A distributional approach to the geometry of \(2D\) dislocations at the continuum scale

DOI10.1007/s11565-012-0149-5zbMath1299.74009OpenAlexW1998468477MaRDI QIDQ473514

Nicolas Van Goethem, François Dupret

Publication date: 24 November 2014

Published in: Annali dell'Università di Ferrara. Sezione VII. Scienze Matematiche (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11565-012-0149-5

zbMATH Keywords

single crystalsdistribution theorydislocationsmultivalued functionscontortiondefect density tensorsdisclinationsstrain incompatibility

Mathematics Subject Classification ID

Classical linear elasticity (74B05) Kinematics of deformation (74A05) Micromechanical theories (74A60) Introductory exposition (textbooks, tutorial papers, etc.) pertaining to mechanics of deformable solids (74-01)

Related Items (9)

Variational evolution of dislocations in single crystals ⋮ Existence and asymptotic results for an intrinsic model of small-strain incompatible elasticity ⋮ A Variational Approach to Single Crystals with Dislocations ⋮ Analytic and geometric properties of dislocation singularities ⋮ A compatible-incompatible decomposition of symmetric tensors inL^pwith application to elasticity ⋮ Thermodynamic forces in single crystals with dislocations ⋮ Point singularities in incompatible elasticity ⋮ Matrix representation of a cross product and related curl-based differential operators in all space dimensions ⋮ Fields of bounded deformation for mesoscopic dislocations

Cites Work

• Matching the inner and outer solutions in the continuum theory of dislocations
• A kinematic model for continuous distributions of dislocations
• A distributional approach to 2D Volterra dislocations at the continuum scale
• An Equilibrium Theory of Dislocation Continua
• The energy of elastic defects: a distributional approach
• Geometry and thermomechanics of structural rearrangements: Ekkehart Kröner's legacy Plenary lecture presented at the 80th Annual GAMM Conference, Augsburg, 25-28 March 2002
• Benefits and shortcomings of the continuous theory of dislocations
• On the characterization of geometrically necessary dislocations in finite plasticity
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