Bounds of the effective elastic moduli of nanoparticle-reinforced composites based on composite sphere assemblage and interface stress model - Tang, Z.; Ye, W. (Archives of Mechanics, 2022)
Three different approaches are formulated to obtain the bounds of the effective elastic moduli of nanoparticle-reinforced composites based on the CSA and the interface stress model. It is found that the effective bulk modulus can be obtained by all three different approaches but the effective shear modulus can be obtained only by the energy approach. The bounds of the effective bulk modulus coincide and depend only on the interface bulk modulus, while those of the effective shear modulus are distinct and depend on two interface elastic constants. Furthermore, limit analysis discloses that the bounds of the effective bulk modulus of nanoparticles coincide but deviate from the bulk modulus of particle in the classical case, and the bounds of the effective shear modulus are distinct in contrast to the effective bulk modulus of nanoparticles or both effective moduli of conventional composites.