The gauge theory of dislocations: static solutions of screw and edge dislocations

Abstract

We investigate the T(3)-gauge theory of static dislocations in continuous solids. We use the most general linear constitutive relations bilinear in the elastic distortion tensor and dislocation density tensor for the force and pseudomoment stresses of an isotropic solid. The constitutive relations contain six material parameters. In this theory both the force and pseudomoment stresses are asymmetric. The theory possesses four characteristic lengths l1, l2, l3 and l4 which are given explicitely. We first derive the three-dimensional Green tensor of the master equation for the force stresses in the translational gauge theory of dislocations. We then investigate the situation of generalized plane strain (anti-plane strain and plane strain). Using the stress function method, we find modified stress functions for screw and edge dislocations. The solution of the screw dislocation is given in terms of one independent length l1=l4. For the problem of an edge dislocation, only two characteristic lengths l2 and l3 arise with one of them being the same l2=l1 as for the screw dislocation. Thus, this theory possesses only two independent lengths for generalized plane strain. If the two lengths l2 and l3 of an edge dislocation are equal, we obtain an edge dislocation which is the gauge theoretical version of a modified Volterra edge dislocation. In the case of symmetric stresses we recover well known results obtained earlier.

arXiv comment33 pages, 17 figures

References in corpus (8)

• Metric-Affine Gauge Theory of Gravity: Field Equations, Noether Identities, World Spinors, and Breaking of Dilation Invariance
• An elastoplastic theory of dislocations as a physical field theory with torsion
• A nonsingular solution of the edge dislocation in the gauge theory of dislocations
• Dislocation theory as a 3-dimensional translation gauge theory
• The Dislocation Stress Functions From the Double Curl T(3)-Gauge Equation: Linearity and a Look Beyond
• The gauge theory of dislocations: conservation and balance laws
• Screw dislocations in the field theory of elastoplasticity
• The Einsteinian T(3)-Gauge Approach and the Stress Tensor of the Screw Dislocation in the Second Order: Avoiding the Cut-off at the Core

Cited by in corpus (19)

• A unifying perspective: the relaxed linear micromorphic continuum
• Cartan's spiral staircase in physics and, in particular, in the gauge theory of dislocations
• Korn inequalities for incompatible tensor fields in three space dimensions with conformally invariant dislocation energy
• Irreducible decomposition of strain gradient tensor in isotropic strain gradient elasticity
• On the fundamentals of the three-dimensional translation gauge theory of dislocations
• A gauge theoretic approach to elasticity with microrotations
• The gauge theory of dislocations: a uniformly moving screw dislocation
• Quantized Dislocations
• Green's functions for the isotropic planar relaxed micromorphic model -- concentrated force and concentrated couple
• Dislocation Field Theory in 2D: Application to Graphene
• On the Higgs mechanism and stress functions in the translational gauge theory of dislocations
• The gauge theory of dislocations: a nonuniformly moving screw dislocation
• A global higher regularity result for the static relaxed micromorphic model on smooth domains
• Diffusion in the presence of a chiral topological defect
• Using torsion to manipulate spin currents
• On gradient enriched elasticity theories: A reply to "Comment on 'On non-singular crack fields in Helmholtz type enriched elasticity theories' " and important theoretical aspects
• Plasticity as Spontaneous Breaking of Symmetry
• A Novel Discrete Theory of a Screw Dislocation in the BCC Crystal Lattice
• A screw dislocation in a functionally graded material using the translation gauge theory of dislocations