Thermoelastic Interaction Between Singularities and Interfaces in an Anisotropic Trimaterial

2007 ◽  
Vol 74 (6) ◽  
pp. 1285-1288
Author(s):  
Seung Tae Choi
Keyword(s):  
Analytic Continuation ◽  
Anisotropic Medium ◽  
Dissimilar Materials ◽  
Infinite Body ◽  
Series Form ◽  
Alternating Technique ◽  
Thermoelastic Interaction ◽  
General Plane ◽  
Homogeneous Anisotropic Medium ◽  
Plane Deformations

The method of analytic continuation and Schwarz-Neumann’s alternating technique were applied to the thermoelastic interaction problems of singularities and interfaces in an anisotropic “trimaterial,” which denotes an infinite body composed of three dissimilar materials bonded along two parallel interfaces. It was assumed that the linear thermoelastic materials are under general plane deformations in which the plane of deformation is perpendicular to the planes of the two parallel interfaces. The author then showed that by alternately applying the method of analytic continuation across two parallel interfaces the solution for the thermoelastic singularities in an anisotropic trimaterial can be obtained in a series form from a solution for the same singularities in a homogeneous anisotropic medium.

Anisotropic and Isotropic Elasticity, and its Equivalence for Singularity, Interface and Crack in Bimaterials and Trimaterials

2004 ◽  
Vol 261-263 ◽  
pp. 23-32
Author(s):  
Y.Y. Earmme ◽  
S.T. Choi ◽  
H. Shin
Keyword(s):  
Thin Film ◽  
Analytic Continuation ◽  
Homogeneous Solution ◽  
Dissimilar Materials ◽  
Anisotropic Elasticity ◽  
Infinite Body ◽  
Finite Strip ◽  
Straight Line ◽  
Isotropic Elasticity ◽  
Complex Forms

The equivalence between anisotropic and isotropic elasticity is investigated in this study for two-dimensional deformation under certain conditions. That is, the isotropic elasticity can be reconstructed in the same framework of the anisotropic elasticity, when the interface between dissimilar media lies along a straight line. Therefore, many known solutions for an anisotropic bimaterial can be regarded as valid even for a bimaterial, in which one or both of the constituent materials are isotropic. The usefulness of the equivalence is that the solutions for singularities and cracks in an anisotropic/isotropic bimaterial can easily be obtained without solving the boundary value problems directly. Conservation integrals also have the similar analogy between anisotropic and isotropic elasticity so that J integral and J-based mutual integral M are expressed in the same complex forms for anisotropic and isotropic materials, when both end points of the integration paths are on the straight interface. The method of analytic continuation and Schwarz-Neumann's alternating technique are applied to singularity problems in an anisotropic or isotropic 'trimaterial', which denotes an infinite body composed of three dissimilar materials bonded along two parallel interfaces. The method of analytic continuation is alternatively applied across the two parallel interfaces in order to derive the trimaterial solution in a series form from the corresponding homogeneous solution. The trimaterial solution studied here can be applied to a variety of problems, e.g. a bimaterial (including a half-plane problem), a finite thin film on semi-infinite substrate, and a finite strip of thin film, etc. Some examples are presented to verify the usefulness of the obtained solutions.

The wave front in a homogeneous anisotropic medium

1980 ◽  
Vol 70 (6) ◽  
pp. 2097-2101
Author(s):  
M. J. Yedlin
Keyword(s):  
Dispersion Relation ◽  
Wave Front ◽  
Group Velocity ◽  
Anisotropic Medium ◽  
Slowness Surface ◽  
Constant Frequency ◽  
Common Notion ◽  
The Common ◽  
Intuitive Method ◽  
Homogeneous Anisotropic Medium

abstract A simple geometric construction is derived for the shape of the wave front in a homogeneous anisotropic medium. It is shown to be equivalent to the intuitive method of constructing a wave front using Huygen's principle. Although this construction has been referred to and tersely described in the literature (Musgrave, 1970; Kraut, 1963; Duff, 1960), it is instructive to demonstrate its relationship to the common notion of the wave front obtained via consideration of the group velocity. The wave front is shown to be the polar reciprocal of the slowness surface (the dispersion relation at constant frequency). An appreciation of the pole-polar correspondence between the two surfaces allows quick inference of some of the important features of the wave front in a homogeneous anisotropic medium.

Singularities Interacting With a Coated Circular Inhomogeneity Revisited

2008 ◽  
Vol 75 (6) ◽  
Author(s):  
Seung Tae Choi
Keyword(s):  
Analytic Continuation ◽  
Building Block ◽  
Homogeneous Medium ◽  
Circular Inclusion ◽  
Specific Information ◽  
General Solutions ◽  
Alternating Technique ◽  
Circular Inhomogeneity

Singularities interacting with a coated circular inhomogeneity are analyzed with the method of analytic continuation and the Schwarz–Neumann’s alternating technique. It is shown that the solution for singularities in a homogeneous medium can be used as a building block of the solution for the same singularities interacting with a coated circular inclusion. The obtained solutions have series forms independent of any specific information about singularities, and thus they can be interpreted as general solutions for a variety of singularities.

Two-dimensional invisibility anti-cloak structured by a homogeneous anisotropic medium

2016 ◽  
Vol 83 (9) ◽  
pp. 532
Author(s):  
Xuan Liu ◽  
Yicheng Wu ◽  
Chengdong He ◽  
Yuzhuo Wang ◽  
Xiaojia Wu ◽  
...  
Keyword(s):  
Anisotropic Medium ◽  
Two Dimensional ◽  
Homogeneous Anisotropic Medium
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