A new approach to a bridging tensor

• Published in: Polymer composites Vol. 36; no. 8; pp. 1417 - 1431
• Main Authors: Wang, Yan-Chao, Huang, Zheng-Ming
• Format: Journal Article
• Language: English
• Published: Newtown Blackwell Publishing Ltd 01.08.2015
• Subjects: Bridging; Fiber composites; Inclusions; Mathematical analysis; Mathematical models; Strength; Stresses; Tensors
• ISSN: 0272-8397; 1548-0569
• DOI: 10.1002/pc.23048

Bridging Model is an efficient micromechanical theory which can be used to predict the effective thermomechanical as well as strength properties of a fiber reinforced composite. The key to the Bridging Model is a bridging tensor, which was obtained on Eshelby's inclusion method [Huang and Zhou, Strength of Fibrous Composites, Vol. 53, Zhejiang University Press, Springer, Hangzhou, (2011)]. A different approach to the closed‐form expressions for the elements of a bridging tensor is presented in this work. The method is based on averaging the stress fields of a single‐fiber inclusion embedded within an infinite matrix subjected to various load conditions. By solving the bridging equations between the averaged stress components in the fiber and those in the matrix, the exact expressions for the bridging tensor elements are obtained. The Bridging Model can be established by neglecting some small quantities in the bridging tensor elements. Effective elastic moduli of a unidirectional (UD) composite are expressed as functions of a bridging tensor. Comparisons of predicted elastic properties of a total number of 18 UD composites on simplified and the exact bridging tensors are made. POLYM. COMPOS., 36:1417–1431, 2015. © 2014 Society of Plastics Engineers