Green’s function for SH-waves in inhomogeneous anisotropic elastic solid with power-function velocity variation

Wave Motion ◽  
2013 ◽  
Vol 50 (2) ◽  
pp. 101-110 ◽  
Author(s):  
C.H. Daros
Keyword(s):  
Green’S Function ◽  
Power Function ◽  
Green's Function ◽  
Elastic Solid ◽  
Velocity Variation ◽  
Sh Waves ◽  
Anisotropic Elastic

Defect Green’s Function of Multiple Point-Like Inhomogeneities in a Multilayered Anisotropic Elastic Solid

2004 ◽  
Vol 71 (5) ◽  
pp. 672-676
Author(s):  
B. Yang
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Elastic Solid ◽  
Anisotropic Elasticity ◽  
Matrix Inversion ◽  
Numerical Results ◽  
Multiple Point ◽  
Present Formulation ◽  
Anisotropic Elastic ◽  
The Continuum

Defect Green’s function (GF) of multiple point-like inhomogeneities in a multilayered solid has been derived within the theory of linear anisotropic elasticity. It is related to the (reference) GF of the multilayered matrix excluding the inhomogeneities through the continuum Dyson’s equation. While the reference GF is available, the defect GF can be solved. The expressions are first analytically reduced by realizing the point-likeness of the inhomogeneities. The subsequent procedure involves the solution of the response of each individual inhomogeneity to a far-field straining in the multilayered matrix and a matrix inversion on the order of the number of inhomogeneities. Furthermore, the defect GF is applied to derive the field induced by inhomogeneous substitutions in a multilayered solid. Numerical results are reported for arrays of cubic and semispherical Ge inclusions in a Si/Ge superlattice. The numerical results have demonstrated the validity and efficiency of the present formulation.

The Interaction of a Cylindrical Elastic Inclusion with Semicircular Disconnected Curve and Linear Cracks in an Homogeneous Medium by SH-Waves

2007 ◽  
Vol 348-349 ◽  
pp. 357-360
Author(s):  
Qi Hui ◽  
Jia Xi Zhao
Keyword(s):  
Green’S Function ◽  
Half Space ◽  
Green's Function ◽  
Function Method ◽  
Dynamic Stress ◽  
Elastic Inclusion ◽  
Complex Function ◽  
Dynamic Stress Intensity Factor ◽  
Homogeneous Medium ◽  
Sh Waves

The scattering of SH waves by a cylindrical elastic inclusion with a semicircular disconnected curve and linear cracks in an homogeneous medium is investigated and the solution of dynamic stress intensity factor is given by Green’s function, complex function method. Firstly, we can divide the space into up-and-down parts along the X axis. In the lower half space, a new suitable Green’s function for the present problem is constructed.In the upper half space, the Green’s function has been given by reference [5]. Thereby the semicircular disconnected curve can be constructed when the two parts are bonded along the interface and the linear cracks can be constructed using the method of crack-division and the integral equations can be obtained by the use of continuity conditions at the X axis. Finally, some examples and results of dynamic stress intensify factor are given and the influence of the parameters is discussed.

Green’s Functions for a Half-Space and Two Half-Spaces Bonded to a Thin Anisotropic Elastic Layer

2008 ◽  
Vol 75 (5) ◽  
Author(s):  
T. C. T. Ting
Keyword(s):  
Thin Layer ◽  
Green’S Function ◽  
Half Space ◽  
Green's Function ◽  
Elastic Material ◽  
The Body ◽  
Reference Length ◽  
Line Force ◽  
Line Dislocation ◽  
Anisotropic Elastic

The Green’s function for an anisotropic elastic half-space that is bonded to a thin elastic material of different anisotropy subject to a line force and a line dislocation is presented. Also presented is the Green’s function for two different anisotropic elastic half-spaces that are bonded to a thin elastic material of different anisotropy subject to a line force and a line dislocation in one of the half-spaces. The thickness h of the thin layer is assumed to be small compared with a reference length. Thus, instead of finding the solution in the thin layer and imposing the continuity conditions at the interface(s), we derive and apply effective boundary conditions for the interface between the layer and the body that take into account the existence of the layer.

Interaction of Multiple Circular Inclusions and a Linear Crack by SH-Wave

2010 ◽  
Vol 452-453 ◽  
pp. 677-680
Author(s):  
Hong Liang Li ◽  
Hong Li
Keyword(s):  
Stress Concentration ◽  
Green’S Function ◽  
Green's Function ◽  
Dynamic Stress ◽  
Analytic Solutions ◽  
Dynamic Stress Concentration ◽  
Elastic Space ◽  
Sh Wave ◽  
Sh Waves ◽  
Out Of Plane

Multiple circular inclusions exists widely in natural media, engineering materials and modern municipal construction, and defects are usually found around the inclusions. When composite material with multiple circular inclusions and a crack is impacted by dynamic load, the scattering field will be produced. The problem of scattering of SH waves by multiple circular inclusions and a linear crack is one of the important and interesting questions in mechanical engineering and civil engineering for the latest decade. It is hard to obtain analytic solutions except for several simple conditions. In this paper, the method of Green’s function is used to investigate the problem of dynamic stress concentration of multiple circular inclusions and a linear crack for incident SH wave. The train of thoughts for this problem is that: Firstly, a Green’s function is constructed for the problem, which is a fundamental solution of displacement field for an elastic space possessing multiple circular inclusions while bearing out-of-plane harmonic line source force at any point: Secondly, in terms of the solution of SH-wave’s scattering by an elastic space with multiple circular inclusions, anti-plane stresses which are the same in quantity but opposite in direction to those mentioned before, are loaded at the region where the crack is in existent actually; Finally, the expressions of the displacement and stress are given when multiple circular inclusions and a linear crack exist at the same time. Then, by using the expression, an example is provided to show the effect of multiple circular inclusions and crack on the dynamic stress concentration.

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