Love wave in a classical linear elastic half-space covered by a surface layer described by the couple stress theory

This paper presents the complete elastic field of a half space under axisymmetric surface loads by taking the influence of material microstructures into account. A well-known couple stress theory is adopted to handle such small scale effect and the resulting governing equations are solved by the method of Hankel integral transform. A selected numerical quadrature is then applied to efficiently evaluate all involved integrals. A set of results is also reported to not only confirm the validity of established solutions but also demonstrate the capability of the selected mathematical model to simulate the size-dependent characteristic of the predicted response when the external and internal length scales are comparable.

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Rayleigh wave equations with couple stress: modeling and dispersion characteristic

Geophysics ◽

10.1190/geo2020-0890.1 ◽

2021 ◽

pp. 1-64

Author(s):

Yanqi Wu ◽

Jianwei Ma

Keyword(s):

Wave Propagation ◽

Half Space ◽

Scale Effect ◽

Linear Elasticity ◽

Rayleigh Waves ◽

Couple Stress ◽

Characteristic Length ◽

Couple Stress Theory ◽

Stress Theory ◽

Homogeneous Half Space

In elastostatics, the scale effect is a phenomenon in which the elastic parameters of a medium vary with specimen size when the specimen is sufficiently small. Linear elasticity cannot explain the scale effect because it assumes that the medium is a continuum and does not consider microscopic rotational interactions within the medium. In elastodynamics, wave propagation equations are usually based on linear elasticity. Thus, nonlinear elasticity must be introduced to study the scale effect on wave propagation. In this work, we introduce one of the generalized continuum theoriescouple stress theoryinto solid earth geophysics to build a more practical model of underground medium. The first-order velocity-stress wave equation is derived to simulate the propagation of Rayleigh waves. Body and Rayleigh waves are compared using elastic theory and couple stress theory in homogeneous half- space and layered space. The results show that couple stress causes the dispersion of surface waves and shear waves even in homogeneous half-space. The effect is enhanced by increasing the source frequency and characteristic length, despite its insufficiently clear physical meaning. Rayleigh waves are more sensitive to couple stress effect than body waves. Based on the phase-shifting method, it was determined that Rayleigh waves exhibit different dispersion characteristics in couple stress theory than in conventional elastic theory. For the fundamental mode, the dispersion curves tend to move to a lower frequency with an increase in characteristic length l. For the higher modes, the dispersion curves energy is stronger with a greater characteristic length l.

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Effects of microstructure and liquid loading on velocity dispersion of leaky Rayleigh waves at liquid–solid interface

Canadian Journal of Physics ◽

10.1139/cjp-2016-0343 ◽

2018 ◽

Vol 96 (1) ◽

pp. 11-17 ◽

Cited By ~ 2

Author(s):

Vikas Sharma ◽

Satish Kumar

Keyword(s):

Phase Velocity ◽

Half Space ◽

Liquid Layer ◽

Rayleigh Waves ◽

Couple Stress ◽

Characteristic Length ◽

Couple Stress Theory ◽

Liquid Loading ◽

Stress Theory ◽

Leaky Rayleigh Waves

Inner atomic interactions at the micro scale produce new effects that cannot be accounted for by the classical theory of elasticity. To study the impact of the microstructures of the material, generalized continuum theories involving additional microstructural material parameters are preferred. One such microcontinuum theory involving an additional material parameter called internal characteristic length (l) is a consistent couple stress theory. The study of leaky Rayleigh waves generated at the interface of solid half-space with liquid layer is of great importance for quick scanning and imaging of large civil engineering structures. The problem of leaky Rayleigh waves propagating in elastic half-space under liquid loading has been studied in the context of this consistent couple stress theory. Dispersion equations are obtained by developing the mathematical model of the problem. Phase velocity of leaky Rayleigh waves is studied for three different values of characteristic length parameter (l), which is of the order of internal cell size of the material. Effects of thickness of liquid layer are also studied on the phase velocity profiles.

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Effect of boundaries on wave propagation in media with microstructure: II. Surface waves in a half-space

Bulletin of the Seismological Society of America ◽

10.1785/bssa0640020387 ◽

1974 ◽

Vol 64 (2) ◽

pp. 387-392

Author(s):

M. Farshad ◽

G. Ahmadi

Keyword(s):

Wave Propagation ◽

Surface Wave ◽

Surface Waves ◽

Half Space ◽

Couple Stress ◽

Couple Stress Theory ◽

Classical Elasticity ◽

Stress Theory ◽

Material Parameters ◽

Surface Wave Propagation

abstract The surface-wave propagation in a half-space according to couple-stress theory is studied herein. Dispersion curves as well as displacement variations with the depth coordinate are obtained for a range of material parameters. Comparison is made with the classical elasticity predictions upon which certain conclusions are reached.

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Physical and Mathematical Representations of Couple Stress Effects on Micro/Nanosolids

International Journal of Applied Mechanics ◽

10.1142/s1758825115400128 ◽

2015 ◽

Vol 07 (01) ◽

pp. 1550012 ◽

Cited By ~ 14

Author(s):

M. Shaat

Keyword(s):

Couple Stress ◽

Couple Stress Theory ◽

Elastic Materials ◽

Additional Material ◽

Stress Theory ◽

Couple Stresses ◽

Linear Elastic ◽

Stress Effects ◽

Points Of View ◽

Alternative Theories

In the present paper, for linear elastic materials, effects of couple stresses on micro/nanosolids are physically discussed and mathematically represented in the context of the classical, the modified and the consistent couple–stress theories. Then, an evaluation is provided showing the validity and the limit of applicability of each one of these theories. At first, the possible couple stress effects on mechanics of particles and on continuum mechanics are represented. Then, a reasoning comparison with examples is performed to discuss and evaluate the way that each one of these theories represents the couple stress effects. In the context of the classical couple–stress theory, two higher-order material constants are introduced in addition to the conventional ones to capture the microstructure rigid rotation effects. Recently, two alternative theories, the modified couple–stress and the consistent couple–stress theories, with only one additional material constant are introduced with contradictory points of view. Authors of these two alternative theories gave apparently strong motivations for their opposed points of view. Therefore, through the present paper, it will be convenient to analyze the essential points of view based on which these alternative theories are proposed since they lead to exactly opposed conclusions. Thus their essential points of view are discussed and evaluated showing their consistency with the fundamental concepts of the couple stress effects. It has been shown that the scientific bases of these two alternative theories are not consistent with the representation of the couple–stress effects on micro/nanocontinua. Based on discussions and results through the paper, both the modified theory and the consistent theory represent, only, simplifications for the classical couple–stress theory but they did not able to well represent the possible effects of couple stresses and they are limited for only two categories of linear elastic materials problems. This demolishes the scientific points of view based on which the two theories are proposed.

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