Effective Elastic Properties of 3-Phase Particle Reinforced Composites with Randomly Dispersed Elastic Spherical Particles of Different Sizes
  • Yu-Fu Ko1,* and Jiann-Wen Woody Ju2
1Civil Engineering and Construction Engineering Management, California State University, Long Beach, CA 90840-5101, USA
2Civil and Environmental Engineering, University of California, Los Angeles, CA 90095-1593, USA
*Corresponding Author: Yu-Fu Ko. Email: yu-fu.ko@csulb.edu
(This article belongs to this Special Issue:Advances in Computational Mechanics and Optimization
To celebrate the 95th birthday of Professor Karl Stark Pister
Received 22 May 2021; Accepted 05 August 2021 ; Published online 14 September 2021
Higher-order multiscale structures are proposed to predict the effective elastic properties of 3-phase particle reinforced composites by considering the probabilistic spherical particles spatial distribution, the particle interactions, and utilizing homogenization with ensemble volume average approach. The matrix material, spherical particles with radius a1, and spherical particles with radius a2, are denoted as the 0th phase, the 1st phase, and the 2nd phase, respectively. Particularly, the two inhomogeneity phases are different particle sizes and the same elastic material properties. Improved higher-order (in ratio of spherical particle sizes to the distance between the centers of spherical particles) bounds on effective elastic properties of 3-phase particle reinforced proposed Formulation II and Formulation I derive composites. As a special case, i.e., particle size of the 1st phase is the same as that of the 2nd phase, the proposed formulations reduce to 2-phase formulas. Our theoretical predictions demonstrate excellent agreement with selected experimental data. In addition, several numerical examples are presented to demonstrate the competence of the proposed frameworks.
Particle reinforced composites; micromechanics; spherical particle interactions; ensemble volume average; homogenization; probabilistic spatial distribution; higher-order bounds; multiscale