Comparison between mori-tanaka and gorbachev-pobedrya methods in the problem of determinination of the effective properties of composites with piezoelectric spherical inclusions | Mekhanika | kompozitsionnykh | materialov i konstruktsii
> Volume 25 > №1 / 2019 / Pages: 57-75

Comparison between mori-tanaka and gorbachev-pobedrya methods in the problem of determinination of the effective properties of composites with piezoelectric spherical inclusions

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Abstract:

The problem of prediction of the effective characteristics of composite materials with polymeric isotropic matrix filled with piezoactive transversely isotropic ceramic particles is considered. Within the framework of the spherical inclusion model, three methods of averaging are compared. Firstly, the Mori-Tanaka method is used, which allows one to obtain analytical estimates of effective properties based on the Eshelby problem solution for an isolated inclusion. Secondly, the Gorbachev-Pobedrya method is considered, which is based on an integral representation of solutions for problems of deformation of a heterogeneous medium and requires numerical solution of auxiliary problems for determining of the so-called structural functions. The predictions obtained in the framework of these methods are compared with the results of numerical modeling of representative fragments of composites, for which effective characteristics are determined as the ratio of the corresponding averaged values of stress, strain, electric field and electric displacements. As a result of the calculations, it was established that the considered methods may lead to different predictions of the properties of piezocomposites. The greatest difference is realized for piezoelectric constants: up to 150-200% with a volume content of inclusions 30-40%. The highest predictions for the elastic tensile moduli and dielectric constants are obtained by using Gorbachev-Pobedrya method and the lowest – by using Mori-Tanaka method. In opposite, the highest shear moduli are predicted by Mori-Tanaka method, while the smallest ones are followed from the finite element simulation.

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