior of cement paste has always been a difficulty. In the past, viscoelastic behavior of cementitious materials has been primarily attributed to the viscoelastic properties of C-S-H components. Recent experimental results show that C-S-H may not exhibit as much creep and relaxation as previously thought. This requires new consideration of different mechanisms leading to the viscoelastic behavior of cement paste. Thus the objective of this thesis is to build a computational model using finite element method to predict the viscoelastic behavior of cement paste, and using this model, virtual tests can be carried out to improve understanding of the mechanisms of viscoelastic behavior. The primary finding from this thesis is that the apparent viscoelastic behavior due to dissolution of load bearing phases is substantial. The dissolution process occurring during the hydration reaction can change the stress distribution inside cementitious materials, resulting in an apparent viscoelastic behavior of the whole cementitious materials. This finding requires new consideration of mechanisms of time-dependent behavior of cementitious materials regarding the dissolution process of cement paste.

The importance of understanding non-metallic material behaviour at high strain rates is becoming ever more important as new materials are being developed and used in shock loading applications. Applying conventional methods for high strain rate testing to non-metallic materials proved ineffective due to impedance mismatch between the specimen and apparatus and so a new test method was developed. A polymeric Hopkinson bar was developed enabling non-metallic materials, such as polycarbonate and rubber, to be tested at strain rates from 500 s^-1 to 4000 s^-1. Conventional Hopkinson bar analysis is invalid due to the viscoelastic nature of the polymeric bar material. As waves propagate along the bar length, the inherent material behaviour causes the waves to undergo a degree of attenuation and dispersion. Through the use of spectral analysis, a comparison of the dispersive relationships for 6061 T-6 aluminium, extruded acrylic and low density polyethylene is presented. The application of spectral methods to viscoelastic wave analysis was validated by three separate methods. A comparison of predicted and measured waves along the bar length allowed the dispersive relationship to be substantiated. The use of an enhanced laser velocity system further verified the predicted wave magnitude. A comparison of results for polycarbonate and ballistic gelatin to published results showed good agreement.

Polyethylene has been studied from many different perspectives; a final application property perspective, in which the response of the material to loads is the topic; a micromechanical point of view, in which the macroscopic state of the material is related to its microstructure, e.g., Alvarado (2007), and a chemical point of view in which the molecular structure and the processes that create polyethylene are investigated. This thesis focuses on the mechanical behavior of polyethylene observed from testing and relates the mechanical behavior to the molecular structure of the material. High density polyethylene is a material used in civil engineering applications such as pipes and containers. There are two general modes of failure for polyethylene: ductile failure that happens at relatively large stresses (up to 200MPa) and in short amount of time, and brittle failure that occurs when a much lower stress is sustained over a long period of time (Cheng 2008). Other than these two modes of failure, excessive deformation of the material that is usually caused by creep is also to be avoided. This thesis studies the relationship between short-term and long-term creep of polyethylene and its molecular structure. In this work three types of mechanical tests were performed on six samples of polyethylene. The existing models that prescribe the constitutive behavior of the material were then critically evaluated against the observed data. Furthermore the molecular properties of the samples that had been obtained from previous research by Cheng (2008) were compared against the mechanical behavior observed from testing in order to assess what molecular properties are important in determining the mechanical behavior of polyethylene. This information can also help polyethylene designers to produce longer lasting material, or a material that has high stiffness, by knowing what molecular properties to control and optimize.

The importance of understanding non-metallic material behaviour at high strain rates is becoming ever more important as new materials are being developed and used in shock loading applications. Applying conventional methods for high strain rate testing to non-metallic materials proved ineffective due to impedance mismatch between the specimen and apparatus and so a new test method was developed. A polymeric Hopkinson bar was developed enabling non-metallic materials, such as polycarbonate and rubber, to be tested at strain rates from 500 s^-1 to 4000 s^-1. Conventional Hopkinson bar analysis is invalid due to the viscoelastic nature of the polymeric bar material. As waves propagate along the bar length, the inherent material behaviour causes the waves to undergo a degree of attenuation and dispersion. Through the use of spectral analysis, a comparison of the dispersive relationships for 6061 T-6 aluminium, extruded acrylic and low density polyethylene is presented. The application of spectral methods to viscoelastic wave analysis was validated by three separate methods. A comparison of predicted and measured waves along the bar length allowed the dispersive relationship to be substantiated. The use of an enhanced laser velocity system further verified the predicted wave magnitude. A comparison of results for polycarbonate and ballistic gelatin to published results showed good agreement.

Polyethylene has been studied from many different perspectives; a final application property perspective, in which the response of the material to loads is the topic; a micromechanical point of view, in which the macroscopic state of the material is related to its microstructure, e.g., Alvarado (2007), and a chemical point of view in which the molecular structure and the processes that create polyethylene are investigated. This thesis focuses on the mechanical behavior of polyethylene observed from testing and relates the mechanical behavior to the molecular structure of the material. High density polyethylene is a material used in civil engineering applications such as pipes and containers. There are two general modes of failure for polyethylene: ductile failure that happens at relatively large stresses (up to 200MPa) and in short amount of time, and brittle failure that occurs when a much lower stress is sustained over a long period of time (Cheng 2008). Other than these two modes of failure, excessive deformation of the material that is usually caused by creep is also to be avoided. This thesis studies the relationship between short-term and long-term creep of polyethylene and its molecular structure. In this work three types of mechanical tests were performed on six samples of polyethylene. The existing models that prescribe the constitutive behavior of the material were then critically evaluated against the observed data. Furthermore the molecular properties of the samples that had been obtained from previous research by Cheng (2008) were compared against the mechanical behavior observed from testing in order to assess what molecular properties are important in determining the mechanical behavior of polyethylene. This information can also help polyethylene designers to produce longer lasting material, or a material that has high stiffness, by knowing what molecular properties to control and optimize.

A recursive-iterative algorithm is developed for predicting nonlinear viscoelastic behaviors of isotropic materials that belong to the thermorheologically complex material (TCM). The algorithm is derived based on implicit stress integration solutions within a general displacement based FE structural analyses for small deformations and uncoupled thermo-mechanical problems. A previously developed recursive-iterative algorithm for a stress-dependent hereditary integral model which was developed by Haj-Ali and Muliana is modified to include time-temperature effects. The recursive formula allows bypassing the need to store entire strain histories at each Gaussian integration point. Two types of iterative procedures, which are fixed point and Newton-Raphson methods, are examined within the recursive algorithm. Furthermore, a consistent tangent stiffness matrix is formulated to accelerate convergence and avoid divergence. The efficiency and accuracy of the proposed algorithm are evaluated using available experimental data and several structural analyses. The performance of the proposed algorithm under multi-axial conditions is verified with analytical solutions of creep responses of a plate with a hole. Next, the recursive-iterative algorithm is used to predict the overall response of single lap-joint. Numerical simulations of time-dependent crack propagations of adhesive bonded joints are also presented. For this purpose, the recursive algorithm is implemented in cohesive elements. The numerical assessment of the TCM and thermorheologically simple material (TSM) behaviors has also been performed. The result showed that TCM are able to describe thermo-viscoelastic behavior under general loading histories, while TSM behaviors are limited to isothermal conditions. The proposed numerical algorithm can be easily used in a micromechanical model for predicting the overall composite responses. Examples are shown for solid spherical particle reinforced composites. Detailed unit-cell FE models of the composite systems are generated to verify the capability of the above micromechanical model for predicting the overall nonlinear viscoelastic behaviors.