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Wave reflection and
Rayleigh waves in the context of the complete Toupin–Mindlin
theory of strain gradient elasticity
Th. Zisis, X. Kuci and H.G. Georgiadis |
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Vol. 18 (2023), No. 4, 567–592
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DOI: 10.2140/jomms.2023.18.567
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Abstract |
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The present work studies the propagation and reflection of plane waves in an elastic 2D half-space. The material microstructure is taken into account assuming the validity of the complete Toupin–Mindlin theory of isotropic gradient elasticity. This theory involves five additional microstructural material constants besides the two standard Lamé constants of elasticity. Our study builds upon the earlier work of Gourgiotis et al. (2013), which considered a simplified version of the Toupin–Mindlin theory with only one microstructural constant, in wave reflection. Our aim here is to consider the most general material response in the isotropic setting of the strain gradient theory, providing, thus, more general results as compared with those of the earlier work. More specifically, we study the effect of the gradient parameters upon the amplitudes, reflection angles and phase shift of the reflected waves, which proved to be four in the context of gradient elasticity (i.e., two waves propagating in the material volume and two surface waves with exponential decay from the surface), due to an incident either dilatational or distortional wave at the free surface of a 2D half-space. In addition, special emphasis is given here in the Rayleigh waves arising along the surface of the half-space. |
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Keywords
half-space, micromechanics, strain gradient theory,
microinertia, wave reflection, Rayleigh waves, reflected
surface waves
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Milestones
Received: 15 December 2022
Revised: 4 April 2023
Accepted: 19 April 2023
Published: 27 July 2023
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Authors |
| Th. Zisis | |
| Department of Mechanics School of Applied Mathematics and Physical Sciences National Technical University of Athens (NTUA) Zographou Greece |
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| X. Kuci | |
| Department of Mechanics School of Applied Mathematics and Physical Sciences National Technical University of Athens (NTUA) Zographou Greece |
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| H.G. Georgiadis | |
| Department of Mechanics School of Applied Mathematics and Physical Sciences National Technical University of Athens (NTUA) Zographou Greece |
Office of Theoretical and Applied
Mechanics Academy of Athens Athens Greece |
| © 2023 MSP (Mathematical Sciences Publishers). |
