The T(3)-Gauge Model, the Einstein-Like Gauge Equation, and Volterra Dislocations with Modified Asymptotics

Malyshev, C.

doi:10.1006/aphy.2000.6088

Cited by 44 publications

(137 citation statements)

References 37 publications

Supporting

Mentioning

131

Contrasting

Order By: Relevance

“…Moreover, it is not possible to give a correct solution of an edge dislocation. Especially, the stress component σ zz is incorrect and the condition of plane strain is not satisfied [18]. Such a dislocation gauge theory with symmetric force stresses possesses only one additional material parameter and two length scales can be defined to describe size-effects.…”

Section: Reviewing Remarksmentioning

confidence: 99%

“…These drawbacks of the Edelen model have been a motivation for further investigations [18,20]. The so-called Einstein choice has been investigated by Malyshev [18] and Lazar [21,22].…”

Section: Reviewing Remarksmentioning

confidence: 99%

“…The so-called Einstein choice has been investigated by Malyshev [18] and Lazar [21,22]. Their solution of a screw dislocation looks to be acceptable for theories with symmetric force stresses.…”

Section: Reviewing Remarksmentioning

confidence: 99%

See 2 more Smart Citations

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

Lazar¹,

Anastassiadis²

2009

Philosophical Magazine

View full text Add to dashboard Cite

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 ℓ 1 , ℓ 2 , ℓ 3 and ℓ 4 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 ℓ 1 = ℓ 4 . For the problem of an edge dislocation, only two characteristic lengths ℓ 2 and ℓ 3 arise with one of them being the same ℓ 2 = ℓ 1 as for the screw dislocation. Thus, this theory possesses only two independent lengths for generalized plane strain. If the two lengths ℓ 2 and ℓ 3 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.

show abstract

Section: Reviewing Remarksmentioning

confidence: 99%

“…These drawbacks of the Edelen model have been a motivation for further investigations [18,20]. The so-called Einstein choice has been investigated by Malyshev [18] and Lazar [21,22].…”

Section: Reviewing Remarksmentioning

confidence: 99%

See 1 more Smart Citation

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

Lazar¹,

Anastassiadis²

2009

Philosophical Magazine

View full text Add to dashboard Cite

show abstract

“…In our formulation the incompatibility tensor assumes the role of the 'charge' of dislocations, that interacts with the stress potential linearly, and through the variation by the potential it enters the equilibrium condition. A further interesting relation can be obtained by taking the plastic free energy (13) at the equilibrium stress potential χ eq . Substituting equation (6) into equation (13) and performing partial integrations one concludes that…”

Section: Derivation Of the Variational Approachmentioning

confidence: 99%

“…A further interesting relation can be obtained by taking the plastic free energy (13) at the equilibrium stress potential χ eq . Substituting equation (6) into equation (13) and performing partial integrations one concludes that…”

Section: Derivation Of the Variational Approachmentioning

confidence: 99%

Variational approach in dislocation theory

Groma

Györgyi

Ispánovity

2010

Philosophical Magazine

View full text Add to dashboard Cite

A variational approach is presented to calculate the stress field generated by a system of dislocations. It is shown that in the simplest case, when the material containing the dislocations obeys Hooke's law the variational framework gives the same field equations as Kröner's theory. However, the variational method proposed allows to study many other problems like dislocation core regularisation, role of elastic anharmonicity and dislocation-solute atom interaction. The aim of the paper is to demonstrate that these problems can be handled in a systematic manner.

show abstract

Screw dislocations in the field theory of elastoplasticity

Lazar

2002

Ann. Phys.

View full text Add to dashboard Cite

A (microscopic) static elastoplastic field theory of dislocations with moment and force stresses is considered. The relationship between the moment stress and the Nye tensor is used for the dislocation Lagrangian. We discuss the stress field of an infinitely long screw dislocation in a cylinder, a dipole of screw dislocations and a coaxial screw dislocation in a finite cylinder. The stress fields have no singularities in the dislocation core and they are modified in the core due to the presence of localized moment stress. Additionally, we calculated the elastoplastic energies for the screw dislocation in a cylinder and the coaxial screw dislocation. For the coaxial screw dislocation we find a modified formula for the so-called Eshelby twist which depends on a specific intrinsic material length.

show abstract

The T(3)-Gauge Model, the Einstein-Like Gauge Equation, and Volterra Dislocations with Modified Asymptotics

Cited by 44 publications

References 37 publications

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

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

Variational approach in dislocation theory

Screw dislocations in the field theory of elastoplasticity

Contact Info

Product

Resources

About