The Eshelby Tensors in a Finite Spherical Domain—Part I: Theoretical FormulationsSource: Journal of Applied Mechanics:;2007:;volume( 074 ):;issue: 004::page 770DOI: 10.1115/1.2711227Publisher: The American Society of Mechanical Engineers (ASME)
Abstract: This work is concerned with the precise characterization of the elastic fields due to a spherical inclusion embedded within a spherical representative volume element (RVE). The RVE is considered having finite size, with either a prescribed uniform displacement or a prescribed uniform traction boundary condition. Based on symmetry and group theoretic arguments, we identify that the Eshelby tensor for a spherical inclusion admits a unique decomposition, which we coin the “radial transversely isotropic tensor.” Based on this notion, a novel solution procedure is presented to solve the resulting Fredholm type integral equations. By using this technique, exact and closed form solutions have been obtained for the elastic disturbance fields. In the solution two new tensors appear, which are termed the Dirichlet–Eshelby tensor and the Neumann–Eshelby tensor. In contrast to the classical Eshelby tensor they both are position dependent and contain information about the boundary condition of the RVE as well as the volume fraction of the inclusion. The new finite Eshelby tensors have far-reaching consequences in applications such as nanotechnology, homogenization theory of composite materials, and defects mechanics.
keyword(s): Tensors ,
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contributor author | Shaofan Li | |
contributor author | Roger A. Sauer | |
contributor author | Gang Wang | |
date accessioned | 2017-05-09T00:22:28Z | |
date available | 2017-05-09T00:22:28Z | |
date copyright | July, 2007 | |
date issued | 2007 | |
identifier issn | 0021-8936 | |
identifier other | JAMCAV-26645#770_1.pdf | |
identifier uri | http://yetl.yabesh.ir/yetl/handle/yetl/135099 | |
description abstract | This work is concerned with the precise characterization of the elastic fields due to a spherical inclusion embedded within a spherical representative volume element (RVE). The RVE is considered having finite size, with either a prescribed uniform displacement or a prescribed uniform traction boundary condition. Based on symmetry and group theoretic arguments, we identify that the Eshelby tensor for a spherical inclusion admits a unique decomposition, which we coin the “radial transversely isotropic tensor.” Based on this notion, a novel solution procedure is presented to solve the resulting Fredholm type integral equations. By using this technique, exact and closed form solutions have been obtained for the elastic disturbance fields. In the solution two new tensors appear, which are termed the Dirichlet–Eshelby tensor and the Neumann–Eshelby tensor. In contrast to the classical Eshelby tensor they both are position dependent and contain information about the boundary condition of the RVE as well as the volume fraction of the inclusion. The new finite Eshelby tensors have far-reaching consequences in applications such as nanotechnology, homogenization theory of composite materials, and defects mechanics. | |
publisher | The American Society of Mechanical Engineers (ASME) | |
title | The Eshelby Tensors in a Finite Spherical Domain—Part I: Theoretical Formulations | |
type | Journal Paper | |
journal volume | 74 | |
journal issue | 4 | |
journal title | Journal of Applied Mechanics | |
identifier doi | 10.1115/1.2711227 | |
journal fristpage | 770 | |
journal lastpage | 783 | |
identifier eissn | 1528-9036 | |
keywords | Tensors | |
tree | Journal of Applied Mechanics:;2007:;volume( 074 ):;issue: 004 | |
contenttype | Fulltext |