Dislocations in gradient elasticity revisited

DOI10.1098/rspa.2006.1699zbMath1149.74309OpenAlexW2140260391MaRDI QIDQ3502099

Markus Lazar, Gérard A. Maugin

Publication date: 22 May 2008

Published in: Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1098/rspa.2006.1699

zbMATH Keywords

Fourier transformdislocationsgradient elasticity

Mathematics Subject Classification ID

Micromechanical theories (74A60) Elastic materials (74B99)

Related Items (18)

Finite third-order gradient elasticity and thermoelasticity ⋮ A unifying variational framework for stress gradient and strain gradient elasticity theories ⋮ When functionally graded materials meet higher order simplified strain gradient elasticity theory ⋮ On the gradient of the Green tensor in two-dimensional elastodynamic problems, and related integrals: distributional approach and regularization, with application to nonuniformly moving sources ⋮ A micromorphic approach to stress gradient elasticity theory with an assessment of the boundary conditions and size effects ⋮ Plane-strain problems for a class of gradient elasticity models -- a stress function approach ⋮ Singularity-free dislocation dynamics with strain gradient elasticity ⋮ The atomistic representation of first strain-gradient elastic tensors ⋮ Incompatible strain gradient elasticity of Mindlin type: screw and edge dislocations ⋮ Isogeometric analysis of first and second strain gradient elasticity ⋮ Uniformly moving screw dislocation in strain gradient elasticity ⋮ A screw dislocation near a circular nano-inhomogeneity in gradient elasticity ⋮ A Personal View on Current Generalized Theories of Elasticity and Plastic Flow ⋮ The solid angle and the Burgers formula in the theory of gradient elasticity: line integral representation ⋮ Korn inequalities for incompatible tensor fields in three space dimensions with conformally invariant dislocation energy ⋮ Elastic and plastic fields induced by a screw dislocation in a nanowire within Mindlin's second strain gradient theory ⋮ Fields of bounded deformation for mesoscopic dislocations ⋮ Distributional and regularized radiation fields of non-uniformly moving straight dislocations, and elastodynamic Tamm problem

Cites Work

• Nonsingular stress and strain fields of dislocations and disclinations in first strain gradient elasticity
• A simple approach to solve boundary-value problems in gradient elasticity
• Dislocations in second strain gradient elasticity
• A nonsingular solution of the edge dislocation in the gauge theory of dislocations
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