On the surface instability of a highly elastic half-space

1974 ◽  
Vol 4 (4) ◽  
pp. 249-263 ◽  
Author(s):  
S. A. Usmani ◽  
M. F. Beatty
Keyword(s):  
Half Space ◽  
Elastic Half Space ◽  
Surface Instability

Surface Instability and Splitting in Compressed Brittle Elastic Solids Containing Crack Arrays

1982 ◽  
Vol 49 (4) ◽  
pp. 761-767 ◽  
Author(s):  
L. M. Keer ◽  
S. Nemat-Nasser ◽  
A. Oranratnachai
Keyword(s):  
Free Surface ◽  
Half Space ◽  
Special Class ◽  
Compressive Force ◽  
Surface Damage ◽  
Elastic Half Space ◽  
Surface Instability ◽  
Elastic Solids ◽  
Longitudinal Splitting ◽  
Brittle Solids

Surface instability in brittle solids may occur at relatively small values of the inplane compressive force if the solid contains shallow cracks parallel to its free surface. The instability may produce surface damage by spallation. Similarly, the buckling load of a longitudinally compressed strip that contains an array of central cracks is affected to a great extent by the size and the relative spacing of these cracks. The instability in this case may result in longitudinal splitting of the strip. To illustrate these phenomena, the compression of an elastic half space and a layer, each containing an array of coplanar equally spaced cracks, is studied for a special class of hypoelastic materials, and the corresponding weakening due to cracks is analytically estimated.

scholarly journals Surface instability of an elastic half space with material properties varying with depth

2008 ◽  
Vol 56 (3) ◽  
pp. 858-868 ◽  
Author(s):  
Donghee Lee ◽  
N. Triantafyllidis ◽  
J.R. Barber ◽  
M.D. Thouless
Keyword(s):  
Half Space ◽  
Material Properties ◽  
Elastic Half Space ◽  
Surface Instability

scholarly journals Surface instability of elastic half-spaces by using the energy method

2018 ◽  
Vol 474 (2213) ◽  
pp. 20170854 ◽  
Author(s):  
Yi-chao Chen ◽  
Shengyou Yang ◽  
Lewis Wheeler
Keyword(s):  
Eigenvalue Problem ◽  
Half Space ◽  
Elastic Half Space ◽  
Surface Instability ◽  
Second Variation ◽  
Equilibrium Equations ◽  
Stability And Instability ◽  
Complete Set ◽  
Instability Regions ◽  
The Second Variation

Finding the complete set of stability conditions of an elastic half-space has been an open problem ever since Biot (Biot 1963 Appl. Sci. Res. 12 , 168–182 ( doi:10.1007/BF03184638 )) first studied the surface instability of half-spaces by seeking solutions of the incremental equilibrium equations. Towards solving this problem, a method based on the energy stability criterion is developed in the present work. A variational problem of minimizing the elastic energy associated with a half-space is formulated. The second variation condition is derived and is converted to an eigenvalue problem. For a half-space of neo-Hookean materials, the eigenvalue problem is solved, which leads to complete descriptions of stability and instability regions in the deformation space.

The efficiency of application of virtual cross-sections method and hypotheses MELS in problems of wave signal propagation in elastic waveguides with rough surfaces

2016 ◽  
pp. 3564-3575 ◽  
Author(s):  
Ara Sergey Avetisyan
Keyword(s):  
Half Space ◽  
Cross Sections ◽  
Classical Method ◽  
Signal Propagation ◽  
Elastic Half Space ◽  
Layered Systems ◽  
Surface Layers ◽  
Inhomogeneous Surface ◽  
Wave Signal ◽  
The Impact

The efficiency of virtual cross sections method and MELS (Magneto Elastic Layered Systems) hypotheses application is shown on model problem about distribution of wave field in thin surface layers of waveguide when plane wave signal is propagating in it. The impact of surface non-smoothness on characteristics of propagation of high-frequency horizontally polarized wave signal in isotropic elastic half-space is studied. It is shown that the non-smoothness leads to strong distortion of the wave signal over the waveguide thickness and along wave signal propagation direction as well.  Numerical comparative analysis of change in amplitude and phase characteristics of obtained wave fields against roughness of weakly inhomogeneous surface of homogeneous elastic half-space surface is done by classical method and by proposed approach for different kind of non-smoothness.

Guided Surface Waves on an Elastic Half Space

1971 ◽  
Vol 38 (4) ◽  
pp. 899-905 ◽  
Author(s):  
L. B. Freund
Keyword(s):  
Wave Propagation ◽  
Surface Wave ◽  
Surface Waves ◽  
Half Space ◽  
Body Wave ◽  
Three Dimensional ◽  
Elastic Half Space ◽  
Normal Displacement ◽  
Rigid Barrier ◽  
Wave Disturbances

Three-dimensional wave propagation in an elastic half space is considered. The half space is traction free on half its boundary, while the remaining part of the boundary is free of shear traction and is constrained against normal displacement by a smooth, rigid barrier. A time-harmonic surface wave, traveling on the traction free part of the surface, is obliquely incident on the edge of the barrier. The amplitude and the phase of the resulting reflected surface wave are determined by means of Laplace transform methods and the Wiener-Hopf technique. Wave propagation in an elastic half space in contact with two rigid, smooth barriers is then considered. The barriers are arranged so that a strip on the surface of uniform width is traction free, which forms a wave guide for surface waves. Results of the surface wave reflection problem are then used to geometrically construct dispersion relations for the propagation of unattenuated guided surface waves in the guiding structure. The rate of decay of body wave disturbances, localized near the edges of the guide, is discussed.

Sign in / Sign up

Export Citation Format

Share Document