@Article{cmes.2021.017589,
AUTHOR = {Yu-Fu Ko, Jiann-Wen Woody Ju},
TITLE = {Effective Elastic Properties of 3-Phase Particle Reinforced Composites with Randomly Dispersed Elastic Spherical Particles of Different Sizes},
JOURNAL = {Computer Modeling in Engineering \& Sciences},
VOLUME = {129},
YEAR = {2021},
NUMBER = {3},
PAGES = {1305--1328},
URL = {http://www.techscience.com/CMES/v129n3/45690},
ISSN = {1526-1506},
ABSTRACT = {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 a<sub>1</sub>, and spherical particles with radius a<sub>2</sub>, are denoted as the 0<sup>th</sup> phase, the 1<sup>st</sup> phase, and the 2<sup>nd</sup>
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 1<sup>st</sup> phase is the same as that of the 2<sup>nd</sup>
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.},
DOI = {10.32604/cmes.2021.017589}
}