Open Access
ARTICLE
Effective Elastic Properties of 3-Phase Particle Reinforced Composites with Randomly Dispersed Elastic Spherical Particles of Different Sizes
Yu-Fu Ko1,* , 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:
(This article belongs to this Special Issue: Advances in Computational Mechanics and Optimization
To celebrate the 95th birthday of Professor Karl Stark Pister)
Computer Modeling in Engineering & Sciences 2021, 129(3), 1305-1328. https://doi.org/10.32604/cmes.2021.017589
Received 22 May 2021; Accepted 05 August 2021; Issue published 25 November 2021
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
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.
Keywords
Cite This Article
Ko, Y., Ju, J. W. (2021). Effective Elastic Properties of 3-Phase Particle Reinforced Composites
with Randomly Dispersed Elastic Spherical Particles of
Different Sizes.
CMES-Computer Modeling in Engineering & Sciences, 129(3), 1305-1328