Geometric Model and Elastic Constant Prediction of 3D Four-Step Braided Composites Based on the Cubic Spline Curve

In this paper, the three-dimensional (3D) four-step (1x1) rectangular braided composites are analyzed, the internal yarn spatial topology and mechanical model are determined, a new geometric model, which uses a cubic spline curve to fit yarn trajectory, is presented. The new geometric model can be divided into three types of unit cell models which are the interior, surface and corner unit cell. Based on the new proposed geometric model and the stiffness averaging theory, the corresponding elastic constants are predicted. The predicted numerical results are calculated, and compared with the experimental results. Numerical examples indicate that the numerical calculations well agree with the experimental results. Error values between numerical calculations and experimental results are less than 7.5%. The numerical results verify the validity and accuracy of the new geometrical model.