The Elastic Moduli of the Random Ellipse Inclusion Model With Spring-Layer Imperfect Interfaces

Abstract This work presents new formulas for determining the elastic moduli of a random ellipse-inclusion model with spring-layer imperfect interfaces in a two-dimensional space. The surface of the ellipse inclusion, with an infinitely thin coating, has a significant influence on the macroscopic elastic moduli of the composite materials, one of those cases is called spring-layer imperfect interfaces. Using the polarization approximation for the coated-ellipse inclusion model, we have constructed new solutions to determine the elastic moduli of the ellipse inclusion with spring-layer imperfect interfaces. From this, solutions can be obtained to determine the macroscopic elastic moduli of the random ellipse-inclusion model with spring-layer imperfect interfaces in the matrix, using polarization approximation (PA), differential approximation (DA), and fast Fourier transform (FFT). Comparative results demonstrate the effectiveness of these methods.