Multiscale homogenization for nearly periodic structures

In this paper, we propose a new numerical multiscale homogenization method for nearly periodic structures, where perfect periodicity is disturbed due to unintended geometrical imperfections. Geometrical imperfection is introduced as an input to the calculation, and the calculation is always done using the idealized perfect geometry. This has a distinct advantage in numerical calculations where the same mesh can be used for a series of imperfect geometries. The method is implemented using commercially available finite element code ABAQUS. The proposed method is validated by comparing the results to those of a conventional calculation. The results demonstrate that the proposed method can accurately capture the stress distribution when the amplitude of the imperfection is small. Finally, the method is applied to the analysis of the effect of fiber waviness on the mechanical properties of a low cost CFRP. The simulation results reveal that the fiber waviness has little effect on the macroscopic stiffness, but significantly degrades the uniaxial tensile strength.