This paper presents the semi-analytical solution for the transverse local fields and overall transverse properties of composite materials with aligned multiple cylindrical nanofibers. The interface between each fiber and the matrix is treated as a material surface described by the Steigmann–Ogden model, which accounts for the effects of surface tension as well as for membrane and bending stiffness of the surface. Assuming a plane strain setting, the problem is formulated in the transverse plane as an infinite elastic matrix with multiple circular inhomogeneities subjected to a uniform far-field load. The expressions for all elastic fields in the composite system are obtained analytically in the form of infinite series expressions. The Maxwell methodology is used to obtain the overall transverse elastic properties. The goal of this work is twofold: (a) to study the influence of the interactions between the inhomogeneities on the local fields and overall transverse properties of the composite system, and (b) to reveal the connection of the Steigmann–Ogden model (with zero surface tension) to a specific uniform interphase layer model. The results presented in this paper demonstrate that for fiber composite materials with medium to high volume fractions, the influence of the interactions can be significant.
Bibliographical noteFunding Information:
This research was performed at the Department of Civil, Environmental, and Geo- Engineering of the University of Minnesota, where the first author (Zhilin Han) has been working as part of a joint Ph.D. training program. He gratefully acknowledges the support of the China Scholarship Council (CSC, 201706690019) that made this training possible. The second author (Sofia Mogilevskaya) gratefully acknowledges the support provided by the Theodore W. Bennett Chair, University of Minnesota. The third author (Dominik Schillinger) gratefully acknowledges support from the National Science Foundation through the NSF CAREER Award No.1651577 and the grant CISE-156599.
- Circular inhomogeneities
- Effective transverse properties
- Steigmann–Ogden model
- Surface effects