Formulation Co-rotationnelle efficace pour les poutres composites en 3D avec glissement dans deux directions

<div> This thesis deals with advanced numerical formulations to accurately model the nonlinear behavior of composite beams with partial interaction under three-dimensional (3D) loading, considering non-uniform torsional effects. Initially, a linear elastic formulation is presented. This model incorporates a deformable interlayer connection, allowing for longitudinal and lateral slip. Based on the principle of virtual work, the weak formulation and equilibrium equations are derived. A closed-form analytical solution is obtained for specific mono-symmetrical sections. Slip-locking phenomena within the displacementbased formulation are analyzed, and additional axial displacement degrees of freedom are proposed to mitigate these issues. Subsequently, material nonlinearity is introduced. A general material law, based on free energy and the Clausius-Duhem inequality, is developed, incorporating damage mechanics and a return mapping algorithm for stress updates. Analogously, a connector constitutive law is formulated, utilizing connector free energy and a similar return mapping algorithm to model shear force-slip relationships. Finally, geometric nonlinearity is addressed using a co-rotational approach. This method decomposes element motion into rigid body and deformable components within a continuously rotating local frame. In this local frame, a second-order Green-Lagrange strain tensor approximation is employed. To address membrane and slip-locking issues, an averaging strain technique and quadratic axial displacement fields are introduced. At the global frame, special attention is given to the representation of upper layer rotations, the transformation of interlayer slips, and the handling of eccentric loading conditions. </div>