An analytical micromechanics‐based multiscale model for the analysis of functionally graded nanocomposites

Abstract

An analytical multiscale model is presented in this article for the analysis of functionally graded nanocomposites. The multiscale scheme is composed of a microscale problem whose solution provides the constitutive model for the macroscale problem. For nanoparticle‐reinforced composites, the microscale problem consists of three phases, namely the nanoparticle, the matrix, and an interphase layer between the matrix and the nanoparticle. An analytical micromechanical model based on Green's function is employed to solve the triple‐phase microscale problem. The homogenized properties of the FG nanocomposite are determined by the micromechanical problem and used in the macroscale level, at every macroscopic material point in which the constitutive model is required. As an example, a nanocomposite beam under bending is considered as the macroscale problem which is investigated by classical, first‐order, and third‐order shear deformation theories. The results obtained from the presented method are compared with the relevant data for similar problems using various higher‐order elasticity theories. By comparing the results of higher‐order theories and those obtained by the presented multiscale method, the internal length parameter of the higher‐order theories is correlated to the volume fraction of the interphase layer between the nanoparticle and the matrix.