On the application of the Sommerfeld representation in a two-dimensional rotationally invariant anisotropic medium

1990 ◽  
Vol 38 (7) ◽  
pp. 1028-1034 ◽  
Author(s):  
J.C. Monzon
Keyword(s):  
Anisotropic Medium ◽  
Two Dimensional ◽  
Rotationally Invariant

Electric and heat conduction across an elliptic cavity in an anisotropic medium

2019 ◽  
Vol 24 (10) ◽  
pp. 3279-3294 ◽  
Author(s):  
Kunkun Xie ◽  
Haopeng Song ◽  
Cunfa Gao
Keyword(s):  
Heat Conduction ◽  
Anisotropic Medium ◽  
Crack Surface ◽  
Two Dimensional ◽  
Intensity Factors ◽  
Elliptical Cavity ◽  
Loading Direction ◽  
Elliptic Cavity ◽  
Field Intensity Factors ◽  
Potential Gradients

It is well known that the anisotropy of materials will significantly affect heat conduction, and the corresponding results have been applied to the thermal analysis of materials. An elliptic cavity in a nonlinearly coupled anisotropic medium, on the other hand, is much more difficult to analyze. Based on the complex variable method, the problem of a two-dimensional elliptical cavity in an anisotropic material is analyzed in this paper, and the field distributions have been obtained in closed-form. The field intensity factors are discussed in detail. The results show that both the temperature and electric potential gradients at a crack tip are always perpendicular to the crack surface, regardless of the anisotropy and the nonlinearity in the constitutive equations and the arbitrariness of loading direction. These results provide a powerful tool to analyze the effective behavior and reliability of anisotropic materials with cavities.

On isotropic rank 1 convex functions

1999 ◽  
Vol 129 (5) ◽  
pp. 1081-1105 ◽  
Author(s):  
Miroslav Šilhavý
Keyword(s):  
Arbitrary Dimension ◽  
Sufficient Conditions ◽  
Singular Values ◽  
Invariant Function ◽  
Two Dimensional ◽  
Rank 1 Convexity ◽  
Definition Of ◽  
Necessary And Sufficient ◽  
Rotationally Invariant ◽  
Positive Determinant

Let f be a rotationally invariant function defined on the set Lin+ of all tensors with positive determinant on a vector space of arbitrary dimension. Necessary and sufficient conditions are given for the rank 1 convexity of f in terms of its representation through the singular values. For the global rank 1 convexity on Lin+, the result is a generalization of a two-dimensional result of Aubert. Generally, the inequality on contains products of singular values of the type encountered in the definition of polyconvexity, but is weaker. It is also shown that the rank 1 convexity is equivalent to a restricted ordinary convexity when f is expressed in terms of signed invariants of the deformation.

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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