THE ELASTIC MODULI OF THE THREE-PHASE COMPOSITES IN 3D WITH IMPERFECT INTERFACES

Elastic moduli of a sphere with imperfect interfaces can be accurately determined based on the coated spherical assemblage model of Hashin–Shtrikman (HS). From there, we can develop some solutions with explicit algebraic expressions to determine the elastic moduli of three-phase materials with imperfect interfaces in 3D, where two different sphere inclusions with imperfect interfaces are randomly distributed in the matrix phase. The polarization approximation (PA) and differential approximation (DA) are also developed to construct estimating the effective moduli of the three-phase composite with imperfect interfaces. The results of the PA method will be compared with the DA results and HS bounds with different variable material cases to show the effectiveness of the applied methods.