A topology optimization approach used to assess the effect of the matrix impregnation on the effective elastic properties of a unidirectional carbon nanotube bundle composite

Abstract

The present work aims to find the optimum distribution of a certain amount of matrix around a pack of fibers, which is the representative volume element of a bundle of carbon nanotubes, in order to maximize a linear combination of the effective properties of the media. The homogenization by asymptotic expansion is used to find the effective properties and a topology optimization procedure is conducted to find the optimal material distribution. In the adopted Representative Volume Element (RVE), the fibers are fixed in the domain, and the optimization is performed only at matrix, whose properties are parameterized by the Solid Isotropic Material with Penalization (SIMP) method. Three distinct linear combinations of the components of the fourth order stiffness tensor are chosen, as well as three distinct admissible volume fractions for the matrix. Qualitative results, showing the topologies of the RVEs, and numerical results are presented. The qualitative results are shown by both the optimal material distributions in the RVEs and the convergence plots of the objective functions. The numerical results are highlighted by both the optimal numerical solutions and the full fourth order elasticity tensor. The results show which regions of the RVE play a significant role for the effective properties of the composite and may be used for a careful manufacturing process guide.