A three-dimensional semi-analytical finite element method (SAFEM-3D) is implemented in this work to calculate the effective properties of periodic elastic-reinforced nanocomposites. Different inclusions are also considered, such as discs, ellipsoidals, spheres, carbon nanotubes (CNT) and carbon nanowires (CNW). The nanocomposites are assumed to have isotropic or transversely isotropic inclusions embedded in an isotropic matrix. The SAFEM-3D approach is developed by combining the two-scale asymptotic homogenization method (AHM) and the finite element method (FEM). Statements regarding the homogenized local problems on the periodic cell and analytical expressions of the effective elastic coefficients are provided. Homogenized local problems are transformed into boundary problems over one-eighth of the cell. The FEM is implemented based on the principle of the minimum potential energy. The three-dimensional region (periodic cell) is divided into a finite number of 10-node tetrahedral elements. In addition, the effect of the inclusion’s geometrical shape, volume fraction and length on the effective elastic properties of the composite with aligned or random distributions is studied. Numerical computations are developed and comparisons with other theoretical results are reported. A comparison with experimental values for CNW nanocomposites is also provided, and good agreement is obtained.
Effective elastic properties of transversely isotropic materials with concave pores