2008/02/29 by Markus Lazar, Charalampos Anastassiadis · 39 citations
Engineering · Materials Science · Mathematics · Physics and Astronomy · #Cauchy stress tensor #Classical mechanics #Condensed matter physics #Dislocation #Dislocation creep #Distortion (music) #Enhanced Data Rates for GSM Evolution #Gauge theory #Geometry #Infinitesimal strain theory #Isotropy #Materials science #Mathematical analysis #Mathematical physics #Mathematics #Microstructure and mechanical properties #Nonlocal and gradient elasticity in micro/nano structures #Numerical methods in engineering #Optics #Peierls stress #Physics #Plane (geometry) #Plane stress #Quantum mechanics #Tensor (intrinsic definition) #Thermodynamics #cond-mat.mtrl-sci
paper · pdf · doi:10.1080/14786430802558551
published in The Philosophical Magazine A Journal of Theoretical Experimental and Applied Physics 89(3), 199-231 (Taylor & Francis) · 33 pages, 17 figures
arxiv created 2008/10/02 · openalex publication_date 2009/01/21 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We investigate the T(3)-gauge theory of static dislocations in continuous solids. We use the most general linear constitutive relations in terms of 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 explicitly. 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.