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.

Les matériaux viscoélastiques sont utilisés dans tous les domaines de l'ingénierie et des systèmes mécaniques, de l'électroménager, spatial, l'automobile, l'aéronautique ou le génie civil (ponts...) grâce à leur capacité d’amortir les chocs ou de filtrer les vibrations. Ce travail constitue une contribution à l’étude du comportement dynamique non linéaire des composants viscoélastiques notamment les élastomères. Dans ce mémoire, on introduit, d’abord, les propriétés mécaniques des élastomères, pour les aspects viscoélasticité et friction. Un rappel des différents phénomènes physiques et une liste non-exhaustive des modèles existants dans la littérature sont présentés. Ensuite, on propose des techniques expérimentales afin de décrire le comportement dynamique sous sollicitations uniaxiales d’un élastomère. Une description des bancs d’essais, des chaines d’analyse vibratoire, des méthodes de traitement des données des essais et d’analyse des mesures expérimentales est détaillée dans ce manuscrit. Une nouvelle approche du modèle de Maxwell généralisé a été proposée pour décrire le comportement dynamique du composant viscoélastique. Ce modèle permet une description précise et une bonne connaissance du comportement dynamique des composants viscoélastiques en fonction de l’amplitude, de la précharge et de la fréquence. La dissipation d'énergie identifiée sous forme d'amortissement peut être issue de l'amortissement intrinsèque des matériaux polymère comme de la friction aux interfaces dans le cas de composants caoutchoucs non adhérisés sur les pièces, dans ce travail, un nouveau modèle visco-tribologique a été développé en couplant les propriétés rhéologiques linéaires du modèle de Maxwell généralisé et le modèle de frottement de Dahl pour la description du comportement de frottement hystérétique des liaisons viscoélastiques non adhérisées. / Viscoelastic materials are used in all areas of engineering and mechanical systems, appliances, aerospace, automotive, aerospace and civil engineering (bridges...) through their ability to absorb shock and vibration filtering. This work is a contribution to the study of nonlinear dynamic behavior of viscoelastic components particularly elastomers. In this dissertation, we introduced the mechanical properties of elastomers, for both viscoelasticity and friction aspects. A review of the different physical phenomena and a non-exhaustive list of existing models in the literature are presented. Then, we propose experimental techniques to describe the dynamic behavior under uniaxial stress of an elastomer. A description of test benches, vibration analysis chains, methods of processing data and analysis of experimental measurements is detailed in this manuscript. A new approach of generalized Maxwell model was proposed to describe the dynamic behavior of viscoelastic component. This model allows an accurate description and a good knowledge of the dynamic behavior of viscoelastic components depending on amplitude, frequency and preload. Energy dissipation identified as damping can be from intrinsic damping of the polymer as friction at the interfaces in case of not bonded rubber component to mechanical part, a new viscoelastic model tribological was developed by combining the rheological properties of linear generalized Maxwell model and the Dahl friction model for describing the behavior of viscoelastic hysteretic friction of not bonded connections.

No description available.

京都大学 / 0048 / 新制・論文博士 / 博士(工学) / 乙第13337号 / 論工博第4186号 / 新制||工||1740(附属図書館) / 京都大学大学院工学研究科材料化学専攻 / (主査)教授 瀧川 敏算, 教授 中村 洋, 教授 古賀 毅 / 学位規則第4条第2項該当 / Doctor of Philosophy (Engineering) / Kyoto University / DFAM

Ligaments and tendons are rope-like structures in our body that possess time- and history-dependent material properties. Despite the many advances made in experimental and theoretical biomechanics, the material properties of these biological structures are still not fully characterized. This dissertation represents a step forward in the development of combined theoretical and experimental tools that capture the time- and history-dependent material properties of ligaments and tendons. The mechanical behavior of bundles of collagen fibers which form ligaments and tendons was investigated. Axial stress-stretch data and stress relaxation data at different axial stretches were collected by testing rat tail tendon fascicles. The experimental results demonstrated, for the first time, that the shape of the normalized axial stress relaxation curve depends on the axial stretch level thus suggesting that the fascicles are nonlinear viscoelastic. A constitutive model was then formulated within the nonlinear integral representation frame- work proposed by Pipkin and Rogers (1968). Unlike the well-known quasi-linear viscoelastic model, the proposed constitutive law was able to capture the observed nonlinearities in the stress relaxation response of rat tail tendon fascicles. By extending the constitutive model for collagen fiber bundles, a new nonlinear three- dimensional model for the stress relaxation of skeletal ligaments was formulated. The model accounts for the contribution of the collagen fibers and the group substance in which they are embedded. Published uniaxial experimental data on the stress relaxation of human medial collateral ligaments were used to determine the model parameters. The model predictions for simple shear in the fiber direction, simple shear transverse to the fiber direction, and equibiaxial extension were then examined and, for the case of simple shear in the fiber direction, such predictions were found to be in good agreement with published experimental data. The relationship between the mechanical response and structure of suspensory ligaments was examined by performing state-of-the-art small angle x-ray diffraction experiments in tandem with incremental stress relaxation tests. Specifically, small angle x-ray diffraction was used to measure changes in strain and orientation of collagen fibrils during the stress relaxation tests. Throughout the tests the collagen fibrils were found to gradually orient towards the loading direction. However, the collagen fibril strain did not change significantly suggesting that collagen fibers do not play a significant role in dissipating load during stress relaxation. / Ph. D.

A combination of theoretical, numerical, and experimental methods were utilized to determine that shock waves can form in brain tissue from smooth boundary conditions. The conditions that lead to the formation of shock waves were determined. The implication of this finding was that the high gradients of stress and strain that could occur at the shock wave front could contribute to mechanism of brain injury in blast loading conditions. The approach consisted of three major steps. In the first step, a viscoelastic constitutive model of bovine brain tissue under finite step-and-hold uniaxial compression with 10 1/s ramp rate and 20 s hold time has been developed. The assumption of quasi-linear viscoelasticity (QLV) was validated for strain levels of up to 35%. A generalized Rivlin model was used for the isochoric part of the deformation and it was shown that at least three terms (C_10, C_01 and C_11) are needed to accurately capture the material behavior. Furthermore, for the volumetric deformation, a linear bulk modulus model was used and the extent of material incompressibility was studied. The hyperelastic material parameters were determined through extracting and fitting to two isochronous curves (0.06 s and 14 s) approximating the instantaneous and steady-state elastic responses. Viscoelastic relaxation was characterized at five decay rates (100, 10, 1, 0.1, 0 1/s) and the results in compression and their extrapolation to tension were compared against previous models. In the next step, a framework for understanding the propagation of stress waves in brain tissue under blast loading was developed. It was shown that tissue nonlinearity and rate dependence are key parameters in predicting the mechanical behavior under such loadings, as they determine whether traveling waves could become steeper and eventually evolve into shock discontinuities. To investigate this phenomenon, the QLV material model developed based on finite compression results mentioned above was extended to blast loading rates, by utilizing the stress data published on finite torsion of brain tissue at high rates (up to 700 1/s). It was shown that development of shock waves is possible inside the head in response to compressive pressure waves from blast explosions. Furthermore, it was argued that injury to the nervous tissue at the microstructural level could be attributed to the high stress and strain gradients with high temporal rates generated at the shock front and this was proposed as a mechanism of injury in brain tissue. In the final step, the phenomenon of shock wave formation and propagation in brain tissue was further studied by developing a one-dimensional model of brain tissue using the Discontinuous Galerkin finite element method. This model is capable of capturing high-gradient waves with higher accuracy than commercial finite element software. The deformation of brain tissue was investigated under displacement input and pressure input boundary conditions relevant to blast over-pressure reported in the literature. It was shown that a continuous wave can become a shock wave as it propagates in the tissue when the initial changes in acceleration are beyond a certain limit. The high spatial gradients of stress and strain at the shock front cause large relative motions at the cellular scale at high temporal rates even when the maximum strains and stresses are relatively low. This gradient-induced local deformation occurs away from the boundary and can therefore contribute to the diffuse nature of blast-induced injuries.   / Mechanical Engineering

Selon l’Eurocode 8 et la norme EN 1337-3, le comportement de l’Appareil d'Appui en Néoprène Fretté (AANF) est considéré comme élastique linéaire ou hystérétique linéaire. En réalité, les comportements mécaniques de l’AANF sont très complexes et sont essentiellement ceux du néoprène tels que l’élasticité non linéaire, la viscosité, la plasticité, l’effet Payne, l’effet Mullins, etc. Toutefois, très peu d’études de l’effet Mullins et de la piezo-dépendance existent, et aucun modèle par éléments finis ne permet de modéliser ces phénomènes dans l’AANF. L’objectif de cette thèse est donc l’étude de ces phénomènes sur le néoprène et sur l’AANF. Pour atteindre ces objectifs, la caractérisation de ces phénomènes sur le néoprène est tout d’abord réalisée avec différents types de chargements tels que la relaxation, la traction cyclique, la compression cyclique, le couplage compression statique – cisaillement cyclique. De plus, un dispositif biaxial original est fabriqué afin de caractériser l’AANF sous le chargement de compression statique couplé au cisaillement cyclique. Grâce à ces résultats expérimentaux, un nouveau modèle est développé, permettant de modéliser simultanément l’effet Mullins, la piezo-dépendance ainsi que la viscoélasticité non linéaire du néoprène. / High Damping Rubber Bearings (HDRB) composed of alternating thin horizontal layers of elastomer bonded to steel plates are used to support permanent static loading in compression and cyclic shear in case of earthquakes. The behaviour of HDRB is considered to be linear elastic or linear hysteretic according to The European Standard Eurocode 8 and The Standard EN 1337 - 3. The mechanical behaviour of HDRB under loading is actually very complex and essentially linked to the behaviour of elastomer such as nonlinear elasticity, viscosity, plasticity, Payne effect, and Mullins effect. However, the coupling of Mullins effect and nonlinear viscosity as well as influence of hydrostatic stress on viscoelasticity of elastomer or of HDRB has not been studied yet. The aim of this thesis is thus the study of these effects on elastomer and on HDRB. In order to reach these objectives, characterization of these effects on elastomer is firstly performed with different types of loading such as relaxation test, cyclic tensile test, cyclic compression test and combined static compression – cyclic shear test. Furthermore, an original biaxial device is designed and manufactured in order to characterize the behaviour of HDRB under combined static compression – cyclic shear. Based on these experiments a new finite model is developped to simulate simultaneously Mullins effect, nonlinear viscosity and influence of hydrostatic stress on viscoelasticity of elastomer. Subsequently, this model is used to simulate the response of the HDRB under combined static compression - cyclic shear.

La relation entre les propriétés viscoélastiques complexes de liquides polymères et leur structure microscopique et la dynamique est une question clé dans la science des matériaux et de la biophysique. Les théories modernes de la dynamique des polymères et la rhéologie décrivent les aspects universels du comportement viscoélastique sur la base de l'idée que les enchevêtrements moléculaires confinent filaments individuels à une dimension, la dynamique diffusifs (reptation) dans le tube-comme les régions dans l'espace. Alors que le modèle de tube est validé par son succès, ses éléments constitutifs (les statistiques et la dynamique de l'axe du tube ou des chemins primitifs et de l'confinement "cage" de chaînes voisines) ne sont pas directement observables. (1) Nous présentons un vaste ensemble de résultats de simulation pour la relaxation des contraintes à l'équilibre et l'étape-tendues perles printemps polymères fondus (En collaboration avec: C. Svaneborg et GS Grest). Les données nous permettent d'explorer la dynamique de la chaîne et le module de la relaxation de cisaillement dans le régime plateau pour les chaînes avec Z~40 enchevêtrements et dans le régime de relaxation terminale pour Z~10. Nous avons effectué des tests sans paramètres de plusieurs modèles différents de tubes à l'aide de (Rouse) la mobilité connue des chaînes unentangled et la longueur d'enchevêtrement de fusion déterminé par l'analyse du chemin primitif de l'état microscopique topologique de nos systèmes. (2) Nous présentons une compréhension complète pour la détente des empêtré polymère linéaire fond que les liens de la dynamique et la théorie de Rouse tube par une interprétation dynamique qui s’appellel’analyse du chemin primitive. La chaîne primitive, qui est la moyenne d'ensemble des conformations de la chaîne, se rétrécit strictement d’après la dynamique Rouse jusqu'à ce qu'il renconte les obstacles formés par d'autres chaînes primitives. Le temps d'arrêt de la diminution peut être déterminée par l'argument que la zone balayée par la chaîne primitive sur une longueur de propagation de tension qui est égale à la taille du maille de filet du travail formé par les chaînes de primitives. Le processus physique avant l'heure d'arrêt est assez présenté par l'analyse du chemin primitif. Après le temps d'arrêt, les longueurs primitives seront rétrécites par la reptation et la fluctuation de la longueur de contour .Cette procedure peut être décrite comme la modèle du tube, par exemple, Likhtman-McLeish (LM) la théorie. (3) Nous constatons que la théorie sous-estime la relaxation LM module de cisaillement dû à un double comptage de l'effet de courte longueur d'onde (p> Z) dans les modes partie de relaxation de Rouse et en fonction de la trompe de mémoire μ (t). LM extrapolé μ (t) à la limite du continuum, ce qui entraîne une décroissance sur des échelles de temps inférieur au temps de l'intrication, où le mouvement de la chaîne primitive devrait être négligeable. Pour corriger cela, nous avons retiré de la partie de fluctuation contour longueur de μ (t) la contribution des modes avec un temps de relaxation plus court que le temps d'enchevêtrement. Nous trouvons un excellent accord entre nos données de simulation et la théorie LM modifiée en utilisant l'approximation reptation double pour la libération de contrainte, ce qui démonte que l'analyse du chemin primitif de la structure microscopique apporte du modèle de tube avec une puissance prédictive des processus dynamiques. L'utilisation de systèmes plus complexes pour le traitement de la libération de contrainte devrait conduire à un accord encore mieux. / The relation between the complex viscoelastic properties of polymer liquids and their microscopic structure and dynamics is a key issue in materials science and biophysics. Modern theories of polymer dynamics and rheology describe the universal aspects of the viscoelastic behavior based on the idea that molecular entanglements confine individual filaments to a one-dimensional, diffusive dynamics (reptation) in tube-like regions in space. While the tube model is validated through its success, its constituting elements (the statistics and dynamics of the tube axis or primitive paths and of the confining "cage" of neighboring chains) are not directly observable. (1) We present an extensive set of simulation results for the stress relaxation in equilibrium and step-strained bead-spring polymer melts (In cooperation with: C. Svaneborg and G. S. Grest). The data allow us to explore the chain dynamics and the shear relaxation modulus into the plateau regime for chains with Z~40 entanglements and into the terminal relaxation regime for Z~10. We have performed parameter-free tests of several different tube models by using the known (Rouse) mobility of unentangled chains and the melt entanglement length determined via the primitive path analysis of the microscopic topological state of our systems. (2) We present a full understanding for relaxation of entangled linear polymer melts that links the Rouse dynamics and tube theory via a dynamic interpretation of the so called primitive path analysis. The primitive chain, which is the ensemble average of the chain conformations, shrinks strictly following the Rouse dynamic until it encounters the obstacles formed by other primitive chains. The stop time of the shrinking can be determined by the argument that the area swept by the primitive chain over a tension propagation length is equal to the mesh size of the net work formed by the primitive chains. The physical process before the stop time is fairly presented by primitive path analysis. After the stop time, the primitive length shrinks via reptation and contour length fluctuation, which is well described by the tube theory, e.g. Likhtman-McLeish (LM) theory. (3) We find that the LM theory underestimates the shear relaxation modulus due to a double-counting of the effect of short-wavelength (p>Z) modes in Rouse relaxation part and in tube memory function μ(t). LM extrapolated μ(t) to the continuum limit, resulting a decay on time scales smaller than the entanglement time, where the motion of the primitive chain should be negligible. To correct this, we have removed from the contour length fluctuation part of μ(t) the contribution of modes with a relaxation time shorter than entanglement time. We find excellent agreement between our simulation data and the modified LM theory using the double reptation approximation for constraint release, which demonstrates that the primitive path analysis of the microscopic structure endows the tube model with predictive power for dynamical processes. The use of more elaborate schemes for treating constraint release should lead to even better agreement.

La prévision du comportement mécanique macroscopique de matériaux hétérogènes à partir des propriétés de leurs constituants est possible pour diverses classes de comportement (élastique, viscoélastique, etc) et ce, grâce à la théorie de l'homogénéisation. Néanmoins l'extension de cette théorie pour des matériaux possédant un comportement viscoélastique non linéaire (ou élasto-viscoplastique) reste une question ouverte à laquelle nous nous attaquons dans ce travail afin de prédire le comportement macroscopique des combustibles oxydes mixtes uranium-plutonium (MOX) utilisés dans les réacteurs nucléaires à eau sous pression (REP) français. Dans cette optique des solutions analytiques et purement nunériques ont été obtenues et le modèle retenu est utilisé pour simuler le comportement des combustibles / The prediction of the macroscopic mechanical behavior of heterogeneous materials from the properties of their constituents is possible for various classes of behavior (elastic, viscoelastic, etc.) thanks to the theory of homogenization. Nevertheless, the extension of this theory for materials with a non-linear (or elasto-viscoplastic) viscoelastic behavior remains an open question that we are tackling in this work in order to predict the macroscopic behavior of uranium-plutonium (MOX) mixed oxide fuels used in french pressurized water reactors (PWRs). From this perspective analytical and purely numerical solutions have been obtained and the model adopted is used to simulate the behavior of fuels.

In this dissertation, the effect of temperature and humidity on the viscoelastic and fracture properties of proton exchange membranes (PEM) used in fuel cell applications was studied. Understanding and accurately modeling the linear and nonlinear viscoelastic constitutive properties of a PEM are important for making hygrothermal stress predictions in the cyclic temperature and humidity environment of operating fuel cells. In this study, Nafion® NRE 211, Gore-Select® 57, and Ion Power® N111-IP were characterized under various humidity and temperature conditions. These membranes were subjected to a nominal strain in a dynamic mechanical analyzer (DMA), and their stress relaxation behavior was characterized over a period of time. Hygral master curves were constructed noting hygral shift factors, followed by thermal shifts to construct a hygrothermal master curve. This process was reversed (thermal shifts followed by hygral shifts) and was seen to yield a similar hygrothermal master curve. Longer term stress relaxation tests were conducted to validate the hygrothermal master curve. The Prony series coefficients determined based on the hygrothermal stress relaxation master curves were utilized in a linear viscoelastic stress model. The nonlinear viscoelastic behavior of the membranes was characterized by conducting creep tests on uniaxial tensile specimens at various constant stress conditions and evaluating the resulting isochronal stress-strain plots. The nonlinearity was found to be induced at relatively moderate stress/strain levels under dry conditions. To capture the nonlinearity, the well known Schapery model was used. To calculate the nonlinear parameters defined in the Schapery model, creep/recovery tests at various stress levels and temperatures were performed. A one-dimensional Schapery model was developed and then validated using various experiments. The fracture properties were studied by cutting membranes using a sharp knife mounted on a specially designed fixture. Again, various temperature and humidity conditions were used, and the fracture energy of the membranes was recorded as a function of cutting rate. Fracture energy master curves with respect to reduced cutting rates were constructed to get some idea about the intrinsic fracture energy of the membrane. The shift factors obtained from the fracture tests were found to match with those obtained from the stress relaxation experiments, suggesting that the knife cutting process is viscoelastic in nature. The rate and temperature dependence for these fracture energies are consistent with the rate, temperature, and moisture dependence of the relaxation modulus, suggesting the usefulness of a viscoelastic framework for examining and modeling durability of fuel cell membranes. The intrinsic fracture energy was initially thought to be a differentiating factor, which would separate various membranes tested in this study from one another. However, it was later found that all the membranes tested showed similar values at lower cutting rates, but showed significant variation at higher reduced cutting rates, and thus was thought to be a more meaningful region to differentiate the membranes for durability understanding. While the preceding work was undertaken to characterize as-received commercial PEMs, it is possible to modify material properties through treatment processes including thermal annealing and water treatment. The transient and dynamic viscoelastic properties of water-treated Nafion membranes revealed unusual behavior. Such unusual properties might have originated from irreversible morphological changes in PEM. Besides the constitutive viscoelastic properties, another set of properties useful for the stress modeling is the hygral strain induced as a function of relative humidity (RH) The effect of pretreatment on hygral strains induced as a function of RH was also investigated. These studies suggest that pretreatment significantly changes the mechanical properties of proton exchange membranes. / Ph. D.