Elastic fields in joined half-spaces due to nuclei of strain

Yu, Hao; Sanday, S. C.

doi:10.1098/rspa.1991.0110

Cited by 46 publications

(15 citation statements)

References 9 publications

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“…Mindlin and Cheng (1950a) derived the Galerkin vectors for the nuclei of strain in a half-space. The Glerkin vectors in two joined half-spaces, either perfectly bonded or in frictionless contact with each other, were further presented by Yu and Sanday (1991a). Based on the Galerkin vectors, Liu and Wang (2005) described a general and direct method to express the stress field in a half-space due to an arbitrary inclusion.…”

Section: Introductionmentioning

confidence: 99%

Analytical solutions for elastic fields caused by eigenstrains in two joined and perfectly bonded half-spaces and related problems

Wang

2016

International Journal of Plasticity

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Please cite this article as: Wang, Z., Yu, H., Wang, Q., Analytical solutions for elastic fields caused by eigenstrains in two joined and perfectly bonded half-spaces and related problems, International Journal of Plasticity (2015), AbstractThis paper reports the derivation of the explicit integral kernels for the elastic fields due to eigenstrains in two joined and perfectly bonded half-space solids or bimaterials. The domain integrations of these kernels result in the analytical solutions to displacements and stresses.When the eigenstrains are all in solid I, the kernel for the elastic fields has four groups in this solid and two groups in the other joined solid. Explicit closed-form solutions for a cuboidal inclusion with uniform eigenstrains are derived as the basic solutions, i.e., the influence coefficients. When the computational domain is meshed into cuboidal elements of the same sizes, the total elastic fields can be quickly obtained by implementing three-dimensional fast Fourier transform-based algorithms. The results for the fields due to a cuboidal, a spherical, and a cylindrical inclusion, as well as multiple cuboidal inclusions are presented and discussed.Residual stresses in an elasto-plastic contact involved a coated substrate is further analyzed with the new solution approach.

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Section: Introductionmentioning

confidence: 99%

Analytical solutions for elastic fields caused by eigenstrains in two joined and perfectly bonded half-spaces and related problems

Wang

2016

International Journal of Plasticity

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“…For example, Guell and Dunders [15] utilized the Papkovitch-Neuber displacement potentials for determination of the elastic fields of a spherical region in one of the joined elastic half-paces with constant dilatational eigenstrain field. 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.…”

Section: Introductionmentioning

confidence: 99%

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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“…The solution for a point force acting in the interior of a semi-infinite solid was first solved by Mindlin (1936). By using Galerkin vector stress functions, solutions for the complete set of 40 nuclei of strain that have physical significance have been presented by Mindlin and Cheng (1950a) for a half-space, and by Yu and Sanday (1991a) for two joined half-spaces (bimaterials). By using a matrix representation of stresses and displacements, and solving the matrix equations, Vijayakumar and Cormack (1987a,b) obtained the stresses and displacements for different nuclei of strain in bimaterials.…”

Section: Introductionmentioning

confidence: 99%

Axisymmetric nuclei of strain and their applications for multilayered solids

Pande

2007

International Journal of Solids and Structures

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In this paper, the effect of several axisymmetric elastic singularities (i.e., point forces, double forces, sum of two double forces and centers of dilatation) on the elastic response of a multilayered solid is investigated. The boundary conditions in an infinite solid at the plane passing through the singularity are derived first using Papkovich-Neuber harmonic functions. Then, a Green's function solution for multilayered solids is obtained by solving a set of simultaneous linear algebraic equations using both the boundary conditions for the singularity and the layer interfaces. Finally, the elastic solutions in a single layer on an infinite substrate due to point defects and infinitesimal prismatic dislocation loops are presented to illustrate the application of these Green's function solutions. Published by Elsevier Ltd.

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Elastic fields in joined half-spaces due to nuclei of strain

Cited by 46 publications

References 9 publications

Analytical solutions for elastic fields caused by eigenstrains in two joined and perfectly bonded half-spaces and related problems

Analytical solutions for elastic fields caused by eigenstrains in two joined and perfectly bonded half-spaces and related problems

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

Axisymmetric nuclei of strain and their applications for multilayered solids

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