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Anti-plane shear waves in a fibre-reinforced composite with a non-linear imperfect interface

Danishevs׳kyy, Vladyslav V.; Kaplunov, Julius D.; Rogerson, Graham A.

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Authors

Vladyslav V. Danishevs׳kyy

Graham A. Rogerson



Abstract

The propagation of non-linear elastic anti-plane shear waves in a unidirectional fibre-reinforced composite material is studied. A model of structural non-linearity is considered, for which the non-linear behaviour of the composite solid is caused by imperfect bonding at the “fibre–matrix” interface. A macroscopic wave equation accounting for the effects of non-linearity and dispersion is derived using the higher-order asymptotic homogenisation method. Explicit analytical solutions for stationary non-linear strain waves are obtained. This type of non-linearity has a crucial influence on the wave propagation mode: for soft non-linearity, localised shock (kink) waves are developed, while for hard non-linearity localised bell-shaped waves appear. Numerical results are presented and the areas of practical applicability of linear and non-linear, long- and short-wave approaches are discussed.

Journal Article Type Article
Acceptance Date Dec 21, 2014
Online Publication Date Jan 8, 2015
Publication Date 2015-11
Publicly Available Date Mar 28, 2024
Journal International Journal of Non-Linear Mechanics
Print ISSN 0020-7462
Publisher Elsevier
Peer Reviewed Peer Reviewed
Volume 76
Pages 223 -232
DOI https://doi.org/10.1016/j.ijnonlinmec.2014.12.009
Keywords non-linear wave, solitary wave, composite material, imperfect bonding, asymptotic homogenisation
Publisher URL http://dx.doi.org/10.1016/j.ijnonlinmec.2014.12.009

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