Two-Level Computation of the Elastic Characteristics of Woven Composites

Homogenization methods in the mechanics of composites make it possible to theoretically determine the characteristics of composite materials on the basis of known properties of their structural components. For woven composites with a complex braid geometry, numerical homogenization methods are most common. In this paper, a numerical method for calculating the effective elastic properties of woven composites is developed using a two-level approach in the homogenization problem. At the microscale level, the averaged properties of yarns are calculated on the basis of known fiber and matrix properties. At the macroscale level, the stress state of the representative volume of a woven composite is analyzed, and parameters of the elasticity tensor of an equivalent homogeneous material are determined. In this case, the effective elastic characteristics of yarns found at the first stage are used, and the rotation of principal directions of the elastic properties of yarns is taken into account. For the woven carbon fiber-reinforced plastic considered, numerical results obtained by the finite-element method within the framework of the two-level approach to the homogenization of composites are presented.