Construction of second order gradient media of discrete structures by the discrete asymptotic homogenization method *K. El Nady, J.F. Ganghoffer LEMTA, Universite de Lorraine. 2, Avenue de la Fort de Haye, 54504 Vanduvre-ls-Nancy Cedex, France. *khaled.el-nady@univ-lorraine.fr, jean-francois.ganghoffer@univ-lorraine.fr The consideration of higher order gradients of the kinematic variables is required when localization of the deformation takes place within distances comparable or less than the typical microstructure size or spacing. This issue is of relevance in homogenization theories when the load applied to a representative unit cell can no more be considered as homogeneous. Composites with strong contrast or properties between the phases or with high volume fractions of reinforcements are typical situations requiring an extension of the framework of materially simple media in the sense of Noll. Such structures exhibit size effects that the classical Cauchy continuum cannot properly address. We presently address the issue of constructing an effective continuum medium from an initially discrete medium exhibiting such strong variations of the deformation field due to non affine motions of the internal nodes under an externally applied strain field. Many man-made and biological structures present a discrete topology, such as fibrous materials (textiles, collagen fiber networks, biological membranes), with a more or less complex organization of the fibrous microstructure. We presently focus on such fibrous structures having a regular architecture, so that a representative unit cell can be identified at a mesoscopic level. The individual segments of the fibrous architecture are described as beams endowed with a tensile and flexural rigidity. We extend the first homogenization schemes recently developed for the determination of the effective mechanical properties of periodical lattices considered as Cauchy or micropolar continua. We focus in this contribution to the theory behind the construction of the second order gradient continuum. The expressions of the stresses and hyperstresses of the second order effective continuum are obtained by an identification of the principle of virtual power of internal forces for both the postulated equivalent second order continuum and the obtained homogenized continuum. The internal lengths of the second order gradient continua are evaluated versus the obtained effective second order mechanical moduli; their comparison with the size of the representative unit cell provides a criterion to assess the impact of higher order effects at the mesoscopic continuum level. Academic examples in 1D and 2D illustrate the proposed methodology for the scale transition accounting for strain gradient effects. Keywords: Second order gradient, Discrete homogenization, Fibrous materials, Meso-scale unit-cell model, Micropolar theory