Equivalent inclusions in micromechanics with interface energy effect

doi:10.1007/s10483-017-2276-9

Abstract

Abstract:

In order to apply classical micromechanics in predicting the effective properties of nanocomposites incorporating interface energy, a concept of equivalent inclusion (EI) is usually adopted. The properties of EI are obtained by embedding a single inclusion with the interface into an infinite matrix. However, whether such an EI is universal for different micromechanics-based methods is rarely discussed in the literature. In this paper, the interface energy theory is used to study the applicability of the above mentioned EI. It is found that some elastic properties of the EI are related only to the properties of the inclusion and the interface, whereas others are also related to the properties of the matrix. The former properties of the EI can be applied to both the classical Mori-Tanaka method (MTM) and the generalized self-consistent method (GSCM). However, the latter can be applied only to the MTM. Two kinds of new EIs are proposed for the GSCM and used to estimate the effective mechanical properties of nanocomposites.

Key words: gravitation field, Hamilton equation, perturbation, canonical transformation, Mori-Tanaka method (MTM), equivalent inclusion (EI), interface effect, generalized self-consistent method (GSCM)

2010 MSC Number:

74A40

Zhenguo ZHANG, Yongqiang CHEN, Zhuping HUANG. Equivalent inclusions in micromechanics with interface energy effect. Applied Mathematics and Mechanics (English Edition), 2017, 38(11): 1497-1516.

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