Riemann–Cartan Geometry of Nonlinear Dislocation Mechanics

2012/03/08 by Arash Yavari, Alain Goriely · 179 citations
Engineering · Materials Science · Mathematics · #Affine connection #Affine transformation #Classical mechanics #Continuum mechanics #Dislocation #Elasticity and Material Modeling #Geometry #Manifold (fluid mechanics) #Mathematical analysis #Mathematics #Nonlinear system #Nonlocal and gradient elasticity in micro/nano structures #Physics #Quantum mechanics #Riemannian manifold #Thermoelastic and Magnetoelastic Phenomena #Torsion (gastropod)

paper · doi:10.1007/s00205-012-0500-0

published in Archive for Rational Mechanics and Analysis 205(1), 59-118 (Springer Science+Business Media)

openalex publication_date 2012/03/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/25

Citations

• Some geometrical relations in dislocated crystals
• Materially uniform simple bodies with inhomogeneities
• On the geometric structures of simple bodies, a mathematical foundation for the theory of continuous distributions of dislocations
• Allgemeine Kontinuumstheorie der Versetzungen und Eigenspannungen
• The thermodynamics of elastic materials with heat conduction and viscosity

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• Toward the mechanics of fractal materials: mechanics of continuum with fractal metric
• Nonlinear mechanics of accretion
• On Universal Deformations of Compressible Cauchy Elastic Solids Reinforced by Inextensible Fibers
• Geometric theory of generalised continua using moving frames
• Variation of the Affine Connection in the kinematics of hypersurfaces
• Thermoplasticity as a nonsmooth phenomenon
• A Riemannian approach to reduced plate, shell, and rod theories
• On Hamiltonian continuum mechanics
• Variational convergence of discrete geometrically-incompatible elastic models
• Nonlinear elastic inclusions in isotropic solids. [europepmc]
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• The anelastic Ericksen problem: universal eigenstrains and deformations in compressible isotropic elastic solids. [europepmc]
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• Geometrical frustration in nonlinear mechanics of screw dislocation. [europepmc]
• Biot-Savart law in the geometrical theory of dislocations. [europepmc]
• Revisiting Volterra defects: geometrical relation between edge dislocations and wedge disclinations. [europepmc]