An elastoplastic theory of dislocations as a physical field theory with torsion

We consider a static theory of dislocations with moment stress in an anisotropic or isotropic elastoplastical material as a T(3)-gauge theory. We obtain Yang-Mills type field equations which express the force and the moment equilibrium. Additionally, we discuss several constitutive laws between the dislocation density and the moment stress. For a straight screw dislocation, we find the stress field which is modified near the dislocation core due to the appearance of moment stress. For the first time, we calculate the localized moment stress, the Nye tensor, the elastoplastic energy and the modified Peach-Koehler force of a screw dislocation in this framework. Moreover, we discuss the straightforward analogy between a screw dislocation and a magnetic vortex. The dislocation theory in solids is also considered as a three-dimensional effective theory of gravity.Comment: 38 pages, 6 figures, RevTe

Remarkable Objects: Supporting Collaboration in a Creative Environment

In this paper, we report the results of a field trial of a Ubicomp system called CAM that is aimed at supporting and enhancing collaboration in a design studio environment. CAM uses a mobile-tagging application which allows designers to collaboratively store relevant information onto their physical design objects in the form of messages, annotations and external web links. The purpose of our field trial was to explore the role of augmented objects in supporting and enhancing creative work. Our results show that CAM was used not only used to support participants’ mutual awareness and coordination but also to facilitate designers in appropriating their augmented design objects to be explorative, extendable and playful supporting creative aspects of design work. In general, our results show how CAM transformed static design objects into ‘remarkable’ objects that made the creative and playful side of cooperative design visible

Torsional Monopoles and Torqued Geometries in Gravity and Condensed Matter

Torsional degrees of freedom play an important role in modern gravity theories as well as in condensed matter systems where they can be modeled by defects in solids. Here we isolate a class of torsion models that support torsion configurations with a localized, conserved charge that adopts integer values. The charge is topological in nature and the torsional configurations can be thought of as torsional `monopole' solutions. We explore some of the properties of these configurations in gravity models with non-vanishing curvature, and discuss the possible existence of such monopoles in condensed matter systems. To conclude, we show how the monopoles can be thought of as a natural generalization of the Cartan spiral staircase.Comment: 4+epsilon, 1 figur

Stress-free states of continuum dislocation fields: Rotations, grain boundaries, and the Nye dislocation density tensor

We derive general relations between grain boundaries, rotational deformations, and stress-free states for the mesoscale continuum Nye dislocation density tensor. Dislocations generally are associated with long-range stress fields. We provide the general form for dislocation density fields whose stress fields vanish. We explain that a grain boundary (a dislocation wall satisfying Frank's formula) has vanishing stress in the continuum limit. We show that the general stress-free state can be written explicitly as a (perhaps continuous) superposition of flat Frank walls. We show that the stress-free states are also naturally interpreted as configurations generated by a general spatially-dependent rotational deformation. Finally, we propose a least-squares definition for the spatially-dependent rotation field of a general (stressful) dislocation density field.Comment: 9 pages, 3 figure

The Dislocation Stress Functions From the Double Curl T(3)-Gauge Equation: Linearity and a Look Beyond

T(3)-gauge model of defects based on the gauge Lagrangian quadratic in the gauge field strength is considered. The equilibrium equation of the medium is fulfilled by the double curl Kroner's ansatz for stresses. The problem of replication of the static edge dislocation along third axis is analysed under a special, though conventional, choice of this ansatz. The translational gauge equation is shown to constraint the functions parametrizing the ansatz (the stress functions) so that the resulting stress component $\sigma_{3 3}$ is not that of the edge defect. Another translational gauge equation with the double curl differential operator is shown to reproduce both the stress functions, as well as the stress tensors, of the standard edge and screw dislocations. Non-linear extension of the newly proposed translational gauge equation is given to correct the linear defect solutions in next orders. New gauge Lagrangian is suggested in the Hilbert-Einstein form.Comment: 21 pages, LaTeX, no figure

Volume elements and torsion

We reexamine here the issue of consistency of minimal action formulation with the minimal coupling procedure (MCP) in spaces with torsion. In Riemann-Cartan spaces, it is known that a proper use of the MCP requires that the trace of the torsion tensor be a gradient, $T_\mu=\partial_\mu\theta$, and that the modified volume element $\tau_\theta = e^\theta \sqrt{g} dx^1\wedge...\wedge dx^n$ be used in the action formulation of a physical model. We rederive this result here under considerably weaker assumptions, reinforcing some recent results about the inadequacy of propagating torsion theories of gravity to explain the available observational data. The results presented here also open the door to possible applications of the modified volume element in the geometric theory of crystalline defects.Comment: Revtex, 8 pages, 1 figure. v2 includes a discussion on $\lambda$-symmetr

A gauge theoretic approach to elasticity with microrotations

We formulate elasticity theory with microrotations using the framework of gauge theories, which has been developed and successfully applied in various areas of gravitation and cosmology. Following this approach, we demonstrate the existence of particle-like solutions. Mathematically this is due to the fact that our equations of motion are of Sine-Gordon type and thus have soliton type solutions. Similar to Skyrmions and Kinks in classical field theory, we can show explicitly that these solutions have a topological origin.Comment: 15 pages, 1 figure; revised and extended version, one extra page; revised and extended versio

Aharonov-Bohm Effect and Disclinations in an Elastic Medium

In this work we investigate quasiparticles in the background of defects in solids using the geometric theory of defects. We use the parallel transport matrix to study the Aharonov-Bohm effect in this background. For quasiparticles moving in this effective medium we demonstrate an effect similar to the gravitational Aharonov- Bohm effect. We analyze this effect in an elastic medium with one and $N$ defects.Comment: 6 pages, Revtex

Volterra Distortions, Spinning Strings, and Cosmic Defects

Cosmic strings, as topological spacetime defects, show striking resemblance to defects in solid continua: distortions, which can be classified into disclinations and dislocations, are line-like defects characterized by a delta function-valued curvature and torsion distribution giving rise to rotational and translational holonomy. We exploit this analogy and investigate how distortions can be adapted in a systematic manner from solid state systems to Einstein-Cartan gravity. As distortions are efficiently described within the framework of a SO(3) {\rlap{\supset}\times}} T(3) gauge theory of solid continua with line defects, we are led in a straightforward way to a Poincar\'e gauge approach to gravity which is a natural framework for introducing the notion of distorted spacetimes. Constructing all ten possible distorted spacetimes, we recover, inter alia, the well-known exterior spacetime of a spin-polarized cosmic string as a special case of such a geometry. In a second step, we search for matter distributions which, in Einstein-Cartan gravity, act as sources of distorted spacetimes. The resulting solutions, appropriately matched to the distorted vacua, are cylindrically symmetric and are interpreted as spin-polarized cosmic strings and cosmic dislocations.Comment: 24 pages, LaTeX, 9 eps figures; remarks on energy conditions added, discussion extended, version to be published in Class. Quantum Gra

On the incompatibility of strains and its application to mesoscopic studies of plasticity

Structural transitions are invariably affected by lattice distortions. If the body is to remain crack-free, the strain field cannot be arbitrary but has to satisfy the Saint-Venant compatibility constraint. Equivalently, an incompatibility constraint consistent with the actual dislocation network has to be satisfied in media with dislocations. This constraint can be incorporated into strain-based free energy functionals to study the influence of dislocations on phase stability. We provide a systematic analysis of this constraint in three dimensions and show how three incompatibility equations accommodate an arbitrary dislocation density. This approach allows the internal stress field to be calculated for an anisotropic material with spatially inhomogeneous microstructure and distribution of dislocations by minimizing the free energy. This is illustrated by calculating the stress field of an edge dislocation and comparing it with that of an edge dislocation in an infinite isotropic medium. We outline how this procedure can be utilized to study the interaction of plasticity with polarization and magnetization.Comment: 6 pages, 2 figures; will appear in Phys. Rev.