In this study, a mathematical model is developed for investigating the discrete sound propagation in viscoelastic medium to identify its viscoelastic properties. The outcome of the model suggests that pulse repetition frequency is a very important parameter for the determination of relaxation time. Adjusting the order of magnitude of the pulse repetition frequency, the corresponding relaxation time which has similar magnitude with pulse repetition frequency is filtered while the others in the spectrum are discarded. Discrete relaxation spectrum can be obtained by changing the magnitude of the pulse repetition frequency. Therefore, the model enables to characterize the relaxation times by ultrasonic measurements.

Wormlike micelles are viscoelastic fluids that present an intermediate behavior between solids and ordinary liquids since they are elastic at short time scales but flow easily at large time scales. In opposition to Newtonian fluids, which have constant viscosity, these fluids usually exhibit a non-Newtonian response with a rate-dependent shear viscosity. Wall-bounded oscillatory flows of Newtonian and complex fluids are found in many practical situations. Oscillatory pipe flows are especially important in physiology in connection with the circulatory and respiratory systems of human beings, as well as in industrial processes such as fluid pumping, secondary oil recovery or filtration, and in acoustics. Pulsating flows are of particular interest also in the rheological characterization of complex fluids. We analyze the laminar oscillatory flow of viscoelastic fluids using the Maxwell and Oldroyd-B models. We have shown that in wall-bounded oscillatory flows of viscoelastic fluids the two characteristic lengths of the Ferry waves, the damping length and wavelength, together with the characteristic separation of the walls, define all the flow properties for fluid models with a linear shear-stress equation in unidirectional flow. In wall-bounded settings there exists the possibility that shear waves generated at different locations superpose themselves before decaying so that the shear waves interfere, giving rise to a resonant flow at well defined frequencies of driving. The theoretical predictions obtained for the laminar velocity profiles are validated by carrying out time-resolved Particle Image Velocimetry (PIV) experiments in a vertical pipe at small driving amplitudes. The oscillatory pipe flow has been investigated in the whole range of experimentally accessible driving frequencies and amplitudes, and classified in three main flow regimes: laminar, vortical, and non-axisymmetric vortical. By ramping up and down the driving amplitude at constant frequency we have been able to characterize the transition from laminar to more complex flows, under controlled driving conditions. The first hydrodynamic instability occurs when the laminar base flow becomes unstable against the formation of axisymmetric toroidal vortices that appear distributed along the cylinder. The calculation of root-mean-square fluctuations in the vertical direction, of the vertical and radial components of the velocity (averaged in time or over the tube diameter) has allowed to determine the critical amplitude at which the instability sets in with high accuracy. In the vortical flow an abrupt increase of the fluctuations is observed, that accounts for the loss of the vertical translational symmetry and the formation of vortices in the flow. This transition exhibits hysteresis when the driving amplitude is ramped up and down, which makes us presume that the bifurcation from the laminar flow has a subcritical nature. A second hydrodynamic instability occurs when the vortical flow loses the axial symmetry. In this flow regime the vortices are heavily distorted and no longer axisymmetric. The velocity and vorticity maps of the vortical flow measured in a meridional plane of the tube appear periodic in time, on time scales comparable to the driving period. Interestingly, the vortex formation is favored in the acceleration phases of the piston oscillation. Besides, we have uncovered a spatio-temporal dynamics on long time scales (much larger than the relaxation time of the fluid) that substantially modifies the flow organization. This slow dynamics is more effective in the bottom half of the cylinder, specially next to the driving piston. A global inspection of the vortical flow along the tube length reveals that the instability takes place earlier in the bottom part of the tube, in the vicinity of the driving piston. At increasing the driving amplitude the boundary between laminar and vortical flow progressively raises towards the top regions. And above a critical driving amplitude the entire fluid flow is vortical. The mechanism triggering the hydrodynamic instability from the laminar to the axisymmetric vortical flow is not yet clear. / L'objectiu d'aquesta Tesi és estudiar el flux oscil•latori vertical en fluids micel•lars. Els fluids micel•lars són fluids complexos amb propietats viscoelàstiques, de manera que mostren un comportament intermedi entre els sòlids i els líquids: són elàstics a escales de temps curtes però flueixen a escales de temps més llargues. En contraposició als fluids Newtonians, que tenen una viscositat constant, els fluids complexos mostren un comportament no-Newtonià, amb una viscositat que depèn del ritme de deformació. El fluxos oscil•latoris de fluids Newtonians o complexos en geometries confinades són especialment importants en fisiologia, en relació amb el sistema circulatori i respiratori d'éssers humans, i també en processos industrials com el bombejat de fluids, l'extracció de petroli, i en particular són interessants en la caracterització reològica de fluids complexos. Primer estudiem el flux oscil•latori des d'una perspectiva teòrica i analitzem el flux laminar de fluids viscoelàstics utilitzant els models de Maxwell i Oldroyd-B en un tub vertical. Hem mostrat que en fluxos confinats existeix la possibilitat que les ones de cisalla generades a les diferents parets se sobreposin abans d'esmorteir-se i que eventualment donin lloc a un fenomen de ressonància. Les prediccions teòriques obtingudes pel flux laminar són validades duent a terme experiments de Velocimetria d'Imatges de Partícules (PIV) en un tub vertical, per amplituds petites del forçament oscil•latori. Quan s'incrementa l'amplitud de l'oscil•lació el flux laminar evoluciona cap a fluxos que presenten una dependència espai-temporal més complexa. Fent rampes d'amplitud creixent a una freqüència fixada hem pogut caracteritzar experimentalment la transició del flux laminar a aquests fluxos més complexos, sota condicions de forçament ben controlades. La primera inestabilitat apareix quan el flux laminar esdevé inestable amb la corresponent formació d'anells de vorticitat apilats al llarg del tub. Es manifesta una segona inestabilitat per amplituds del forçament més grans, per la qual el flux vortical perd la simetria axial. En aquest nou règim els vòrtex estan fortament distorsionats i no són axisimètrics. Fent rampes d’amplitud creixent i decreixent hem observat que aquestes dues transicions presenten histèresi, i que per tant són de caràcter subcrític.

This study introduces a new three-dimensional (3D) multi-scale constitutive framework for the nonlinear viscoelastic analysis of laminated and pultruded composites. Two previously developed nonlinear micromechanical models for unidirectional and in-plane random composite layers are modified to include time-dependent and nonlinear behavior. A new recursive-iterative numerical integration method is introduced for the Schapery nonlinear viscoelastic model and is used to model the isotropic matrix subcells in the two micromodels. In addition, a sublaminate model is used to provide for a through-thickness 3D nonlinear equivalent continuum of a layered medium. The fiber medium is considered as transversely isotropic and linear elastic. Incremental micromechanical formulations of the above three micromodels are geared towards the time integration scheme in the matrix phase. New iterative numerical algorithms with predictor-corrector type steps are derived and implemented for each micromodel to satisfy both the constitutive and homogenization equations. Experimental creep tests are performed for off-axis pultruded specimens in order to calibrate and examine the predictions of the constitutive framework for the multi-axial nonlinear viscoelastic response. Experimental creep data, available in the literature, is also used to validate the micromodel formulation for laminated composite materials. Nonlinear viscoelastic effects at the matrix level, such as aging, temperature, and moisture effects can be easily incorporated in the constitutive framework. The multi-scale constitutive framework is implemented in a displacement-based finite element (FE) code for the analysis of laminated and pultruded structures. Several examples are presented to demonstrate the coupled multi-scale material and structural analysis.

Ballistic fabrics made from high performance polymeric fibers such as Kevlar®, Twaron® and Spectra® fibers and composites utilizing these fabrics are among the leading materials for modern body armor systems. Polymeric fibers used to produce ballistic fabrics often behave viscoelastically and exhibit time- and rate-dependent stress-strain relations. This necessitates the study of the constitutive behavior of composites filled by ballistic fabrics. Rheological models based on discrete rheological components (including spring and dashpot) have been widely used to study the viscoelastic behavior of polymeric fabrics. Such rheological (or viscoelasticity) models are qualitatively useful in understanding the effects of various micro-mechanisms and molecular features on the macroscopic responses of ballistic fabrics. In the present work, the constitutive behavior of Twaron CT709® fabric/natural rubber (Twaron®/NR) composite is studied using three viscoelasticity models (i.e., a four-parameter Burgers model, a three-parameter generalized Maxwell (GMn=1) model, a five-parameter generalized Maxwell (GMn=2) model) and a newly developed para-rheological model. The new model utilizes a three-parameter element to represent the Twaron® fabric and the affine network based molecular theory of rubber elasticity to account for the deformation mechanisms of the NR constituent. The uniaxial stress-strain relation of the Twaron®/NR composite at two constant strain rates is experimentally determined. The values of the parameters involved in all the models are extracted from the experimental data obtained in this study. The stress-relaxation response (under a uniaxial constant strain) and the creep deformation (under a uniaxial constant stress) of the composite are also experimentally measured. The three viscoelasticity models considered here are capable of predicting the viscoelastic constitutive behavior of the composite with different levels of accuracy. The stress-strain relation at each strain rate predicted by the newly developed para-rheological model is seen to be in good agreement with the measured stress-strain curve over the entire strain range studied. It is shown that the new model also predicts the elastic moduli and ultimate stress of the Twaron®/NR composite well. All the four models are found to predict the initial relaxation response of the composite fairly well, while the long-term stress relaxation is more accurately represented by the para-rheological model. An implicit solution provided by the para-rheological model is shown to predict the creep response of the composite more accurately than all the other models at both the primary and secondary stages. The mathematical complexity that arises from including an additional Maxwell element to the GMn=1 model to obtain the GMn=2 model with enhanced predictability is traded with the use of simple characteristic time functions in the para-rheological model. These functions are found to greatly improve the predictability of the newly developed model for the stress relaxation modulus and creep compliance. This study also explores the utility of the para-rheological model as a tool to probe the micromechanisms and molecular features that are causally related to the macroscopically observed viscoelastic behavior of the composite. The relaxation and creep trends predicted by the para-rheological model indicate that the long time viscoelastic response of the composite lies between that of a crosslinked polymer and a semi-crystalline thermoplastic.

The impact strength of Nylon 6 was improved by adding Ethylene- n-Butyl acrylate- maleic anhydride (E-nBA-MAH) terpolymer with various concentrations from 0% (w/w) to 15% (w/w). The bare interaction energy between two polymers was investigated by using melting point depression approach utilizing both the Flory-Huggins (FH) theory and the Sanchez-Lacombe Equation of State (SL EOS). The solution of the mixture was electrospun, and the effects of process parameters on the expected radii of nanofibers were investigated. The effects of process parameters such as polymer concentration in solution, electrical field, diameter of syringe needle, feed rate, and collector geometry on nanofibers were studied. The statistical analysis to relate these parameters on the diameter of nanofibers was carried out by using Johnson SB distribution. The ratio of elastic modulus to viscosity coefficient of nanofibers was worked out by using AFM and combined viscoelastic models. The experiments were carried out on single fiber. The ratio came out to be a function of nanofiber diameter and terpolymer concentration. Isothermal crystallization kinetics and WAXS diffraction patterns of blends revealed and also SEM images supported that after 5% addition of elastomeric terpolymer, the interaction between the components of the blend gets weaker. The elastic modulus of the blend with 5% of terpoymer was greater than that of the neat Nylon 6, but the elastic modulus decreased for the blends containing more than 5% terpolymer.

The main objective in this work was to learn how the instrument, the Interfacial Shear Rheometer (ISR400), worked and to investigate how the rheological properties, storage modulus (elasticity), G' and loss modulus (viscous), G'', changes when the surface pressure at the air-liquid interphase changes. The second objective were to examine the different kind of magnetic needles used in the experiments and to conclude which type of needle is best for its specific field of analysis. It was concluded that the relative heavy needle with mass 70.6 mg and length 50 mm was best for systems where the viscous and elastic components are significantly large, where the inertia of the needle is not dominant. It also worked of using the heavier needle for a system of phospholipids. For the hydroxystearic acid (HSA) experiment that were tested on NaCl sub-phase there was a clear improvement after switching from the heavy needle (mass 41.5 mg; length 51 mm) to the relative lighter needle (mass 6.94 mg; length 34.7 mm). The values for the dynamic modulus therefore had a better agreement with reference literature. A spread layer of class II hydrophobins (HFBII) could be compressed to a surface pressure of 46 mNm-1. The G' and G'' values from the frequency sweep were discarded because the monolayer turned into a very viscous-like liquid, and the oscillating needle, after compression, was kind of stuck in the sub-phase and moved very staggering during a frequency sweep. The needle comparison experiment with silica particles 10 wt% Bindzil CC30 (BCC30), at pH 3.5 was done to see if there was any difference in the sensitivity for the needles at the interface which consisted of a pure 10 mM NaCl solution or a 10 mM NaCl solution with BCC30 added to it. The differences were negligible in terms of surface tension but there was a clear difference between the heavy needle and the light needle, when oscillating at higher frequencies (>≈6 rad/s). With this study, the understanding of ISR400 has increased largely. Several issues have been addressed and the results provide a good basis for further studies within the many areas the instrument can be used for. Despite the project's time limit, and the fact that the instrument was new and untested where the project was carried out, focus areas were prioritized so good results could be achieved within reasonable goals. / Huvudmålet med detta arbete var att lära sig hur instrumentet ytskiktsreometern (ISR400) fungerade och undersöka hur de reologiska egenskaperna, elasticitetsmodulen G' och viskositetsmodulen G'', kommer att förändras när det sker en förändring för yttrycket vid gränsskiktet mellan luft och vätska. Det sekundära målet var att undersöka vilken typ av magnetiska nålar som är bäst att använda för respektive gränsskiktssystem. Av att använda den tyngre nålen med massan 70.6 mg och längden 50 mm kunde man dra slutsatsen att den är bäst att använda för system där de viskösa och elastiska komponenterna är signifikant stora, där nålens tröghet inte är dominant. Den fungerade även att mäta med i ett fosfolipidsystem. I experimentet med 12-hydroxy-stearinsyra (HSA) som utfördes på en subfas av NaCl, syntes en klar förbättring efter att byta från en tyngre nål (massa 41.5 mg; längd 51 mm) till en lättare (massa 6.94 mg; längd 34.7 mm). Värdena för dynamiska modulen stämde därför bättre överens med referenslitteraturen. Det utspridda lagret av klass II hydrophobins (HFBII) kunde komprimeras upp till yttrycket 46 mNm-1. Värdena för G' och G'' förkastades därför att monolagret förvandlades till en väldigt viskösliknande vätska, och den oscillerande nålen, efter kompressionen, satt fast i denna tröga vätska och rörde sig väldigt hackigt och oregelbundet under tiden ett frekvenssvep utfördes. Då en jämförelse av olika typer av nålar genomfördes med kiseldioxidpartiklar (10 % (viktsprocent) Bindzil CC30 med pH 3.5), för att se om det är någon skillnad i känslighet för nålarna vid gränssnittet, som bestod av en ren 10 mM NaCl-lösning eller en 10 mM NaCl-lösning med tillsatt BCC30. Skillnaderna var försumbara gällande ytspänningen, men det var en klar skillnad mellan den tunga nålen och den lätta nålen vid oscillering vid höga frekvenser (>≈6 rad/s). I och med detta arbete så har förståelsen för hur ISR400 fungerar förbättrats mycket sedan starten. Flera frågeställningar har behandlats och resultaten ger en bra grund för fortsatta studier inom de många områden som utrustningen kan användas till. Trots projektets tidsbegränsning, och det faktum att instrumentet var nytt och oprövat på platsen där detta arbete utfördes, så prioriterades fokusområden så att goda resultat kunde uppnås inom rimliga mål.

A persistent challenge in the design of composite materials is the ability to fabricate materials that simultaneously display high stiffness and high loss factors for the creation of structural elements capable of passively suppressing vibro-acoustic energy. Relevant recent research has shown that it is possible to produce composite materials whose macroscopic mechanical stiffness and loss properties surpass those of conventional composites through the addition of trace amounts of materials displaying negative stiffness (NS) induced by phase transformation [R. S. Lakes, et al., Nature, 410, pp. 565-567, (2001)]. The present work investigates the ability to elicit NS behavior without employing physical phenomena such as inherent nonlinear material behavior (e.g., phase change or plastic deformation) or dynamic effects, but rather the controlled buckling of small-scale structural elements, metamaterials, embedded in a continuous viscoelastic matrix. To illustrate the effect of these buckled elements, a nonlinear hierarchical multiscale material model is derived which estimates the macroscopic stiffness and loss of a composite material containing pre-strained microscale structured inclusions. The nonlinear multiscale model is then utilized in a set-based hierarchical design approach to explore the design space over a wide range of inclusion geometries. Finally, prototype NS inclusions are fabricated using an additive manufacturing technique and tested to determine quasi-static inclusion stiffness which is compared with analytical predictions. / text

Traumatic brain injury (TBI) has a 20% mortality rate and a 10-15% rate of resultant permanent disability. The consequences of TBI range from brief loss of consciousness, to prolonged coma or death. Mild TBI is amongst the common causes of admission to trauma centers all over the world. Future technologies such as magnetic resonance elastography and robotic surgery demand information about the physical properties of brain tissue. Walsh and Schettini described the mechanical behavior of brain tissue under normal status as nonlinear viscoelastic behavior and defined the associated biomechanical changes and responses in a quantitative measurement of the material changes. Yet, there is still a lack of data concerning time-dependent deformation and mechanical property changes associated with TBI. My goal in this project was to describe these mechanical responses and to create a system for measuring and evaluating the mechanical response of brain tissue in vivo. This was to be achieved by inducing cortical contusions with a calibrated weight-drop method in seventy-four young adult male Sprague-Dawley rats. Instrumented indentation was performed on control brains and 1 hour to 3 weeks after contusion with intact dura using a 4-mm-diameter flat punch indenter to a maximum depth of 1.2 mm at loading. Loading rates did not exceed 0.34 N/min and 1.2 mm/min. In order to obtain force displacement data, we studied the elastic response of the traumatized brain tissue and the deformation process (creep) during the loading and unloading of indenter. After euthanasia, the brain was removed and evaluated histologically with different methods to reveal acute and chronic changes related to the contusion. The results revealed that the biomechanical properties of the brain tissue were changed after cortical contusion. Brain tissue elasticity decreased in the edematous brain at one day following the contusion and increased at 3 weeks, in association with reactive astroglial changes. This experimental technique, combined with mathematical modeling, might eventually lead to a better understanding of the physical changes in brain following TBI.

During the debonding of a soft adhesive (as are Pressure Sensitive Adhesives or PSA), complex mechanisms enter in competition at the interface and in the bulk of the adhesive film. In order to optimize these adhesives, it is crucial to understand the transitions between the different debonding modes. We studied these transitions using model materials and carried out a quantitative analysis of debonding experiments with a new image analysis method. We also modeled the mechanical behavior of our materials under uniaxial deformation by using a 2-modes Phan-Thien and Tanner (PTT) viscoelastic model. These studies showed the strong heterogeneity of the debonding mechanisms where process at the interface and in the bulk are in competition. To obtain more efficient PSA, we optimized their properties by introducing a gradient in the viscoelastic properties of the film along their thickness. Bi-layer optimized systems showed interesting properties on surfaces with high or low adhesion. Finally, adhesives with a continuous gradient were realized and characterized by the diffusion of a cross-linker in a polymer film followed by an activation of the cross-linking reaction at a given time

Traumatic brain injury (TBI) has a 20% mortality rate and a 10-15% rate of resultant permanent disability. The consequences of TBI range from brief loss of consciousness, to prolonged coma or death. Mild TBI is amongst the common causes of admission to trauma centers all over the world. Future technologies such as magnetic resonance elastography and robotic surgery demand information about the physical properties of brain tissue. Walsh and Schettini described the mechanical behavior of brain tissue under normal status as nonlinear viscoelastic behavior and defined the associated biomechanical changes and responses in a quantitative measurement of the material changes. Yet, there is still a lack of data concerning time-dependent deformation and mechanical property changes associated with TBI. My goal in this project was to describe these mechanical responses and to create a system for measuring and evaluating the mechanical response of brain tissue in vivo. This was to be achieved by inducing cortical contusions with a calibrated weight-drop method in seventy-four young adult male Sprague-Dawley rats. Instrumented indentation was performed on control brains and 1 hour to 3 weeks after contusion with intact dura using a 4-mm-diameter flat punch indenter to a maximum depth of 1.2 mm at loading. Loading rates did not exceed 0.34 N/min and 1.2 mm/min. In order to obtain force displacement data, we studied the elastic response of the traumatized brain tissue and the deformation process (creep) during the loading and unloading of indenter. After euthanasia, the brain was removed and evaluated histologically with different methods to reveal acute and chronic changes related to the contusion. The results revealed that the biomechanical properties of the brain tissue were changed after cortical contusion. Brain tissue elasticity decreased in the edematous brain at one day following the contusion and increased at 3 weeks, in association with reactive astroglial changes. This experimental technique, combined with mathematical modeling, might eventually lead to a better understanding of the physical changes in brain following TBI.