Mathematical modeling of the structure-sensitive composite elastic properties

Results of mathematical simulation of the elastic properties of an isotropic matrix composite reinforced with spherical inclusions are presented. As the spherical inclusions, ball nanoclusters composed of randomly oriented single-wall carbon nanotubes (SWCNT) are taken. Two approaches are used: numerical simulation (using the ANSYS software suite together with a newly developed software module) and analytical treatment using the self-consistent method and the dual formulation of the elasticity problem in a non-heterogeneous solid body. The numerical simulation is carried out in the context of a composite with a reinforcement pattern similar to the cubic lattice. In this formulation, two periodic lattice alternatives are considered: a cube with 1/8 of a sphere in each corner, and a cube with a sphere in its center. Comparison is made between the results of numerical simulation and those obtained analytically. The results make it possible to predict the elastic properties of advanced materials such as a composite reinforced with spherical inclusions.