Macroscopic Elastic Moduli of Randomly Ellipse Inclusions with Surface-Stress Imperfect Interfaces
Abstract
New solutions in this work are developed to estimate the elastic moduli of random ellipse inclusions in the matrix with surface-stress (stiff) imperfect interfaces in a two-dimensional space. The random ellipse inclusion is an extension of the circular inclusion model. The macro-elastic moduli of materials was calculated using approximation and numerical methods including differential approximations (DA), Mori-Tanaka (MTA), and Fast Fourier transformation (FFT) methods. Calculating procedures are developed to derive the results for the ellipse inclusion with surface-stress imperfect interfaces. Based on equivalent inclusion of the ellipse inclusion with surface-stress imperfect interfaces to give explicit algebraic estimates of the elastic moduli. The numerical solutions using FFT analysis will be compared with MTA and DA. From this study, it is possible to obtain the best solution that engineers can use to determine the elastic moduli of the random ellipse inclusion model with surface-stress imperfect interfaces.