Dynamic Analysis for Circular Inclusion Near Interfacial Crack Impacted by SH-Wave in Half Space

2012 ◽  
Vol 28 (1) ◽  
pp. 143-151 ◽  
Author(s):  
H. Qi ◽  
J. Yang ◽  
Y. Shi ◽  
J. Y. Tian
Keyword(s):  
Free Boundary ◽  
Dynamic Analysis ◽  
Green’S Function ◽  
Half Space ◽  
Green's Function ◽  
Interfacial Crack ◽  
Circular Inclusion ◽  
Wave Number ◽  
Complex Method ◽  
Sh Wave

ABSTRACTComplex method and Green's function method are used here to investigate the dynamic analysis for circular inclusion near interfacial crack impacted by SH-wave in bi-material half-space. Firstly, the displacement expression of the scattering wave was constructed which satisfied the free boundary conditions, then Green's function could be constructed, which was an essential solution to the displacement field for an elastic right-angle space with a circular inclusion impacted by out-plane harmonic line source loading at vertical surface. Secondly, crack was made out with “crack-division” technique. Meanwhile, the bi-material media was divided into two parts along the bi-material interface based on the idea of interface “conjunction”, and then the vertical surfaces of the two right-angle spaces were loaded with undetermined anti-plane forces in order to satisfy displacement continuity and stress continuity conditions at linking section. So a series of algebraic equations for determining the unknown forces could be set up through continuity conditions and the Green's function. Finally, some examples and results for dynamic stress concentration factor of the circular elastic inclusion were given. Numerical results show that they are influenced by interfacial crack, the incident wave number and the free boundary in some degree.

Lattice statics of interfaces and interfacial cracks in bimaterial solids

1992 ◽  
Vol 7 (4) ◽  
pp. 1018-1028 ◽  
Author(s):  
V.K. Tewary ◽  
Robb Thomson
Keyword(s):  
Green’S Function ◽  
Half Space ◽  
Green's Function ◽  
Displacement Field ◽  
Nearest Neighbor ◽  
Interfacial Crack ◽  
Continuum Theory ◽  
Two Phase ◽  
Lattice Statics ◽  
Interfacial Cracks

A method for calculating lattice statics Green's function is described for a bimaterial lattice or a bicrystal containing a plane interface. The method involves creation of two half space lattices containing free surfaces and then joining them to form a bicrystal. The two half space lattices may have different structures as in a two-phase bicrystal or may be of the same type but joined at different orientations to form a grain boundary interface. The method is quite general but, in this paper, has been applied only to a simple model bicrystal formed by two simple cubic lattices with nearest neighbor interactions. The bimaterial Green's function is modified to account for an interfacial crack that is used to calculate the displacement field due to an applied external force. It is found that the displacement field, as calculated by using the lattice theory, does not have the unphysical oscillations predicted by the continuum theory.

Impact of point source on fissured poroelastic medium: Green’s function approach

2020 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Shishir Gupta ◽  
Soumik Das ◽  
Rachaita Dutta
Keyword(s):  
Point Source ◽  
Green’S Function ◽  
Half Space ◽  
Porous Layer ◽  
Green's Function ◽  
Anisotropic Fluid ◽  
Complex Frequency ◽  
Sh Wave ◽  
Content Type ◽  
Porous Half Space

Purpose The purpose of this paper is to investigate the mathematical model comprising a heterogeneous fluid-saturated fissured porous layer overlying a non-homogeneous anisotropic fluid-saturated porous half-space without fissures. The influence of point source on horizontally polarized shear-wave (SH-wave) propagation has been studied intensely. Design/methodology/approach Techniques of Green’s function and Fourier transform are applied to acquire displacement components, and with the help of boundary conditions, complex frequency equation has been constructed. Findings Complex frequency relation leads to two distinct equations featuring dispersion and attenuation properties of SH-wave in a heterogeneous fissured porous medium. Using MATHEMATICA software, dispersion and damping curves are sketched to disclose the effects of heterogeneity parameters associated with both media, parameters related to rigidity and density of single porous half-space, attenuation coefficient, wave velocity, total porosity, volume fraction of fissures and anisotropy. The fact of obtaining classical Love wave equation by introducing several particular conditions establishes the validation of the considered model. Originality/value To the best of the authors’ knowledge, effect of point source on SH-wave propagating in porous layer containing macro as well as micro porosity is not analysed so far, although theory of fissured poroelasticity itself has vast applications in real life and impact of point source not only enhances the importance of fissured porous materials but also opens a new area for future research.

Scattering of SH Wave by an Interacting Mode III Crack and a Circular Cavity in Half Space

2007 ◽  
Vol 348-349 ◽  
pp. 861-864 ◽  
Author(s):  
Zai Lin Yang ◽  
Zhi Gang Chen ◽  
Dian Kui Liu
Keyword(s):  
Green’S Function ◽  
Half Space ◽  
Green's Function ◽  
Displacement Field ◽  
Complex Function ◽  
Dynamic Stress Intensity Factor ◽  
Arbitrary Point ◽  
Circular Cavity ◽  
Sh Wave ◽  
Mode Iii

Scattering of SH wave by an elastic half space with a circular cavity and a crack in any position and direction is studied with Green’s function, complex function and multi-polar coordinate method. First, a suitable Green’s function is constructed, which is the fundamental solution of the displacement field for a half space with a circular cavity impacted by an out-plane harmonic line source loading at an arbitrary point in half space. Then a crack in any position and direction is constructed by means of crack-division in half space. Finally the displacement field and stress field are established in the case of coexistence of circular cavity and crack, and the expression of dynamic stress intensity factor (DSIF) at the tip of crack is given. According to numerical examples, the influences of different parameters on DSIF are discussed.

Dynamic Green's Function for SH-Wave in Multi-Dipping Layers Embedded in a Half-Space

1998 ◽  
Vol 14 (4) ◽  
pp. 161-172
Author(s):  
Tsung-Jen Teng ◽  
Juin-Fu Chai ◽  
Chau-Shioung Yeh
Keyword(s):  
Green’S Function ◽  
Half Space ◽  
Green's Function ◽  
Source Term ◽  
Polar Coordinates ◽  
Matrix Formalism ◽  
Sh Wave ◽  
Line Load ◽  
Complementary Part ◽  
T Matrix

ABSTRACTIn this paper, the recursive T-matrix formalism is developed to determine the dynamic Green's function for SH-wave in the multi-dipping layers with arbitrary shape embedded in a half-space. In each layer, the wave field generated by a harmonic line load can be separated into two parts: the source term and the complementary part. The source term is exactly the Green's function for SH-wave in two-dimensional half-space, and the complementary part which causes the SH-wave to satisfy the boundary conditions at the interface is determined by the wave function expansion method. Using the polar coordinates, the basis functions are constructed by Bessel typed cylindrical functions, and their orthogonality conditions at the corresponding interfaces can be derived by means of Betti's third identity. Applying the conditions of continuity at the interface, the recursive T-matrix formalism is developed for determining the expansion coefficients of the complementary part from the associated source dependent constants.

Far Field Solution of Circular Inclusion and Linear Crack by SH-Wave

2011 ◽  
Vol 462-463 ◽  
pp. 455-460
Author(s):  
Hong Liang Li
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Scattered Wave ◽  
Circular Inclusion ◽  
The Other ◽  
Far Field ◽  
Elastic Space ◽  
Sh Wave ◽  
Field Solution ◽  
Scattering Field

Circular inclusion exists widely in natural media, engineering materials and structures, and defects are usually found around the inclusion. When a composite material with circular inclusion and cracks is impacted by the dynamic load, on the one hand, the scattering field produced by the circular inclusion and cracks determines the dynamic stress concentration factor around the circular inclusion, and therefore determines whether the material is damaged or not; on the other hand, the scattering field also presents many characteristic parameters of the inclusion and cracks such as defect composition, location and shape, so the research on the scattering far-field is important to the geological prospects, seismological investigation, non-destruction evaluation and the other fields. In the ocean acoustics, the scattering far-field of the acoustic wave is also used in the under-water survey, object distinguishing and so on. In theory, the scattering solution of elastic waves is one of the basic topics of reverse problems on elastic wave. On the basis of literature, few paper concentrates on the scattering far-field solution of SH-wave by a circular inclusion and a linear crack around the inclusion. In the paper a new model and a new method are presented in order to investigate deeply on this kind problem. The paper uses the Green’s function to study the scattering far-field of an elastic wave by a circular inclusion and a linear crack. The Green’s function should be a fundamental solution of displacement field for an elastic space possessing a circular inclusion while bearing out-of-plane harmonic line source force at any point. In terms of the solution of SH-wave’s scattering by an elastic space with a circular inclusion, anti-plane stresses which are the same in quantity but opposite in direction to those mentioned before, are loaded at the region where the linear crack is in existent actually; Then, the expressions of the displacement and stresses are given when the circular inclusion and linear crack exist at the same time. When the special Green’s function has been constructed and close field solution has been illustrated, the far field of scattered wave is studied. The displacement mode of scattered wave at far field and scattering cross-section are given. At last, an example is given and its numerical results are discussed.

The Dynamic Response of Circular Lining Structure and Multiple Cracks in Half Space under Impact Loading

2009 ◽  
Vol 417-418 ◽  
pp. 713-716
Author(s):  
Zai Lin Yang ◽  
Mei Juan Xu ◽  
Bai Tao Sun
Keyword(s):  
Dynamic Response ◽  
Green’S Function ◽  
Half Space ◽  
Green's Function ◽  
Impact Loading ◽  
Complex Function ◽  
Polar Coordinates ◽  
Multiple Cracks ◽  
Sh Wave ◽  
Lining Structure

The dynamic response of a circular lining structure and multiple cracks in an elastic half space while bearing impact loading is studied in this paper. This problem can be seen as the problem of defending of blast. The methods of Green's function, complex function and multi-polar coordinates are used here. First, the scattering wave which satisfies the condition of stress free on the ground surface of half-space containing a shallow-embedded circular lining structure impacted by incident SH-wave is constructed based on the symmetry of SH-wave scattering and the method of multi-polar coordinates system. Then a crack or multiple cracks in any position and direction can be constructed by Green's function and means of crack-division in half space. Finally the displacement field and stress field are established in the case of coexistence of circular lining structure and cracks, and the expression of dynamic stress intensity factor (DSIF) at the tip of crack is given. The interaction of inclusion and two cracks is chosen as numerical examples finally. According to nu-merical examples, the influences of different parameters on DSIF are discussed.

Far Field Solution of SH-Wave Scattered by a Circular Cavity and a Mode III Crack in Half Space

2008 ◽  
Vol 385-387 ◽  
pp. 157-160 ◽  
Author(s):  
Bai Tao Sun ◽  
Pei Lei Yan ◽  
Zai Lin Yang
Keyword(s):  
Green’S Function ◽  
Half Space ◽  
Green's Function ◽  
Displacement Field ◽  
Far Field ◽  
Circular Cavity ◽  
Sh Wave ◽  
Field Solution ◽  
Displacement Mode ◽  
Arbitrary Position

Based on Green’s function, complex function and multi-polar coordinate system, the far field solution of SH wave scattered by an elastic half space with a circular cavity and a crack at an arbitrary position and orientation is investigated. First, a suitable Green’s function is constructed, which is the fundamental solution of the displacement field for a half space with a circular cavity subjected to an out-plane time-harmonic line force at an arbitrary position in half space. Second, by means of crack-division technique, a crack with any location and orientation can be constructed in the region of the half space. The displacement field and stress field are established in the situation of coexistence of circular cavity and crack. At last expressions of far field, such as displacement mode of scattering wave are deduced. Some examples and numerical results are illustrated. The influences of the combination of different media parameters on solutions of far field are discussed.

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