Homogenisation of a sheared unit cell of textile composites FEA and approximate inclusion model

Meso-mechanical modelling of textile composites on the "meso" (unit cell) level provides information necessary to produce homogenised properties of the composite material (with the reinforcement deformed during draping), to be used in structural analysis on the "macro" (composite part) level. The input data for the meso-calculations include geometrical model of the sheared textile and properties of the fibres and matrix. Inclusion model proceeds then to an approximate description of the reinforcement as a set of stiff inclusions, representing local orientations of the fibers, and employs the Eshelby solution and Mori-Tanaka or self-consistent homogenisation scheme to calculate the effective stiffness matrix of the composite. Finite element modelling goes through stages of (1) converting the geometrical model into a solid model; (2) meshing; (3) applying periodic boundary conditions and (4) solving a set of models necessary to calculate the homogenised stiffness matrix. All these stages present specific challenges for the case of non-orthogonal translational symmetry of the problem, which are dealt with in the paper for two types of textile reinforcements: woven and non-crimp fabrics.