Affine development of closed curves in Weitzenböck manifolds and the Burgers vector of dislocation mechanics

DOI10.1177/1081286512463720zbMath1346.74010OpenAlexW2106968304MaRDI QIDQ2875333

Arash Yavari, Arkadas Ozakin

Publication date: 14 August 2014

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

Full work available at URL: https://doi.org/10.1177/1081286512463720

zbMATH Keywords

torsionflat connectiongeometric elasticitydistributed dislocations

Mathematics Subject Classification ID

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

Related Items (7)

The geometry of discombinations and its applications to semi-inverse problems in anelasticity ⋮ A geometric field theory of dislocation mechanics ⋮ Limits of Distributed Dislocations in Geometric and Constitutive Paradigms ⋮ Riemann-Cartan geometry of nonlinear dislocation mechanics ⋮ Line and point defects in nonlinear anisotropic solids ⋮ The emergence of torsion in the continuum limit of distributed edge-dislocations ⋮ Metric description of singular defects in isotropic materials

Cites Work

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• Riemann-Cartan manifolds
• Torsion and related concepts: An introductory overview
• Lattice incompatibility and a gradient theory of crystal plasticity
• Riemann-Cartan geometry of nonlinear dislocation mechanics
• On the geometric character of stress in continuum mechanics
• On the regions bounded by homotopic curves
• Non-Riemannian and Finslerian approaches to the theory of yielding
• Tensor-fields in non-symmetric connections
• On geometric discretization of elasticity
• Normal frames for general connections
• A geometric theory of thermal stresses
• The Weitzenböck connection and time reparameterization in nonholonomic mechanics
• Ricci-Calculus

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