A parallelogram spring model for predicting the effective elastic properties of 2D braided composites

In this study, a parallelogram spring model, has been proposed to investigate the effects of fabric parameters (such as braid angle, fiber volume fraction and the aspect ratio of height to length in a unit cell) on the elastic moduli of braided composite plates. To consider the crimp arrangement of the fiber tows and the interaction among the fiber tows in the unit cell, this model first treats each fiber tow as a curve composed of a series of springs with only axial rigidity, and thus discretizes the unit cell of braided composites into a finite element mesh with both spring and solid elements. By assigning proper displacement boundary conditions onto the finite element model of the unit cell, the algebraic static equilibrium equations obtained by the finite element method are then solved. Applying a homogenization procedure, six mean stresses and six mean strains are then calculated for each independent boundary condition. This approach finally solves the constitutive equations for all the elastic moduli (E11, E22, E33, G12, G23, G13, …) of braided composite plates. A fairly good agreement is found between the present computed results and the theoretical and/or experimental data from the literatures.