Elastic Displacement and Stress Fields Induced by a Dislocation of Polygonal Shape in an Anisotropic Elastic Half-Space

2012 ◽  
Vol 79 (2) ◽  
Author(s):  
H. J. Chu ◽  
E. Pan ◽  
J. Wang ◽  
I. J. Beyerlein

The elastic displacement and stress fields due to a polygonal dislocation within an anisotropic homogeneous half-space are studied in this paper. Simple line integrals from 0 to π for the elastic fields are derived by applying the point-force Green’s functions in the corresponding half-space. Notably, the geometry of the polygonal dislocation is included entirely in the integrand easing integration for any arbitrarily shaped dislocation. We apply the proposed method to a hexagonal shaped dislocation loop with Burgers vector along [1¯ 1 0] lying on the crystallographic (1 1 1) slip plane within a half-space of a copper crystal. It is demonstrated numerically that the displacement jump condition on the dislocation loop surface and the traction-free condition on the surface of the half-space are both satisfied. On the free surface of the half-space, it is shown that the distributions of the hydrostatic stress (σ11 + σ22)/2 and pseudohydrostatic displacement (u1 + u2)/2 are both anti-symmetric, while the biaxial stress (σ11 − σ22)/2 and pseudobiaxial displacement (u1 − u2)/2 are both symmetric.

2015 ◽  
Vol 203 (2) ◽  
pp. 1193-1206 ◽  
Author(s):  
E. Pan ◽  
A. Molavi Tabrizi ◽  
A. Sangghaleh ◽  
W. A. Griffith

Author(s):  
G. K. ZAKIR’YANOVA ◽  
◽  
L. A. ALEXEYEVA ◽  

The first boundary value problem of the theory of elasticity for an anisotropic elastic half-space is solved when a transport load moves along its surface. The subsonic Raleigh case is considered, when the velocity of motion is less than the velocity of propagation of bulk and surface elastic waves. The Green’s tensor of the transport boundary value problem is constructed and on its basis the solution of boundary value problems for a wide class of distributed traffic loads is given. To solve the problem, the methods of tensor and linear algebra, integral Fourier transform, and operator method for solving systems of differential equations were used. The obtained solution makes it possible to investigate the dynamics of the rock mass for a wide class of transport loads, in a wide range of velocities, both low velocities and high velocities, and to evaluate the strength properties of the rock mass under the influence of road transport. In particular, determine the permissible velocities of its movement and carrying capacity. In addition, a investigation on its basis of the movement of the day surface along the route will make it possible to establish criteria for the seismic resistance of ground structures and the permissible distances of their location from the route.


Author(s):  
J. Kaplunov ◽  
D. Prikazchikov ◽  
L. Sultanova

Elastodynamics of a half-space coated by a thin soft layer with a clamped upper face is considered. The focus is on the analysis of localized waves that do not exist on a clamped homogeneous half-space. Non-traditional effective boundary conditions along the substrate surface incorporating the effect of the coating are derived using a long-wave high-frequency procedure. The derived conditions are implemented within the framework of the earlier developed specialized formulation for surface waves, resulting in a perturbation of the shortened equation of surface motion in the form of an integral or pseudo-differential operator. Non-uniform asymptotic formula for the speeds of the sought for Rayleigh-type waves, failing near zero frequency and the thickness resonances of a layer with both clamped faces, follow from the aforementioned perturbed equation. Asymptotic results are compared with the numerical solutions of the full dispersion relation for a clamped coated half-space. A similarity with Love-type waves proves to be useful for interpreting numerical data. This article is part of the theme issue ‘Modelling of dynamic phenomena and localization in structured media (part 1)’.


1973 ◽  
Vol 40 (1) ◽  
pp. 251-256 ◽  
Author(s):  
D. L. Clements

The problem of an inflated cylindrical tire of infinite length and constant finite width steadily rolling over the surface of an anisotropic elastic half space is examined. The influence of an applied force, acting along the axis of the cylinder, on the width of the region of slip at each end of the tire is determined. In particular, it is shown numerically that when a material exhibits certain anisotropy the presence of an axial force can considerably reduce the width of the zones of slip.


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