Elastic fields due to defects in transversely isotropic bimaterials

Yu, Hao; Sanday, S. C.; Rath, B. B.; Chang, Chia‐Jung

doi:10.1098/rspa.1995.0029

Cited by 13 publications

(5 citation statements)

References 55 publications

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“…This approach is based on the reflectivity method by Kennett (1983) and it has several advantages compared to methods presented in the literature (Pan and Chou, 1979b;Yu et al, 1995). It is physically more transparent, since the answer is expressed in terms of reflection and transmission matrices, and it is also applicable to multi-layered media.…”

Section: Discussionmentioning

confidence: 98%

“…Green's functions in vertically isotropic bi-materials are given by Pan and Chou (1979b); Yu et al (1995); Yu and Rath (2000). One can recover the required equations from these Green's functions by considering the limiting case of a center of dilatation.…”

Section: Anisotropy Effectsmentioning

confidence: 98%

“…The history of the problem and explicit expressions are presented by Pan and Chou (1979a,b);Walker, 1993;Yu et al (1994Yu et al ( , 1995; Yue, 1995;Yu and Rath, 2000. Liao and Wang (1998 review solutions for displacements, strains, and stresses in a half-space subjected to different types of loads.…”

Section: Appendix B Transversely Isotropic Mediummentioning

confidence: 99%

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Elastic and piezoelectric fields due to polyhedral inclusions

Kuvshinov

2008

International Journal of Solids and Structures

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We derive explicit, closed-form expressions describing elastic and piezoelectric deformations due to polyhedral inclusions in uniform half-space and bi-materials. Our analysis is based on the linear elasticity theory and Green's function method. The method involves evaluation of volume and surface integrals of harmonic and bi-harmonic potentials. In case of polyhedra, such integrals are expressed through algebraic functions. Our results generalize numerous studies on this subject, and they allow to obtain fully analytical solutions for a number of physical and engineering problems. In the limiting case of an infinite space, our relations have an essentially more compact form, than relations obtained by other authors. We present solutions to classical Mindlin and Cherruti problems. We describe the elastic relaxation of a misfitting polygonal quantum dot in bi-materials assuming isotropic and vertically isotropic properties. It is explained how to analyze nonhydrostatic and non-uniform inclusions. We also study piezoelectric fields induced by inclusions in materials with cubic and hexagonal lattices. Among other results, we have found that a cubic inclusion in an isotropic material reproduces fields of quantum dots in GaAs (0, 0, 1) and GaAs (1, 1, 1) depending on the orientation of the cube. This suggests that one can qualitatively model crystals with different lattices by choosing an appropriate inclusion shape.

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Section: Discussionmentioning

confidence: 98%

Section: Anisotropy Effectsmentioning

confidence: 98%

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Elastic and piezoelectric fields due to polyhedral inclusions

Kuvshinov

2008

International Journal of Solids and Structures

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“…For the first time, a general stress vector function was applied by Yu and Sanday [16,17] to obtain an analytical solution of the ellipsoidal inclusion problem for isotropic joined half-spaces. Subsequently, Yu et al [18] extended this approach to the case where the half-spaces are transversely isotropic. A closed-form solution for the case of a spherical inclusion with uniform thermal dilatational eigenstrain field was obtained by Yu et al [19].…”

Section: Introductionmentioning

confidence: 98%

Ellipsoidal Domain with Piecewise Nonuniform Eigenstrain Field in One of Joined Isotropic Half-Spaces

Avazmohammadi

Hashemi

Shodja

et al. 2009

J Elast

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Consider an arbitrarily oriented ellipsoidal domain near the interface of an isotropic bimaterial space. It is assumed that a general class of piecewise nonuniform dilatational eigenstrain field is distributed within the ellipsoidal domain. Two theorems relevant to prediction of the nature of the induced displacement field for the interior and exterior points of the ellipsoidal domain are stated and proved. As a resultant the exact analytical expression of the elastic fields are obtained rigorously. In this work a new Eshelby-like tensor, A is introduced. In particular, the closed-form expressions for A associated with the interior points of spherical and cylindrical inclusion are derived. The stress field is presented for a single ellipsoidal inclusion which undergoes a Gaussian distribution of eigenstrain field and one of the principal axes of the domain is perpendicular to the interface. For the limiting case of spherical inclusion the closed-form solution is obtained and the associated strain energy is discussed. For further demonstration, two examples of two concentric spheres and three concentric cylinders with eigenstrain field distributions which are descriptive of the general class of functions defined in this paper. The effect of some parameters such as distance between the inclusion and the interface, and the ratio of the shear moduli of the two media on the induced elastic fields are examined.

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“…Some basic developments in the linear theory of dislocations in anisotropic media was given in [34]. Methods for obtaining the induced linear elastic fields of defects in transversely isotropic bimaterials and orthotropic bicrystals (in 2D) were proposed in [74] and [73], respectively. In particular, some closed-form solutions for inclusions and dislocation lines were presented.…”

Section: Introductionmentioning

confidence: 99%

Line and point defects in nonlinear anisotropic solids

Golgoon

Yavari

2018

Z. Angew. Math. Phys.

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In this paper, we present some analytical solutions for the stress fields of nonlinear anisotropic solids with distributed line and point defects. In particular, we determine the stress fields of i) a parallel cylindricallysymmetric distribution of screw dislocations in infinite orthotropic and monoclinic media, ii) a cylindricallysymmetric distribution of parallel wedge disclinations in an infinite orthotropic medium, iii) a distribution of edge dislocations in an orthotropic medium, and iv) a spherically-symmetric distribution of point defects in a transversely isotropic spherical ball.

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Elastic fields due to defects in transversely isotropic bimaterials

Cited by 13 publications

References 55 publications

Elastic and piezoelectric fields due to polyhedral inclusions

Elastic and piezoelectric fields due to polyhedral inclusions

Ellipsoidal Domain with Piecewise Nonuniform Eigenstrain Field in One of Joined Isotropic Half-Spaces

Line and point defects in nonlinear anisotropic solids

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