A reconciliation of dynamic crack velocity and Rayleigh wave speed in isotropic brittle solids

The elastodynamic image forces on edge and screw dislocations in the presence of a planar-free surface are derived. The explicit form of the elastodynamic fields of an injected, quiescent screw dislocation are also derived. The resulting image forces are affected by retardation effects: the dislocations experience no image force for a period of time defined by the arrival and reflection at the free surface of the dislocation fields. For the case of injected, stationary dislocations, it is shown that the elastodynamic image force tends asymptotically to the elastotatic prediction. For the case of injected, moving dislocations, it is shown that the elastodynamic image force on both the edge and the screw dislocations is magnified by inertial effects, and becomes increasingly divergent with time; this additional effect, missing in the elastostatic description, is shown to be substantial even for slow moving dislocations. Finally, it is shown that the elastodynamic image force of an edge dislocation moving towards the surface at the Rayleigh wave speed becomes repulsive, rather than attractive; this is suggestive of instabilities at the core of the dislocation, and likely resonances with the free surface.

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Impedance of Strip-Traveling Waves on an Elastic Half Space: Asymptotic Solution

Journal of Applied Mechanics ◽

10.1115/1.3423302 ◽

1974 ◽

Vol 41 (2) ◽

pp. 412-416

Author(s):

S. H. Crandall ◽

A. K. Nigam

Keyword(s):

Asymptotic Solution ◽

Rayleigh Wave ◽

Half Space ◽

Traveling Wave ◽

Load Distribution ◽

Wave Speed ◽

Elastic Half Space ◽

Surface Load ◽

Shear Wave Speed ◽

Rayleigh Wave Speed

The dynamic normal-load distribution across a strip that is required to maintain a plane progressive wave along its length is studied for the case where the strip is of infinite length and lies on the surface of a homogeneous isotropic elastic half space. This configuration is proposed as a preliminary idealized model for analyzing the dynamic interaction between soils and flexible foundations. The surface load distribution across the strip and the motion of the strip are related by a pair of dual integral equations. An asymptotic solution is obtained for the limiting case of small wavelength. The nature of this solution depends importantly on the propagation velocity of the strip-traveling wave in comparison with the Rayleigh wave speed, the shear wave speed and the dilatational wave speed. When the strip-traveling wave propagates faster than the Rayleigh wave speed, a pattern of trailing Rayleigh waves is shed from the strip. The limiting amplitude of the trailing waves is provided by the asymptotic solution.

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Mechanics of dynamic debonding

Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences ◽

10.1098/rspa.1991.0070 ◽

1991 ◽

Vol 433 (1889) ◽

pp. 679-697 ◽

Cited By ~ 105

Keyword(s):

Steady State ◽

Stress Intensity ◽

Rayleigh Wave ◽

Wave Speed ◽

Dynamic Stress ◽

Dynamic Stress Intensity Factor ◽

Crack Tip ◽

Interface Fracture ◽

Dynamic Stress Intensity Factors ◽

Rayleigh Wave Speed

Singular fields around a crack running dynamically along the interface between two anisotropic substrates are examined. Emphasis is placed on extending an established frame work for interface fracture mechanics to include rapidly applied loads, fast crack propagation and strain rate dependent material response. For a crack running at non-uniform speed, the crack tip behaviour is governed by an instantaneous steady-state, two-dimensional singularity. This simplifies the problem, rendering the Stroh techniques applicable. In general, the singularity oscillates, similar to quasi-static cracks. The oscillation index is infinite when the crack runs at the Rayleigh wave speed of the more compliant material, suggesting a large contact zone may exist behind the crack tip at high speeds. In contrast to a crack in homogeneous materials, an interface crack has a finite energy factor at the lower Rayleigh wave speed. Singular fields are presented for isotropic bimaterials, so are the key quantities for orthotropic bimaterials. Implications on crack branching and substrate cracking are discussed. Dynamic stress intensity factors for anisotropic bimaterials are solved for several basic steady state configurations, including the Yoffe, Gol’dshtein and Dugdale problems. Under time-independent loading, the dynamic stress intensity factor can be factorized into its equilibrium counterpart and the universal functions of crack speed.

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In vivo measurement of shear modulus of the human cornea using optical coherence elastography

Scientific Reports ◽

10.1038/s41598-020-74383-4 ◽

2020 ◽

Vol 10 (1) ◽

Author(s):

Antoine Ramier ◽

Amira M. Eltony ◽

YiTong Chen ◽

Fatima Clouser ◽

Judith S. Birkenfeld ◽

...

Keyword(s):

Shear Modulus ◽

Rayleigh Wave ◽

Wave Speed ◽

Critical Role ◽

Shear Stiffness ◽

Human Cornea ◽

Optical Coherence ◽

In Vivo Measurement ◽

Rayleigh Wave Speed

Abstract Corneal stiffness plays a critical role in shaping the cornea with respect to intraocular pressure and physical interventions. However, it remains difficult to measure the mechanical properties noninvasively. Here, we report the first measurement of shear modulus in human corneas in vivo using optical coherence elastography (OCE) based on surface elastic waves. In a pilot study of 12 healthy subjects aged between 25 and 67, the Rayleigh-wave speed was 7.86 ± 0.75 m/s, corresponding to a shear modulus of 72 ± 14 kPa. Our data reveal two unexpected trends: no correlation was found between the wave speed and IOP between 13–18 mmHg, and shear modulus decreases with age (− 0.32 ± 0.17 m/s per decade). We propose that shear stiffness is governed by the interfibrillar matrix, whereas tensile strength is dominated by collagen fibrils. Rayleigh-wave OCE may prove useful for clinical diagnosis, refractive surgeries, and treatment monitoring.

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A note on the formula for the Rayleigh wave speed

Wave Motion ◽

10.1016/j.wavemoti.2005.10.002 ◽

2006 ◽

Vol 43 (3) ◽

pp. 272-276 ◽

Cited By ~ 32

Author(s):

M. Rahman ◽

T. Michelitsch

Keyword(s):

Rayleigh Wave ◽

Wave Speed ◽

Rayleigh Wave Speed

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On Propagation of Rayleigh Type Surface Wave in Five Different Theories of Thermoelasticity

International Journal of Applied Mechanics and Engineering ◽

10.2478/ijame-2019-0041 ◽

2019 ◽

Vol 24 (3) ◽

pp. 661-673 ◽

Cited By ~ 1

Author(s):

B. Singh ◽

S. Verma

Keyword(s):

Relaxation Time ◽

Surface Wave ◽

Rayleigh Wave ◽

Half Space ◽

Wave Speed ◽

Thermal Relaxation ◽

Generalized Thermoelasticity ◽

Governing Equations ◽

Particular Solutions ◽

Rayleigh Wave Speed

Abstract The governing equations for a homogeneous and isotropic thermoelastic medium are formulated in the context of coupled thermoelasticity, Lord and Shulman theory of generalized thermoelasticity with one relaxation time, Green and Lindsay theory of generalized thermoelasticity with two relaxation times, Green and Nagdhi theory of thermoelasticity without energy dissipation and Chandrasekharaiah and Tzou theory of thermoelasticity. These governing equations are solved to obtain general surface wave solutions. The particular solutions in a half-space are obtained with the help of appropriate radiation conditions. The two types of boundaries at athe surface of a half-space are considered namely, the stress free thermally insulated boundary and stress free isothermal boundary. The particular solutions obtained in a half-space satisfy the relevant boundary conditions at the free surface of the half-space and a frequency equation for the Rayleigh wave speed is obtained for both thermally insulated and isothermal cases. The non-dimensional Rayleigh wave speed is computed for aluminium metal to observe the effects of frequency, thermal relaxation time and different theories of thermoelasticity.

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