Thesis: M.S., Massachusetts Institute of Technology, Department of Civil Engineering, 1975 / Bibliography: leaf 95. / M.S. / M.S. Massachusetts Institute of Technology, Department of Civil Engineering

In 1998, the United States National Committee on Biomechanics (USNCB) established an evolving discipline called Functional Tissue Engineering (FTE). In establishing this discipline, the goals of the USNCB were to advance FTE by increasing awareness among tissue engineers about the importance of restoring function when engineering tissue constructs. Another goal was to encourage tissue engineers to incorporate these functional criteria in the design, manufacturing and optimization of tissue engineered constructs. Based on this motivation, an investigation of the structure and mechanical properties of the rabbit patellar tendon will be executed, with the ultimate goal of creating a multiscale soft tissue model based on internal state variable (ISV) theory. Many continuum scale models, mostly phenomenological and microstrucutral, have been created to contribute to the understanding of the complex functional properties of the tendon, such as its anisotropy, inhomogeneity, nonlinearity, and viscoelasticity. However, none of these models have represented the mechanical behavior of the tendon in the presence of internal structural change on a multiscale level. The development of a multiscale ISV model will allow the capture of the irreversible, path history dependent aspects of the material behavior. The objective of this study is to contribute to the multiscale ISV model development by quantifying the structure- property relations. In particular, the fibril distribution at the microstructural level and the resultant multiaxial stress states (longitudinal and transverse compression and longitudinal tension) will be examined).

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In dilute polymer solution, polymers are able to change the flow structures and suppress the intensity of turbulence, resulting in a considerable friction drag reduction (DR). Despite the extraordinary progress made in the past few decades, some critical questions remain unanswered. This dissertation will try to address two fundamental questions in dilute polymeric turbulence: (I) interactions between polymers and turbulent motions during the qualitative low-extent to high-extent drag reduction (LDR and HDR) transition in inertia-driven turbulence, (II) roles of the inertia- and elasticity-driven turbulent motions in the dynamics of high elasticity polymeric flows. Many studies in the area of DR turbulence have been focused on the onset of DR and the maximum drag rection (MDR) asymptote. Between these two distinct stages, polymeric turbulent flows can also be classified into the qualitative LDR and HDR stages. Understanding the polymer-turbulence interactions during the drastic LDR-HDR transition is of vital importance for the development of efficient flow control technology. However, knowledge regarding this qualitative transition is still limited. In our DNS (direct numerical simulation) study, differences between the LDR and HDR stages are presented by a number of sharp changes in flow structures and statistics. Drag reduction in the flows is thus governed by two different mechanisms. The first is introduced at the onset of DR, which has been well explained by the indiscriminate suppression of turbulent fluctuations during the coil-stretch transition of polymers. The second mechanism starts at the LDR-HDR transition but its physical origin is not clear. Based on instantaneous observations and indirect statistical evidence, we proposed that polymers, after the LDR-HDR transition, could suppress the lift-up process of the near-wall vortices and modify the turbulent regeneration cycles. However, direct evidence to support this hypothesis is not available without a statistical analysis of the vortex configurations. Therefore, a new vortex tracking algorithm -- VATIP (vortex axis tracking by iterative propagation) -- is developed to analyze statistically the configurations and distribution of vortices. Implementing this method in the polymeric turbulence demonstrates that the lift-up process of streamwise vortices in the buffer layer is restrained at HDR, while the generation of hairpins and other three-dimensional vortices is suppressed. In addition, the characteristic lifting angle of conditional eddies extracted by a conditional sampling method is found to be larger in HDR than in the Newtonian turbulence. These observations all support our hypothesis about the mechanism of LDR-HDR transition. Research on the low elasticity turbulence usually considered the flow motions to be Newtonian-like. Turbulence here is driven by the inertial force (and hence called ``inertia-driven'' turbulence (IDT)) while polymers are responsible for dissipating turbulent kinetic energy. In the high elasticity turbulence, recent studies found a completely different turbulent flow type in which turbulence is driven by the elastic force and polymers could also feed energy to the flow. The behaviors of this ``elasticity-driven'' turbulence (EDT) are of significant interest in this area because of its potential connection to the MDR asymptote. However, EDT is difficult to capture by the traditional pseudo-spectral DNS scheme (SM) as a global artificial diffusion (GAD) term is involved in the polymer constitutive equation to stabilize the simulation. In our study, a new hybrid pseudo-spectral/finite-difference scheme is developed to simulate the polymeric turbulence without requiring a GAD. All of the spatial derivative terms are still discretized by the Fourier-Chebyshev-Fourier pseudo-spectral projection except for the convection term in the constitutive equation which is discretized using a conservative second-order upwind TVD (total variation diminishing) finite difference scheme. The numerical study using the hybrid scheme suggests that turbulent flows can be either driven by the inertial or the elastic forces and respectively result in the IDT and EDT flows. A dynamical flow state is also found in the high elasticity flow regime in which IDT and EDT can be sustained alternatively. / Thesis / Doctor of Philosophy (PhD) / Turbulence is known to consume kinetic energy in a fluid system. To enhance the efficiency of fluid transportation, various techniques are developed. Especially, it was found that a small amount of polymers in turbulent flows can significantly suppress turbulent activity and cause considerable friction drag reduction (DR). Extraordinary progress has been made to study this phenomenon, however, some questions still remain elusive. This dissertation tries to address some fundamental questions that relate to the two typical polymeric turbulent motions: the inertia- (IDT) and elasticity-driven turbulence (EDT). In IDT, mechanisms of transitions between the intermediate stages are investigated from the perspective of vortex dynamics. The different effects of polymers at each stage of the flow lead to different flow behaviors. Particularly, starting from the low- to high-extent DR transition, the lift-up process of vortices is suppressed by polymers. The regeneration cycles of turbulence are thus modified, which results in qualitative changes of flow statistics. Numerical study on EDT is enabled by a newly developed hybrid pseudo-spectral/finite-difference scheme. A systematic investigation of the parameter space indicates that EDT is one self-contain turbulence driven purely by the elastic force. It can also interact with IDT and lead to a dynamical flow state in which EDT and IDT can alternatively occur.

In this paper we present an exponential stability result for a diffusion equation arising from dumbbell models for polymer flow. Using the methods of semigroup theory, we show that the semigroup U(t) associated with the diffusion equation is well defined and that all solutions converge exponentially to an equilibrium solution. Both finitely and infinitely extensible dumbbell models are considered. The main tool in establishing stability is the proof of compactness of the semigroup. / Ph. D.

Over the past several decades, the use of composite materials has grown considerably. Typically, fiber-reinforced polymer-matrix composites are modeled as being linear elastic. However, it is well-known that polymers are viscoelastic in nature. Furthermore, the analysis of complex structures requires a numerical approach such as the finite element method. In the present work, a triangular flat shell element for linear elastic composites is extended to model linear viscoelastic composites. Although polymers are usually modeled as being incompressible, here they are modeled as compressible. Furthermore, the macroscopic constitutive properties for fiber-reinforced composites are assumed to be known and are not determined using the matrix and fiber properties along with the fiber volume fraction. Hygrothermo-rheologically simple materials are considered for which a change in the hygrothermal environment results in a horizontal shifting of the relaxation moduli curves on a log time scale, in addition to the usual hygrothermal loads. Both the temperature and moisture are taken to be prescribed. Hence, the heat energy generated by the viscoelastic deformations is not considered. When the deformations and rotations are small under an applied load history, the usual engineering stress and strain measures can be used and the time history of a viscoelastic deformation process is determined using the original geometry of the structure. If, however, sufficiently large loads are applied, the deflections and rotations will be large leading to changes in the structural stiffness characteristics and possibly the internal loads carried throughout the structure. Hence, in such a case, nonlinear effects must be taken into account and the appropriate stress and strain measures must be used. Although a geometrically-nonlinear finite element code could always be used to compute geometrically-linear deformation processes, it is inefficient to use such a code for small deformations, due to the continual generation of the assembled internal load vector, tangent stiffness matrix, and deformation-dependent external load vectors. Rather, for small deformations, the appropriate deformation-independent stiffness matrices and load vectors to be used for all times can be determined once at the start of the analysis. Of course, the time-dependent viscoelastic effects need to be correctly taken into account in both types of analyses. The present work details both geometrically-linear and nonlinear triangular flat shell formulations for linear viscoelastic composites. The accuracy and capability of the formulations are shown through a range of numerical examples involving beams, rings, plates, and shells. / Ph. D.

The most promising strategy for reducing the cost of manufacturing polymer matrix composites while improving their reliability is the use of sensors during processing to permit control of the cure cycle based on measurements of the material's internal state. While sensors have been demonstrated that infer the material state indirectly through measurements of acoustic impedance, electrical impedance, or refractive index, sensors that directly measure parameters critical to composite manufacturing, such as resin rheology and resin hydrostatic pressure, would improve characterization of thermoset resins during cure. Here we describe the development of a multifunctional fiber optic sensor that may be embedded in a composite part during lay-up to monitor the state of the polymer matrix during processing. This sensor will output quantitative data which will indicate the viscoelasticity of the thermoset matrix resin. The same sensor will additionally function as a strain sensor following fabrication, capable of monitoring residual strains due to manufacturing or in-service internal strains. / Ph. D.

An experimental study was conducted to characterize the dynamic mechanical properties of polymer modified asphalt binders at intermediate and high service temperatures. A typical paving grade asphalt and seven different elastomeric modifiers were used. The modifiers, representing a wide variety of random copolymers and thermoplastic block copolymers, were blended with asphalt at three concentration levels to yield a total of twenty one mixes. The effect of short term aging was simulated by the rolling thin film oven test (RTFOT) procedure. A dynamic shear rheometer with parallel plate configuration was used to conduct the dynamic mechanical tests at frequencies between 0.06 to 188.5 rad/s and temperatures ranging from 5 to 75° C. After establishing the linear viscoelastic range of response through performing stress sweeps, a series of frequency sweeps was carried out. Investigation of the resulting isothermal response curves indicated that simple time-temperature superposition is applicable, and dynamic master curves can be constructed by empirical superposition. Effects of polymer type, polymer content, and aging treatment on the behavior of dynamic master curves and relaxation spectra were studied. Feasibility of using the current mathematical models of frequency dependence to characterize the experimental dynamic master curves of modified binders was investigated. These models were generally found inadequate in representing the behavioral complexities of modified binders. To address this inadequacy, two new analytical expressions were developed to represent the dynamic storage shear modulus and dynamic loss shear modulus of polymer modified asphalts. The predictive capability of the developed equation for storage modulus is high for moduli below 108 Pa. The developed model for loss modulus was found to be accurate over the entire range of measured moduli. A procedure for application of these models to practical engineering problems was presented. The measured shift factor data was used to study the dependency of the viscoelastic response on temperature variations. It was observed that this dependency is dominated by the asphalt phase. Within the studied range of temperatures, the WLF equation with universal constants was found to be adequate in describing the temperature dependence of response. / Ph. D.

This thesis concerns itself with a finite element model of nonproportional viscoelastic damping and its subsequent reduction. The Golla-Hughes-McTavish viscoelastic finite element has been shown to be an effective tool in modeling viscoelastic damping. Unlike previous models, it incorporates physical data into the model in the form of a curve fit of the complex modulus. This curve fit is expressed by minioscillators. The frequency dependence of the complex modulus is accounted for by the addition of internal, or dissipation, coordinates. The dissipation coordinates make the viscoelastic model several times larger than the original. The trade off for more accurate modeling of viscoelasticity is increased model size. Internally balanced model order reduction reduces the order of a state space model by considering the controllability/observability of each state. By definition, a model is internally balanced if its controllability and observability grammians are equal and diagonal. The grammians serve as a ranking of the controllability/observability of the states. The system can then be partitioned into most and least controllable/observable states; the latter can be statically reduced out of the system. The resulting model is smaller, but the transformed coordinates bear little resemblance to the original coordinates. A transformation matrix exists that transforms the reduced model back into original coordinates, and it is a subset of the transformation matrix leading to the balanced model. This whole procedure will be referred to as Yae's method within this thesis. By combining GHM and Yae's method, a finite element code results that models nonproportional viscoelastic damping of a clamped-free, homogeneous, Euler-Bernoulli beam, and is of a size comparable to the original elastic finite element model. The modal data before reduction compares well with published GHM results, and the modal data from the reduced model compares well with both. The error between the impulse response before and after reduction is negligible. The limitation of the code is that it cannot model sandwich beam behavior because it is based on Euler-Bernoulli beam theory; it can, however, model a purely viscoelastic beam. The same method, though, can be applied to more sophisticated beam models. Inaccurate results occur when modes with frequencies beyond the range covered by the curve fit appear in the model, or when poor data are used. For good data, and within the range modeled by the curve fit, the code gives accurate modal data and good impulse response predictions. / Master of Science

Creep compliance of Hot Mix Asphalt (HMA) is an important property to characterize the material's viscoelatic behavior. It is used to predict HMA thermal cracking at low temperature and permanent deformation at high temperatures. There are several experimental methods to measure the creep compliance. Two of these methods were used in this thesis; uniaxial compressive and indirect tension (IDT) creep compliance. The tests were conducted at five temperatures (-15, 5, 20, 30, and 40°C) with a static loading for 1000-sec to characterize two typical HMA mixes used in Virginia, a base and a surface mix. Creep compliance master curves (CCMC) were developed by shifting the curves to a reference temperature using time-temperature superposition. Three mathematical functions, Prony series, power and sigmoidal, were fitted to the experimental data using regression analysis. Uniaxial CCMC were also predicted based on dynamic modulus measurements using method for interconversion of vicoelastic properties recommended in the literature. Finally, the susceptibility of the mixes to thermal cracking was evaluated based on the creep compliance measurements at low temperature. The regression analysis showed that the three mathematical models considered are appropriate to model the CCMC over a wide ranger of reduced times. The sigmoidal model provided the best fit over the entire range of reduced times investigated. This model also produced the best results when used in the interconversion procedures. However, there were noticeable differences between the CCMC predicted using interconversion and the experimental measurements, probably due to nonlinearity in the material behavior. The m-values for the base mix were higher using the creep results measured with both configurations. / Master of Science