Download this article
 Download this article For screen
For printing
Recent Issues

Volume 19
Issue 4, 541–649
Issue 4, 541–572
Issue 3, 303–540
Issue 2, 157–302
Issue 1, 1–156

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 5 issues

Volume 15, 5 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 5 issues

Volume 10, 5 issues

Volume 9, 5 issues

Volume 8, 8 issues

Volume 7, 10 issues

Volume 6, 9 issues

Volume 5, 6 issues

Volume 4, 10 issues

Volume 3, 10 issues

Volume 2, 10 issues

Volume 1, 8 issues

The Journal
About the journal
Ethics and policies
Peer-review process
 
Submission guidelines
Submission form
Editorial board
 
Subscriptions
 
ISSN (electronic): 1559-3959
ISSN (print): 1559-3959
 
Author index
To appear
 
Other MSP journals
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

Vol. 18 (2023), No. 4, 567–592
DOI: 10.2140/jomms.2023.18.567
Abstract

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.

Keywords
half-space, micromechanics, strain gradient theory, microinertia, wave reflection, Rayleigh waves, reflected surface waves
Milestones
Received: 15 December 2022
Revised: 4 April 2023
Accepted: 19 April 2023
Published: 27 July 2023
Authors
Th. Zisis
Department of Mechanics
School of Applied Mathematics and Physical Sciences
National Technical University of Athens (NTUA)
Zographou
Greece
X. Kuci
Department of Mechanics
School of Applied Mathematics and Physical Sciences
National Technical University of Athens (NTUA)
Zographou
Greece
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