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.

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.

Citation

Danishevs׳kyy, V. V., Kaplunov, J. D., & Rogerson, G. A. (2015). Anti-plane shear waves in a fibre-reinforced composite with a non-linear imperfect interface. International Journal of Non-Linear Mechanics, 76, 223 -232. https://doi.org/10.1016/j.ijnonlinmec.2014.12.009

• Journal Article Type: Article
• Acceptance Date: Dec 21, 2014
• Online Publication Date: Jan 8, 2015
• Publication Date: 2015-11
• 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