Anti-plane shear waves in a fibre-reinforced composite with a non-linear imperfect interface |
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| Affiliation: | 1. Department of Structural Mechanics and Strength of Materials, Prydniprovska State Academy of Civil Engineering and Architecture, Ukraine;2. School of Computing and Mathematics, Keele University, UK;1. Dipartimento di Fisica, Università di Parma, Viale Usberti 7/A, I-43100 Parma, Italy;2. Dipartimento di Fisica, Politecnico di Milano, Piazza Leonardo da Vinci 32, I-20133 Milano, Italy;1. Department of Hydraulics and Ocean Engineering, National Cheng Kung University, Tainan, Taiwan, ROC;2. Fifth River Management Office, Water Resources Agency, Chiayi, Taiwan, ROC |
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| 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. |
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| Keywords: | Non-linear wave Solitary wave Composite material Imperfect bonding Asymptotic homogenisation |
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