Directional properties of fibre network materials evaluated by means of discrete homogenization

Lattice fibre materials are challenging the standard modelling approaches due to their specific nature that results in peculiar effective behaviours such as extremely anisotropic materials or generalized continuum media. In this context, the aim of this paper is to the determine qualitatively and quantitatively the role of the morphological and mechanical parameters by investigating simple archetypical microstructures. The study is conducted through a up-scaling approach making use of the Homogenization method of discrete periodic media in the framework of a variational approach. The outcomes of this method are presented for several microstructures considered as Euler beam lattices. The effective modelling are established for rectangular or skew arrays, braced or not braced, with rigid or pivot connections and their properties are analyzed. A particular emphasis is given to anisotropy and strain gradient features in relation with the geometry of the pattern and nature of the connections.