ISSN:
1573-2681
Keywords:
uncoupling of displacements
;
elasticity
;
anisotropy
;
Green's function
;
dislocation
;
elliptic inclusion
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
,
Physics
Notes:
Abstract It was shown in an earlier paper that, under a two-dimensional deformation, there are anisotropic elastic materials for which the antiplane displacement u 3 and the inplane displacements u 1, u 2 are uncoupled but the antiplane stresses σ31, σ32 and the inplane stresses σ11, σ12, σ22 remain coupled. The conditions for this to be possible were derived, but they have a complicated expression. In this paper new and simpler conditions are obtained, and a general anisotropic elastic material that satisfies the conditions is presented. For this material, and for certain monoclinic materials with the symmetry plane at x 3 = 0, we show that the unnormalized Stroh eigenvectors a k for k = 1, 2, 3 are all real. The matrix A =[a 1, a 2, a 3] is a unit matrix when the material has a symmetry plane at x 2 = 0. Thus any one of the u 1, u 2, u 3 can be the only nonzero displacement, and the solution is a one-displacement field. Application to the Green's function due to a line of concentrated force f and a line dislocation with Burgers vector v in the infinite space, the half-space with a rigid boundary, and the infinite space with an elliptic rigid inclusion shows that one can indeed have a one-displacement field u 1, u 2 or u 3. One can also have a two-displacement field polarized on a plane other than the (x 1, x 2)-plane. The material that uncouples u 1, u 2, u 3 is not as restrictive as one might have thought. It can be triclinic, monoclinic, orthotropic, tetragonal, transversely isotropic, or cubic. However, it cannot be isotropic.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1023/A:1007629028023
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