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Elastic continuum theories of lattice defects: a review

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Abstract

The presently available elastic continuum theories of lattice defects are reviewed. After introducing a few elementary concepts and the basic equations of elasticity the Eshelby’s theory of misfitting inclusions and inhomogeneities is outlined. Kovács’ result that any lattice defect can be described by a surface distribution of elastic dipoles is described. The generalization of the isotropic continuum approach to anisotropic models and to Eringen’s isotropic but non-local model is discussed. Kröner’s theroy (where a defect is viewed as a lack of strain compatibility in the medium) and the elastic field equations (formulated in a way analogous to Maxwell’s field equations of magnetostatics) are described. The concept of the dislocation density tensor is introduced and the utility of higher-order dislocation density correlation tensors is discussed. The beautiful theory of the affine differential geometry of stationary lattice defects developed by Kondo and Kröner is outlined. Kosevich’s attempt to include dynamics in the elastic field equations is described. Wadati’s quantum field theory of extended objects is mentioned qualitatively. Some potential areas of research are identified.

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  1. Materials Science Laboratory, Reactor Research Centre, 603 102, Kalpakkam, India

    Debendranath Sahoo

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  1. Debendranath Sahoo
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Sahoo, D. Elastic continuum theories of lattice defects: a review. Bull. Mater. Sci. 6, 775–798 (1984). https://doi.org/10.1007/BF02744004

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