Analytical effective elastic properties of particulate composites with soft interfaces around anisotropic particles

Understanding the effects of interfacial properties on effective elastic properties is of great importance in materials science and engineering. In this work, we propose a theoretical framework to predict the effective moduli of three-phase heterogeneous particulate composites containing spheroidal particles, soft interfaces, and a homogeneous matrix. We first derive the effective moduli of two-phase representative volume elements (RVEs) with matrix and spheroidal inclusions using the variational principle. Subsequently, an analytical model considering the volume fraction of soft interfaces around spheroidal particles is presented. The effective moduli of such three-phase particulate composites are eventually derived by the generalized self-consistent scheme. These theoretical schemes are compared with experimental studies, numerical simulations, and theoretical approximations reported in the literature to verify their validity. We further investigate the dependence of the effective elastic modulus on the interfacial properties and the geometric characteristics of anisotropic particles based on the proposed theoretical framework. Results show that the interfacial volume fraction and the effective elastic modulus of particulate composites are strongly dependent on the aspect ratio, geometric size factor, volume fraction, and particle size distribution of ellipsoidal particles.