Abstract
Connective tissues are biological tissues that maintain the shape of the body and its organs; they ensure their cohesion as well as their internal support. Most connective soft tissues are fibrous, such as arteries, annulus fibrosus, tendons and ligaments, etc. The study of fibrous soft tissue Poisson coefficients has recently attracted the attention of many authors in the field of mechanical modeling, as high and/or negative values have been measured experimentally. This thesis focuses primarily on the evolution of Poisson coefficients in fibrous soft tissues as a function of the arrangement of fibres, and more specifically, their corrugation and spatial organization. First, the state of the art on microstructure and components of fibrous soft tissue is presented. A synthesis of the literature on the Poisson coefficient of fibrous soft tissues, as well as its predictions given by mechanical models are then provided. Then, an analytical micromechanical model of the lamellar structure of the annulus fibrosus is proposed, based on observations from the literature. In this model, the crimped fibre is considered to have a sinusoidal shape. The effect of the structure of the crimped fibres on the Poisson coefficient is thus studied. Then, the observations from the literature on tendon and ligament led us to consider collagen fibres as interconnected helices. Three microstructures are studied: a composite reinforced by unconnected helical fibers, helical fibers with bonds but without matrix and a composite fiber/matrix reinforced by helical fibers with bonds. The three models proposed are studied by the double-scale asymptotic homogenization method. The results of the parametric study show that the presence and position of the bonds between helicoidal fibres radically change the Poisson coefficients of these materials. The presence or absence of the matrix has little effect on the elasticity modules, but affects the Poisson coefficients, especially the negative ones. Finally, a process for manufacturing model materials composed of silicone and helical fibres, which makes it possible to explore behaviors, is proposed.