Colloid and Polymer Science

, Volume 297, Issue 4, pp 529–543 | Cite as

A re-formulation of the Mori–Tanaka method for predicting material properties of fiber-reinforced polymers/composites

  • Jing Pan
  • Lichun BianEmail author
Original Contribution


In this investigation, a re-formulation has been developed to investigate the effect of fiber aspect ratio on the effective elastic moduli of fiber-reinforced polymers/composites. The matrix and inclusions are considered as isotropic materials. The five independent elastic constants are derived based on a modified Mori–Tanaka theory. The relationship between composite elastic constants and inclusion aspect ratio is also established. Three types of composites containing unidirectional aligned fiber and two-dimensional and three-dimensional random orientated inclusions are explicitly analyzed. Moreover, three extreme cases involving long fibers, spheres, and thin discs are taken into account. It is found that the longitudinal elastic properties are very sensitive to fiber-like inclusions, whereas the transverse elastic properties are closely related to disc-like inclusions.


Fiber Elastic constants Aspect ratio Composite materials 



This study was funded by the Science Research Foundation of Hebei Advanced Institutes (ZD2017075) and Graduate Innovation Research Assistant Support Project of Yanshan University (CXZS201708).

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflicts of interest.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Key Laboratory of Mechanical Reliability for Heavy Equipments and Large Structures of Hebei ProvinceYanshan UniversityQinhuangdaoPeople’s Republic of China

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