This thesis focuses on the mathematical modeling of fibrous structures having somepeculiar properties (high strength-to-weight ratio and very good toughness infracture), whose mechanical behavior escapes from standard Cauchy elasticity. Inparticular, it addresses cases in which the presence of a microstructure, consisting ofregularly spaced pivoted beams, entails effects that are well described by generalizedcontinuum models, i.e. models in which the deformation energy density depends notonly on the gradient of the placement but also on the second (and possibly higher)gradients of it. In the Introduction, the state of the art concerning generalizedcontinua and their applications for the description of fibrous structures is describedand some relevant open problems are highlighted. In Chapter 1 and 2 a rigoroushomogenization procedure based on Gamma-convergence arguments is performedfor a lattice (truss-like) structure and for a discrete 1D system (Hencky-type beammodel). In Chapter 3, a variational treatment is employed to formulate acomputationally convenient approach. In Chapter 4 some experimental resultsconcerning the behavior of the structure in various kinds of deformation arediscussed. This motivated the investigation performed in Chapter 5, in which DirectMethods of Calculus of Variations are applied to Euler beams in large deformationsunder distributed load.