Periodic boundary condition and its numerical implementation algorithm for the evaluation of effective mechanical properties of the composites with complicated micro-structures

To evaluate the effective mechanical properties of the composites with complicated micro-structures, the RVE based FE homogenization method with the periodic boundary condition is introduced and implemented in this paper, and the emphasis is on the periodic boundary condition and its numerical implementation algorithm. The pre-processing (such as the generation of geometry model and application of periodic boundary condition), FE analysis and post-processing (such as the average of stress and strain and stress contouring of the surface nodes) concerning the evaluation of the effective mechanical properties of the composites with complicated micro-structures are conducted in the FE package ABAQUS through the Python Interface. Numerical results show that the proposed numerical implementation algorithm of the periodic boundary condition guarantees the stress and strain continuities and uniaxial deformation constraint of the RVEs for the composites with complicated micro-structures. Compared with the Halpin-Tsai model and two-step M-T/Voigt mean-field homogenization method, the RVE based FE homogenization method with the periodic boundary condition is verified to accurately predict the effective elastic properties and elasto-plastic responses of the composites with the complicated micro-structures.