Solutions for elastic moduli of three-phase composite with random distribution of coated-ellipse inclusions

Some solutions in this work are developed to estimate the elastic moduli of three-phase isotropic composite with random coated-ellipse inclusion in the matrix. Solutions to the macro-elastic moduli of materials in two-dimensional space using approximation and numerical methods including equivalent-inclusion (EI), polarization approximation (PA), differential approximations (DA), and fast Fourier transformation (FFT). In which, there is a combination of those methods to give approximations such as EI-PA, EI-DA, FFT-EI. The construction algebraic expressions can be directly applied to the random coated-ellipse model, in special cases it can be used for circular aggregate particles. The numerical solutions using FFT analysis will be compared with EI-PA, EI-DA, and Hashin–Shtrikman’s bounds. From this, it is possible to indicate the best solution that engineers can use to determine the elastic modulus of the coated-ellipse model.