TY - EJOU
AU - Ko, Yu-Fu
AU - Ju, Jiann-Wen Woody
TI - Effective Elastic Properties of 3-Phase Particle Reinforced Composites with Randomly Dispersed Elastic Spherical Particles of Different Sizes
T2 - Computer Modeling in Engineering \& Sciences
PY - 2021
VL - 129
IS - 3
SN - 1526-1506
AB - 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_{1}, and spherical particles with radius a_{2}, are denoted as the 0^{th} phase, the 1^{st} phase, and the 2^{nd}
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^{st} phase is the same as that of the 2^{nd}
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.
KW - Particle reinforced composites; micromechanics; spherical particle interactions; ensemble volume average; homogenization; probabilistic spatial distribution; higher-order bounds; multiscale
DO - 10.32604/cmes.2021.017589