This work aims at facing some challenging aspects of Shell Finite Element modeling in the context of non-linear behavior. Relevant applications of slender structures, such as in the case of reinforced concrete, require to address plastic behavior. To this end, the mixed MISS-4 finite element is extended with non-linear constitutive models and a layer-wise approach to capture solid-like behavior. The assumed stress field, which a priori satisfies the equilibrium, allows for efficient interpolation of displacements only along the boundaries. Concrete is modeled using a confinement-sensitive, plasticity-based yield surface, while reinforcement bars are described by a uniaxial elastic-perfectly plastic law. The method proves effective, with low error even on coarse meshes. Geometrical non-linearity is investigated in the context of laminated composite shells with alternating stiff/soft layers. These structures exhibit a characteristic zig-zag deformation of the cross section due to differential shear strains. To address this behaviour, a hierarchical enrichment of the isogeometric Kirchhoff-Love shell is proposed, introducing arbitrary warping functions along both in-plane directions. Two modeling strategies are evaluated: one assigns independent warping functions to each soft layer, while the other employs a single global function. The results confirm the effectiveness of the method and emphasize the importance of multiple warping modes for accurately modeling heterogeneous laminates. The numerical solution of the equilibrium equations under both material and geometric non-linearities is addressed finally. Displacement-based finite elements suffer from slow convergence in large-rotation problems, particularly when axial/flexural stiffness ratios are high, due to inaccurate stress predictions during iterations. Mixed finite elements offer a solution, but it is the mixed iterative format—not the element formulation itself—that ensures efficiency. Building on this, the study explores both displacement-based and mixed formulations for beams and shells, proposing new iterative schemes and providing a comprehensive picture of the most suitable approach in each context.