Geometric aspects of singular dislocations

DOI10.1177/1081286512465222zbMath1353.74010arXiv1208.4215OpenAlexW2165416908MaRDI QIDQ2875337

Marcelo Epstein, Reuven Segev

Publication date: 14 August 2014

Published in: Mathematics and Mechanics of Solids (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1208.4215

zbMATH Keywords

singularitiesdifferential formsde Rham currentsFrank's rules

Mathematics Subject Classification ID

Crystalline structure (74E15) Applications of differential geometry to physics (53Z05) Micromechanical theories (74A60)

Related Items

On tangent geometry and generalised continuum with defects ⋮ On the Geometry and Kinematics of Smoothly Distributed and Singular Defects ⋮ A proposal for defining continuous distribution of dislocations for objective structures ⋮ Reynolds transport theorem for smooth deformations of currents on manifolds ⋮ Elasto-plastic evolution of single crystals driven by dislocation flow ⋮ A geometric field theory of dislocation mechanics ⋮ Stress theory for classical fields ⋮ Regular and Singular Dislocations ⋮ Limits of Distributed Dislocations in Geometric and Constitutive Paradigms ⋮ Modeling continuous distributions of dislocations in multi-walled nanotube composites ⋮ A Variational Method for Generating $n$-Cross Fields Using Higher-Order $Q$-Tensors

Cites Work

• Allgemeine Kontinuumstheorie der Versetzungen und Eigenspannungen
• Materially uniform simple bodies with inhomogeneities
• On the geometric structures of simple bodies, a mathematical foundation for the theory of continuous distributions of dislocations
• Material symmetry and singularities in solids
• Notes on Metric Independent Analysis of Classical Fields
• The Geometrical Language of Continuum Mechanics