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.

Le pli vocal humain possède des propriétés vibratoires exceptionnelles. Il est capable de supporter de grandes déformations, pour différent type de chargement, de manière répétée et réversible. Ces propriétés vibro-mécaniques particulières sont étroitement liées à sa microstructure: une structure multi-couches complexe fortement hétérogène composées de réseaux de fibres protéique. Cependant, il est encore aujourd'hui difficile de décrire précisément l'implication des spécificités microstructurales du pli dans son comportement biomécanique.Afin de préciser ce lien et d'aller vers une meilleure compréhension du comportement du tissu vocal, cette étude se propose d'aborder la problématique sous trois approches complémentaires, mélant caractérisation microstructurale, caractérisation mécanique et modélisation numérique. Dans un premier temps, la microstructure du pli a été étudiée emph{ex vivo} à l'aide d'une technique originale basée sur la tomographie à rayon X. L'usage de tomographie synchrotron par contraste de phase a permis de révéler la structure du tissu à différentes échelles. En particulier, des clichés 3D à forte résolution de la structure fibreuse des couches supérieures et musculaires du tissu ont pu être acquis. Ces clichés ont donné lieu à une analyse 3D quantitative de l'arrangement fibreux, permettant la détermination de descripteur d'orientation et de géométrie 3D des fibres.Dans un second temps, le comportement mécanique du tissu sous différentes conditions de chargement a été étudié. Un protocole a été proposé, afin de caractériser un même échantillon en traction, en compression et en cisaillement. Ces essais ont permis de compléter les connaissances existantes sur la biomécanique de pli, et constitue des données de références importantes pour la construction et la validation de modèle numérique.A partir des données acquises expérimentalement, un modèle micro mécanique a été développé. Ce modèle a la spécificité de prendre en compte l'arrangement 3D du tissu à travers une représentation idéalisée mais pertinente de sa microstructure fibreuse. Les réponses macroscopiques prédites pour différents chargements ont pu être comparées à l'expérience pour validation. A l'échelle microscopique, la cinématique des fibres au cours du chargement a pu être simulée. Les micromécanismes ayant lieu au cours de la déformation du réseau fibreux ont ainsi pu être identifiés, ouvrant de nouvelles perspectives dans la compréhension des propriétés multi-échelles du tissu. / The human vocal fold owns exceptional vibratory properties. It is capable of withstanding large deformations, for different types of loading, in a repeated and reversible manner. These particular vibro-mechanical properties are closely linked to its microstructure: a multi-layer complex structure composed of highly heterogeneous protein fibre networks. However, it is still difficult today to describe precisely the implication of the microstructural specificities of the fold in its biomechanical behaviour.In order to clarify this link and to move towards a better understanding of the behaviour of the vocal tissue, this study proposes to approach the problem under three complementary approaches, combining microstructural characterization, mechanical characterization and numerical modelling. First, the microstructure of the fold was studied emph{ex vivo} using an original technique based on X-ray tomography. The use of synchrotron tomography in phase retrieval mode has revealed the structure of the tissue at different scales. In particular, high-resolution 3D images of the fibrous structure of the upper and muscular layers of the tissue were acquired. These images gave rise to a quantitative 3D analysis of the fibrous arrangement, allowing the determination of descriptors of orientation and 3D geometry of the fibers.In a second step, the mechanical behaviour of the fabric under different loading conditions was studied. A protocol has been proposed to characterize the same sample in tension, compression and shear. These tests have complemented existing knowledge on fold biomechanics, and constitute important reference data for the construction and validation of digital models.Finally, based on the data acquired experimentally, a micro-mechanical model was developed. This model has the specificity to take into account the 3D arrangement of the tissue through an idealized but relevant representation of its fibrous microstructure. The macroscopic responses predicted for different loading conditionds could be compared to the experiment for validation. At the microscopic scale, the kinematics of the fibres during the loading could be simulated. The micromechanisms that occur during the deformation of the fibrous network could thus be identified, opening new perspectives in the understanding of the multi-scale properties of the tissue.