New numerical algorithm for the periodic boundary condition for predicting the coefficients of thermal expansion of composites

In this paper, a new algorithm for the periodic boundary condition used for numerically predicting the coefficients of thermal expansion (CTEs) of different composite systems based on the finite element homogenization method is proposed. The results demonstrate that the proposed algorithm guarantees stress and strain continuities on the opposite surfaces of the representative volume elements (RVEs) for composites with spherical particles and plain woven fabrics but not for composites with cylindrical fibers and three-dimensional four-directional braided yarns. Meanwhile, the proposed algorithm ensures the micro–macro energy balance (Hill's lemma) and the zero macro-stress constraint of the RVEs for all composite systems. Through the comparison with experimental tests and other numerical methods, the proposed algorithm is validated to be capable of accurately predicting the CTEs of composites.