Les cartilages articulaires sont des tissus conjonctifs constitués essentiellement d’eau, de fibres de collagènes et de protéoglycanes. Ces organes permettent des mouvements sans frottement entre les os tout en transmettant et amortissant les efforts mécaniques associés. Toutefois, la faible fraction volumétrique (2%) qu’occupent les cellules (i.e., les chondrocytes) couplée à l’absence de vascularisation entraîne une certaine lenteur dans les processus de croissance et de réparation des cartilages qui se trouvent ainsi limités. Nos travaux se sont concentrés sur le modèle in vitro de "pellet" de cartilage articulaire. Ils mêlent expérimentations, modélisations mécanique et numérique, et sont menés en croisant des compétences en mécanique et en biologie cellulaire et tissulaire. Ces travaux visent notamment la compréhension des paramètres fondamentaux responsables de la genèse et la croissance des cartilages (flux de nutriments, facteurs de croissance, chargements mécaniques…)

By means of extensive three-dimensional contact dynamics simulations, we analyze the strength properties and microstructure of a granular asteroid, modeled as a self-gravitating cohesive granular aggregate composed of spherical particles, and subjected to diametrical compression tests. We show that, for a broad range of system parameters (shear rate, cohesive forces, asteroid diameter), the behavior can be described by a modified inertial number that incorporates interparticle cohesion and gravitational forces. At low inertial numbers, the behavior is ductile with a well-defined stress peak that scales with internal pressure with a prefactor 0.9. As the inertial number increases, both the prefactor and fluctuations around the mean increase, evidencing a dynamical crisis resulting from the destabilizing effect of particle inertia. From a micromechanical description of the contact and force networks, we propose a model that accounts for solid fraction, local stress, particle connectivity, and granular texture. In the limit of small inertial numbers, we find a very good agreement of the theoretical estimate of compressive strength, evidencing the major role of these structural parameters for the modeled aggregates.

An elastic cylinder spinning about a rigid axis buckles beyond a critical angular velocity, by an instability driven by the centrifugal force. This instability and the competition between the different buckling modes are investigated using analytical calculations in the linear and weakly nonlinear regimes, complemented by numerical simulations in the fully post-buckled regime. The weakly nonlinear analysis is carried out for a generic incompressible hyperelastic material. The key role played by the quadratic term in the expansion of the strain energy density is pointed out: this term has a strong effect on both the nature of the bifurcation, which can switch from supercritical to subcritical, and on the buckling amplitude. Given an arbitrary hyperelastic material, an equivalent shear modulus is proposed, allowing the main features of the instability to be captured by an equivalent neo-Hookean model.