We calculate the stress response, or rheology, of a micro-mechanical model suspension of rigid, Brownian spheroids in a Newtonian fluid in an oscillatory shear flow. The straining and rotation components of a linear flow affects the microstructure, or particle orientation in space and time, and thus, the suspension stress. A statistical description of the microstructure is given by an orientation probability distribution function, which quantifies the likelihood of a particle possessing a particular orientation at an instance in time. The evolution of the microstructure results from the memory of the material, advection from the flow, and rotational Brownian motion. The macroscopic stress response is calculated from ensemble averages of the stresslet weighted by the orientation distribution function. First, we calculate the linear stress response of a dilute suspension of rigid, spheroidal, self-propelled particles under a small-amplitude oscillatory shear deformation using regular perturbation theory. The particle activity leads to a direct contribution to the material stress, via self-propulsion, and an indirect contribution due to correlated tumbling events. The mechanism and strength of self-propulsion and correlation between tumbling events can be determined from the linear stress response of an active suspension. Next, we develop a framework for determining the relaxation moduli of a viscoelastic material through the combination of a memory integral expansion and a multimode-frequency oscillatory shear flow. We analytically determine the first nonlinear relaxation modulus of the model suspension through a comparison of the second normal stress difference from the microstructural stress response, calculated via regular perturbation theory, and a co-rotational memory integral expansion. The stress response of the system is reconstructed for the start-up and cessation of steady simple shear and uniaxial extension. Finally, we numerically calculate the nonlinear viscoelasticity of the model system subject to a large-amplitude oscillatory shear flow. In a sufficiently strong flow with oscillation frequency comparable to the material relaxation rate, secondary overshoots in the stress response occur. We attribute the origin of secondary overshoots to particles undergoing a Jeffery orbit during a (half) cycle of the oscillation, analogous to the case of non-Brownian spheroids in steady shear flow.

[pt] Este trabalho apresenta a modelagem teórica e correspondentes soluções numéricas, associadas ao problema de tensões e deformações num cilindro longo de material viscoelástico, submetido a resfriamento em meio homogêneo. Apresentam-se as hipóteses adotadas na caracterização térmica e mecânica do material, bem como procedimentos e resultados experimentais obtidos na aplicação destas suposições e técnicas para a resina poliéster. / [en] The problem of computing stress and strain histories under viscoelastic behaviour in a long cylinder subjected to rapid cooling is considered. The theoretical formulation is presented together with the assumptions made in both thermal and mechanical material characterization. Experimental techniques and results obtained to polyester resin are also presented.

Various models are currently in existence for determining the deflection of lithospheric plates under an applied transverse load. The most popular models treat lithospheric plates as thin elastic or thin viscoelastic plates. The equations governing the deflection of such plates have been solved successfully in two dimensions using integral transform techniques. Three dimensional models have been solved using Fourier Series expansions assuming a sinusoidal variation for the load and deflection. In the engineering context, the finite element technique has also been employed. The current aim, however, is to develop an efficient solver for the three dimensional elastic and viscoelastic problems using finite difference techniques. A variety of loading functions may therefore be considered with minimum work involved in obtaining a solution for different forcing functions once the main program has been developed. The proposed method would therefore provide a valuable technique for assessing new models for the loading of lithospheric plates as well as a useful educational tool for use in geophysics laboratories. The multigrid method, which has proved to be a fast, efficient solver for elliptic partial differential equations, is examined as the basis for a solver of both the elastic and viscoelastic problems. The viscoelastic problem, being explicitly time-dependent, is the more challenging of the two and will receive particular attention. Multigrid proves to be a very effective method applicable to the solution of both the elastic and viscoelastic problems. / Science, Faculty of / Mathematics, Department of / Graduate

Les engrenages en matériau polymère sont de plus en plus utilisés dans des domaines variés, notamment dans des applications automobiles, où il est courant de trouver des engrènements polymère / métal ou polymère / polymère. Pour bon nombre d’applications, les polymères choisis pour réaliser des engrenages moulés ou taillés sont des semi-cristallins de type polyamides (nylon). Néanmoins, leur caractère viscoélastique introduit une difficulté supplémentaire dans la modélisation. En effet, le comportement viscoélastique des polymères dépend de la température et de la vitesse de rotation. Pour les Polyamides, il dépend également de l’humidité. Par conséquent, la viscoélasticité peut influencer la répartition des charges, l’erreur de transmission sous charge, la raideur d’engrènement… Dans cette thèse, une méthode numérique originale modélisant le comportement mécanique des engrenages en Polyamide 6,6 est proposée. L’approche développée utilise le modèle rhéologique linéaire de Kelvin généralisé pour simuler le comportement viscoélastique du matériau et prendre en compte la température, la vitesse de rotation et l’humidité. Ensuite ce modèle rhéologique est intégré dans le modèle quasi-statique du partage des charges développé par le LaMCoS. Ce processus de calcul permet d’obtenir les résultats essentiels pour les engrenages (répartition des charges, pressions de contact, erreur de transmission sous charge, raideur d’engrènement) avec un temps de calcul assez court. Enfin, un banc expérimental avec des engrenages en Polyamide 6,6 est développé et fabriqué dans le cadre de cette thèse. Il permet d’obtenir deux résultats : la température de l’engrenage pendant son fonctionnement et l’erreur de transmission sous charge. Cette dernière permet de valider le modèle quasi-statique du partage des charges. / Polymer gears are increasingly used, especially in automotive applications, where it is common to find meshing polymer / metal or polymer / polymer.For many applications, the polymer selected to produce gears by cutting or by injection moulding is polyamide (nylon) which has semi-crystalline structure. However, the viscoelastic character of Polyamide material introduces an additional difficulty in modeling. Indeed, the viscoelastic behavior of polymers is temperature and rotation speed dependent. In addition for polyamides, it also humidity dependent. Therefore, viscoelasticity influences the load sharing, the load transmission error, the meshing stiffness... In this thesis, an original numerical method modeling the mechanical behavior of polyamide 6.6 gears is proposed. This approach uses the linear rheological model of generalized Kelvin to simulate the viscoelastic behavior of the material and take into account the temperature, speed and humidity. The rheological model is integrated into the quasi-static load sharing model developed by the LaMCoS. This process provides the essential results for gears (load sharing, contact pressure, load transmission error, meshing stiffness) with short computation time. Finally, an experimental test bench with Polyamide 6.6 gears is developed. It provides two experimental results: the temperature of the gear during operation and the load transmission error which validates the quasi-static load sharing model

Environmental issues enforce transportation sectors to limit their carbon dioxide emissions in various ways. Automotive manufacturers attempt to reduce carbon dioxide emission by seeking various strategies, e.g., increasing aerodynamic efficiency, using more fuel-efficient engines, reducing friction and wear of transmission systems, and, most importantly, by using lightweight materials and structures. This dissertation is a contribution toward a lightweight design of structures by proposing numerical models suitable for damage prediction of thermoplastic composite materials. In this dissertation, predictive damage models for two different length scales, namely micromechanics, and mesomechanics, were proposed. Micromechanics is used to predict the nonlinear damage behavior of elementary thermoplastic composite ply, while the mesomechanics is used to predict the failure behavior of thermoplastic composite laminates (test coupon or plate scale). For the micromechanics, a representative volume element (RVE) of such materials was rigorously determined using a geometrical two-point probability function and the eigenvalue stabilization of homogenized elastic tensor obtained by Hill-Mandel kinematic homogenization. We proposed a viscoelastic viscoplastic model for the polypropylene matrix to extend the capability of the micromechanics model in predicting the damage behavior of the composite ply at higher rates. At the mesoscale, we improved the classical mesomechanics damage modeling in the off-axis direction by introducing the confinement effect. The pragmatic approach consists of separating the progressive damage into two parts, namely “diffuse damage regime” and “transverse-cracking regime”, were described by two distinct damage parameters. We also enriched the mesomechanics model by proposing a viscoelastic and viscoplastic model to account for the rate-dependent behavior of the thermoplastic composites. We showed that the predictions given by the proposed micromechanics and mesomechanics models were in excellent agreement with the experimental results in terms of the global stress-strain curves, including the linear and nonlinear portion of the response and also the failure point, making it useful virtual testing tools for the design of thermoplastic composites.

Thesis: M.S., Massachusetts Institute of Technology, Department of Civil Engineering, 1976 / Bibliography: leaves 126-131. / by Joseph A. Martore. / M.S. / M.S. Massachusetts Institute of Technology, Department of Civil Engineering

This work focuses on polymer glasses relaxation behavior. Polymethylmethacrylate was chosen as a typical representative of polymer glasses. Relaxation processes were studied by dynamical mechanical spectroscopy and differential scanning calorimetry was used as a supplemental analysis. Relaxation process above Tg and high values of rubberlike plateau modulus were observed in thermomechanical spectra. High temperature relaxation transition was studied from the perspective of thermal history, frequency and axial stress dependence and influence of molecular structure was also investigated. Apparent activation energies of studied processes and their axial stress dependence for polymethylmethacrylate were determined. On the basis of obtained data, a hypothesis was developed which connects high temperature relaxation process with molecular process responsible for strain hardening.

Les solutions de micelles géantes sont utilisées dans plusieurs domaines industriels pour augmenter la viscosité d'une solution. Elles présentent un caractère viscoélastique bénéfique pour la fracturation hydraulique des roches pétrolifères car elles permettent de transporter le sable et de le maintenir en suspension. Cette thèse étudie les propriétés rhéologiques d’une solution commerciale destinée à la fracturation hydraulique. Cette solution est particulièrement délicate à caractériser car ses écoulements semblent être toujours instables. Nous avons mis au point une méthodologie permettant de la caractériser en régime laminaire, et avons montré que ce régime n’existe à température ambiante que pour des très faibles valeurs de taux de cisaillement. Habituellement, le comportement rhéologique dans le régime linéaire de ce type de solution est prédit par le modèle de Maxwell. Nous mettons en évidence que le comportement rhéologique de la solution étudiée ne correspond pas à ce modèle. Nous avons établi un modèle viscoélastique compatible avec les données expérimentales.Les instabilités d’écoulement de ces solutions sont d’origine élastique. Ce phénomène est largement étudié dans la littérature. Le comportement rhéologique dans le domaine non linéaire possède des caractéristiques propres à ces solutions. Notamment l’apparition d’un plateau de contrainte dans la courbe d’écoulement, précédé par une augmentation linéaire de la contrainte avec le cisaillement. Le début de ce plateau coïncide avec le déclenchement des instabilités, on parle de taux de cisaillement critique. La particularité de cette solution est la valeur faible de la contrainte plateau ainsi que du taux de cisaillement critique. Les valeurs observées sont cohérentes avec la valeur des paramètres rhéologiques obtenus dans les régimes d’écoulement laminaire. L’effet de certains paramètres physico-chimiques sur la rhéologie est également exploré. / Giant micelle solutions are used in several industrial domains to increase the viscosity of solution. Their viscoelastic characteristic is beneficial for hydraulic fracturing of oil rocks because these solutions are able to transport sand and to keep it in suspension. This thesis examines the rheological properties of a commercial solution, designed for hydraulic fracturing. This solution is particularly difficult to characterize because its flows seem to be always unstable. We have developed a methodology to characterize it in the laminar regime and we have shown that this regime exists at room temperature only for very low shear rate values. Usually, the rheological behavior of this type of solution, in the linear regime, is predicted by the Maxwell model. We prove that the rheological behavior of the studied solution doesn’t match this model. We have designed a viscoelastic model that is compatible with experimental data.The origin of flow instabilities of these solutions is elastic. This phenomenon is widely studied in the literature. The rheological behavior in the nonlinear regime has characteristics specific to these solutions. In particular, the appearance of a stress plateau in the flow curve, preceded by a linear increase of stress with shear. The beginning of this plateau match the onset of instabilities at a critical shear rate. The feature of this solution is the low value of the stress plateau as well as the critical shear rate value. They are consistent with the value of rheological parameters obtained in laminar flow regimes. The effect of some physico-chemical parameters on rheology is also explored.

The goal of elastography is to map the mechanical properties of soft tissues associated with health and disease. The mechanical property of interest in this work is the complex shear modulus, composed of a real part, the storage modulus, which is a measure of elasticity, and an imaginary part, the loss modulus, which is a measure of viscosity. Together, they determine the speed and attenuation of shear waves in the medium. Elastography techniques based on either ultrasound imaging or MRI can image shear wave propagation and thus are capable of measuring shear wave speed and attenuation. Dispersion, or the frequency-dependence of material parameters, is a primary confounding factor when comparing measurements between different shear wave elastography implementations. Prior attempts at quantifying this frequency-dependence suffered from inaccurate modeling assumptions and low signal-to-noise ratios (SNR). To overcome these limitations, a high-fidelity forward model of shear wave propagation in homogeneous media was developed. The model is an exact semi-analytical solution of Navier's equation and is well-suited for acoustic radiation force impulse shear wave elastography (ARFI-SWE) because it does not require precise knowledge of the strength of the source, nor its spatial or temporal distribution. Unlike models used in ARFI-SWE heretofore, it accounts for the vector polarization of shear waves and exactly represents geometric spreading of the shear wavefield, whether spherical, cylindrical, or neither. Furthermore, it is material-model independent, i.e. it makes no assumption about the frequency-dependence of material parameters. It overcomes the problem of low SNR through spatial averaging and enables estimation of the frequency-dependent complex shear modulus over a wider frequency range than has hitherto been possible. This improved ARFI-SWE was named Shear Wave Rheometry (SWR). By combining SWR with a novel torsional vibration rheometry, dispersion in tissue-mimicking gels was quantified from 1--1800 Hz. The measurements show sizable frequency-dependent variation in the shear modulus of gelatin, a material often assumed to be non-dispersive based on narrow-band measurements. SWR measurements in ex vivo bovine liver tissue yielded complex shear modulus estimates from 25--250 Hz and showed that liver tissue exhibits significant dispersion in this frequency range: a factor of 4 increase in the storage modulus and a factor of 10 increase in the loss modulus. Quality metrics showed that liver tissue can be reasonably approximated as homogeneous and isotropic for ARFI-SWE measurements in this frequency range. Results demonstrate that accounting for dispersion is essential for meaningful comparisons of measurements between systems. Moreover, improved tissue characterization enabled by SWR may have clinical relevance, for example, in the diagnosis and monitoring of chronic liver disease.

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