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Markus Lazar

Publications and source records attributed to Markus Lazar.

At least 55 records · Page 3Linked to original sources
arXiv2012

On the non-uniform motion of dislocations: The retarded elastic fields, the retarded dislocation tensor potentials and the Liénard-Wiechert tensor potentials

The purpose of this paper is the fundamental theory of the non-uniform motion of dislocations in two and three space-dimensions. We investigate the non-uniform motion of an arbitrary distribution of dislocations, a dislocation loop and straight dislocations in infinite media using the theory of incompatible elastodynamics. The equations of motion are derived for non-uniformly moving dislocations. The retarded elastic fields produced by a distribution of dislocations and the retarded dislocation tensor potentials are determined. New fundamental key-formulae for the dynamics of dislocations are derived (Jefimenko type and Heaviside-Feynman type equations of dislocations). In addition, exact closed-form solutions of the elastic fields produced by a dislocation loop are calculated as retarded line integral expressions for subsonic motion. The fields of the elastic velocity and elastic distortion surrounding the arbitrarily moving dislocation loop are given explicitly in terms of the so-called three-dimensional elastodynamic Liénard-Wiechert tensor potentials. The two-dimensional elastodynamic Liénard-Wiechert tensor potentials and the near-field approximation of the elastic fields for straight dislocations are calculated. The singularities of the near-fields of accelerating screw and edge dislocations are determined.

cond-mat.mtrl-sci↗
arXiv2012

The fundamentals of non-singular dislocations in the theory of gradient elasticity: dislocation loops and straight dislocations

The fundamental problem of non-singular dislocations in the framework of the theory of gradient elasticity is presented in this work. Gradient elasticity of Helmholtz type and bi-Helmholtz type are used. A general theory of non-singular dislocations is developed for linearly elastic, infinitely extended, homogeneous, and isotropic media. Dislocation loops and straight dislocations are investigated. Using the theory of gradient elasticity, the non-singular fields which are produced by arbitrary dislocation loops are given. `Modified' Mura, Peach-Koehler, and Burgers formulae are presented in the framework of gradient elasticity theory. These formulae are given in terms of an elementary function, which regularizes the classical expressions, obtained from the Green tensor of the Helmholtz-Navier equation and bi-Helmholtz-Navier equation. Using the mathematical method of Green's functions and the Fourier transform, exact, analytical, and non-singular solutions were found. The obtained dislocation fields are non-singular due to the regularization of the classical singular fields.

cond-mat.mtrl-sci↗
arXiv2012

The elastodynamic Liénard-Wiechert potentials and elastic fields of non-uniformly moving point and line forces

The purpose of this paper is to investigate the fundamental problem of the non-uniform subsonic motion of a point force and line forces in an unbounded, homogeneous, isotropic medium in analogy to the electromagnetic Liénard-Wiechert potentials. The exact closed-form solutions of the displacement and elastic fields produced by the point force and line forces are calculated. The displacement fields can be identified with the elastodynamic Liénard-Wiechert tensor potentials. For a non-uniformly moving point force, we decompose the elastic fields into a radiation part and a non-radiation part. We show that the solution of a non-uniformly moving point force is the generalization of the Stokes solution towards the non-uniform motion. For line forces the mathematical solutions are given in the form of time-integrals and, therefore, their motion depends on the history.

math-ph↗
arXiv2011

A screw dislocation in a functionally graded material using the translation gauge theory of dislocations

The aim of this paper is to provide new results and insights for a screw dislocation in functionally graded media within the gauge theory of dislocations. We present the equations of motion for dislocations in inhomogeneous media. We specify the equations of motion for a screw dislocation in a functionally graded material. The material properties are assumed to vary exponentially along the x and y-directions. In the present work we give the analytical gauge field theoretic solution to the problem of a screw dislocation in inhomogeneous media. Using the dislocation gauge approach, rigorous analytical expressions for the elastic distortions, the force stresses, the dislocation density and the pseudomoment stresses are obtained depending on the moduli of gradation and an effective intrinsic length scale characteristic for the functionally graded material under consideration.

cond-mat.mtrl-sci↗
arXiv2010

Cartan's spiral staircase in physics and, in particular, in the gauge theory of dislocations

In 1922, Cartan introduced in differential geometry, besides the Riemannian curvature, the new concept of torsion. He visualized a homogeneous and isotropic distribution of torsion in three dimensions (3d) by the "helical staircase", which he constructed by starting from a 3d Euclidean space and by defining a new connection via helical motions. We describe this geometric procedure in detail and define the corresponding connection and the torsion. The interdisciplinary nature of this subject is already evident from Cartan's discussion, since he argued - but never proved - that the helical staircase should correspond to a continuum with constant pressure and constant internal torque. We discuss where in physics the helical staircase is realized: (i) In the continuum mechanics of Cosserat media, (ii) in (fairly speculative) 3d theories of gravity, namely a) in 3d Einstein-Cartan gravity - this is Cartan's case of constant pressure and constant intrinsic torque - and b) in 3d Poincare gauge theory with the Mielke-Baekler Lagrangian, and, eventually, (iii) in the gauge field theory of dislocations of Lazar et al., as we prove for the first time by arranging a suitable distribution of screw dislocations. Our main emphasis is on the discussion of dislocation field theory.

cond-mat.mtrl-sci↗
arXiv2010

Generalized dynamics of moving dislocations in quasicrystals

A theoretical framework for dislocation dynamics in quasicrystals is provided according to the continuum theory of dislocations. Firstly, we present the fundamental theory for moving dislocations in quasicrystals giving the dislocation density tensors and introducing the dislocation current tensors for the phonon and phason fields, including the Bianchi identities. Next, we give the equations of motion for the incompatible elastodynamics as well as for the incompatible elasto-hydrodynamics of quasicrystals. We continue with the derivation of the balance law of pseudomomentum thereby obtaining the generalized forms of the Eshelby stress tensor, the pseudomomentum vector, the dynamical Peach-Koehler force density and the Cherepanov force density for quasicrystals. The form of the dynamical Peach-Koehler force for a straight dislocation is obtained as well. Moreover, we deduce the balance law of energy that gives rise to the generalized forms of the field intensity vector and the elastic power density of quasicrystals. The above balance laws are produced for both models. The differences between the two models and their consequences are revealed. The influences of the phason fields as well as of the dynamical terms are also discussed.

cond-mat.mtrl-sci↗
arXiv2010

The gauge theory of dislocations: a nonuniformly moving screw dislocation

We investigate the nonuniform motion of a straight screw dislocation in infinite media in the framework of the translational gauge theory of dislocations. The equations of motion are derived for an arbitrary moving screw dislocation. The fields of the elastic velocity, elastic distortion, dislocation density and dislocation current surrounding the arbitrarily moving screw dislocation are derived explicitely in the form of integral representations. We calculate the radiation fields and the fields depending on the dislocation velocities.

cond-mat.mtrl-sci↗
arXiv2010

On the fundamentals of the three-dimensional translation gauge theory of dislocations

We propose a dynamic version of the three-dimensional translation gauge theory of dislocations. In our approach, we use the notions of the dislocation density and dislocation current tensors as translational field strengths and the corresponding response quantities (pseudomoment stress, dislocation momentum flux). We derive a closed system of field equations in a very elegant quasi-Maxwellian form as equations of motion for dislocations. In this framework, the dynamical Peach-Koehler force density is derived as well. Finally, the similarities and the differences between the Maxwell field theory and the dislocation gauge theory are presented.

cond-mat.mtrl-sci↗
arXiv2009

The gauge theory of dislocations: a uniformly moving screw dislocation

In this paper we present the equations of motion of a moving screw dislocation in the framework of the translation gauge theory of dislocations. In the gauge field theoretical formulation, a dislocation is a massive gauge field. We calculate the gauge field theoretical solutions of a uniformly moving screw dislocation. We give the subsonic and supersonic solutions. Thus, supersonic dislocations are not forbidden from the field theoretical point of view. We show that the elastic divergences at the dislocation core are removed. We also discuss the Mach cones produced by supersonic screw dislocations.

cond-mat.mtrl-sci↗
arXiv2009

On the Higgs mechanism and stress functions in the translational gauge theory of dislocations

In this letter we discuss the Higgs mechanism in the linear and static translational gauge theory of dislocations. We investigate the role of the Nambu-Goldstone field and the Proca field in the dislocation gauge theory. In addition, we give the constitutive relations for (homogeneous) anisotropic, hemitropic and isotropic materials and also stress function tensors for the gauge theory of dislocations.

cond-mat.mtrl-sci↗
arXiv2008

The gauge theory of dislocations: conservation and balance laws

We derive conservation and balance laws for the translational gauge theory of dislocations by applying Noether's theorem. We present an improved translational gauge theory of dislocations including the dislocation density tensor and the dislocation current tensor. The invariance of the variational principle under the continuous group of transformations is studied. Through Lie's-infinitesimal invariance criterion we obtain conserved translational and rotational currents for the total Lagrangian made up of an elastic and dislocation part. We calculate the broken scaling current. Looking only on one part of the whole system, the conservation laws are changed into balance laws. Because of the lack of translational, rotational and dilatation invariance for each part, a configurational force, moment and power appears. The corresponding J, L and M integrals are obtained. Only isotropic and homogeneous materials are considered and we restrict ourselves to a linear theory. We choose constitutive laws for the most general linear form of material isotropy. Also we give the conservation and balance laws corresponding to the gauge symmetry and the addition of solutions. From the addition of solutions we derive a reciprocity theorem for the gauge theory of dislocations. Also, we derive the conservation laws for stress-free states of dislocations.

cond-mat.mtrl-sci↗
arXiv2008

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

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.

cond-mat.mtrl-sci↗
arXiv2005

Nonsingular stress and strain fields of dislocations and disclinations in first strain gradient elasticity

The aim of this paper is to study the elastic stress and strain fields of dislocations and disclinations in the framework of Mindlin's gradient elasticity. We consider simple but rigorous versions of Mindlin's first gradient elasticity with one material length (gradient coefficient). Using the stress function method, we find modified stress functions for all six types of Volterra defects (dislocations and disclinations) situated in an isotropic and infinitely extended medium. By means of these stress functions, we obtain exact analytical solutions for the stress and strain fields of dislocations and disclinations. An advantage of these solutions for the elastic strain and stress is that they have no singularities at the defect line. They are finite and have maxima or minima in the defect core region. The stresses and strains are either zero or have a finite maximum value at the defect line. The maximum value of stresses may serve as a measure of the critical stress level when fracture and failure may occur. Thus, both the stress and elastic strain singularities are removed in such a simple gradient theory. In addition, we give the relation to the nonlocal stresses in Eringen's nonlocal elasticity for the nonsingular stresses.

cond-mat.mtrl-sci↗
arXiv2005

Peach-Koehler forces within the theory of nonlocal elasticity

We consider dislocations in the framework of Eringen's nonlocal elasticity. The fundamental field equations of nonlocal elasticity are presented. Using these equations, the nonlocal force stresses of a straight screw and a straight edge dislocation are given. By the help of these nonlocal stresses, we are able to calculate the interaction forces between dislocations (Peach-Koehler forces). All classical singularities of the Peach-Koehler forces are eliminated. The extremum values of the forces are found near the dislocation line.

cond-mat.mtrl-sci↗
arXiv2003

Dislocations in the Field Theory of Elastoplasticity

By means of linear theory of elastoplasticity, solutions are given for screw and edge dislocations situated in an isotropic solid. The force stresses, strain fields, displacements, distortions, dislocation densities and moment stresses are calculated. The force stresses, strain fields, displacements and distortions are devoid of singularities predicted by the classical elasticity. Using the so-called stress function method we found modified stress functions of screw and edge dislocations.

cond-mat.mtrl-sci↗
arXiv2003

Twist disclination in the field theory of elastoplasticity

In this paper we study the twist disclination within the elastoplastic defect theory. Using the stress function method, we found exact analytical solutions for all characteristic fields of a straight twist disclination in an infinitely extended linear isotropic medium. The elastic stress, elastic strain and displacement have no singularities at the disclination line. We found modified stress functions for the twist disclination. In addition, we calculate the disclination density, effective Frank vector, disclination torsion and effective Burgers vector of a straight twist disclination. By means of gauge theory of defects we decompose the elastic distortion into the translational and rotational gauge fields of the straight twist disclination.

cond-mat.mtrl-sci↗
arXiv2003

Group Theoretical Analysis of Light-Cone Dominated Hadronic Processes and Twist Decomposition of Nonlocal Operators in Quantum Chromodynamics

In the framework of nonlocal light-cone expansion of two current operators we construct bilocal as well as trilocal QCD light-cone operators with definite geometric twist. We are able to decompose uniquely the appearing QCD light-cone operators into all their twist parts on the light-cone. The quark distribution functions and the vector meson distribution amplitudes which are defined as forward and skewed nucleonic matrix elements of nonlocal light-cone operators are classified with respect to geometric twist. Hereby we found well-kown and new Wandzura-Wilczek type relations between the quark distribution functions with dynamical twist and, additionally, between the vector meson distribution amplitudes with dynamical twist. Using group theoretical methods we are able to construct all bilocal off-cone QCD operators with twist 2 and 3. Additionally, we calculate their nucleonic matrix elements (double distribution functions, scalar and vector meson distribution amplitudes). In some special cases we give also the twist decomposition of off-cone QCD operators from minimal up to infinite twist.

hep-ph↗