10,898 research outputs found
The effect of forest dislocations on the evolution of a phase-field model for plastic slip
We consider the gradient flow evolution of a phase-field model for crystal dislocations in a single slip system in the presence of forest dislocations. The model is based on a Peierls-Nabarro type energy penalizing non-integer slip and elastic stress. Forest dislocations are introduced as a perforation of the domain by small disks where slip is prohibited. The Γ-limit of this energy was deduced by Garroni and Müller (2005 and 2006). Our main result shows that the gradient flows of these Γ-convergent energy functionals do not approach the gradient flow of the limiting energy. Indeed, the gradient flow dynamics remains a physically reasonable model in the case of non-monotone loading. Our proofs rely on the construction of explicit sub- and super-solutions to a fractional Allen-Cahn equation on a flat torus or in the plane, with Dirichlet data on a union of small discs. The presence of these obstacles leads to an additional friction in the viscous evolution which appears as a stored energy in the Γ-limit, but it does not act as a driving force. Extensions to related models with soft pinning and non-viscous evolutions are also discussed. In terms of physics, our results explain how in this phase field model the presence of forest dislocations still allows for plastic as opposed to only elastic deformation
Dislocation microstructures and strain-gradient plasticity with one active slip plane
We study dislocation networks in the plane using the vectorial phase-field
model introduced by Ortiz and coworkers, in the limit of small lattice spacing.
We show that, in a scaling regime where the total length of the dislocations is
large, the phase field model reduces to a simpler model of the strain-gradient
type. The limiting model contains a term describing the three-dimensional
elastic energy and a strain-gradient term describing the energy of the
geometrically necessary dislocations, characterized by the tangential gradient
of the slip. The energy density appearing in the strain-gradient term is
determined by the solution of a cell problem, which depends on the line tension
energy of dislocations. In the case of cubic crystals with isotropic elasticity
our model shows that complex microstructures may form, in which dislocations
with different Burgers vector and orientation react with each other to reduce
the total self energy
Interstitials, Vacancies and Dislocations in Flux-Line Lattices: A Theory of Vortex Crystals, Supersolids and Liquids
We study a three dimensional Abrikosov vortex lattice in the presence of an
equilibrium concentration of vacancy, interstitial and dislocation loops.
Vacancies and interstitials renormalize the long-wavelength bulk and tilt
elastic moduli. Dislocation loops lead to the vanishing of the long-wavelength
shear modulus. The coupling to vacancies and interstitials - which are always
present in the liquid state - allows dislocations to relax stresses by climbing
out of their glide plane. Surprisingly, this mechanism does not yield any
further independent renormalization of the tilt and compressional moduli at
long wavelengths. The long wavelength properties of the resulting state are
formally identical to that of the ``flux-line hexatic'' that is a candidate
``normal'' hexatically ordered vortex liquid state.Comment: 21 RevTeX pgs, 7 eps figures uuencoded; corrected typos, published
versio
Deblocking of interacting particle assemblies: from pinning to jamming
A wide variety of interacting particle assemblies driven by an external force
are characterized by a transition between a blocked and a moving phase. The
origin of this deblocking transition can be traced back to the presence of
either external quenched disorder, or of internal constraints. The first case
belongs to the realm of the depinning transition, which, for example, is
relevant for flux-lines in type II superconductors and other elastic systems
moving in a random medium. The second case is usually included within the
so-called jamming scenario observed, for instance, in many glassy materials as
well as in plastically deforming crystals. Here we review some aspects of the
rich phenomenology observed in interacting particle models. In particular, we
discuss front depinning, observed when particles are injected inside a random
medium from the boundary, elastic and plastic depinning in particle assemblies
driven by external forces, and the rheology of systems close to the jamming
transition. We emphasize similarities and differences in these phenomena.Comment: 20 pages, 8 figures, submitted for a special issue of the Brazilian
Journal of Physics entitled: Statistical Mechanics of Irreversible Stochastic
Models - I
Defects in Chiral Columnar Phases: Tilt Grain Boundaries and Iterated Moire Maps
Biomolecules are often very long with a definite chirality. DNA, xanthan and
poly-gamma-benzyl-glutamate (PBLG) can all form columnar crystalline phases.
The chirality, however, competes with the tendency for crystalline order. For
chiral polymers, there are two sorts of chirality: the first describes the
usual cholesteric-like twist of the local director around a pitch axis, while
the second favors the rotation of the local bond-orientational order and leads
to a braiding of the polymers along an average direction. In the former case
chirality can be manifested in a tilt grain boundary phase (TGB) analogous to
the Renn-Lubensky phase of smectic-A liquid crystals. In the latter case we are
led to a new "moire" state with twisted bond order. In the moire state polymers
are simultaneously entangled, crystalline, and aligned, on average, in a common
direction. In the moire state polymers are simultaneously entangled,
crystalline, and aligned, on average, in a common direction. In this case the
polymer trajectories in the plane perpendicular to their average direction are
described by iterated moire maps of remarkable complexity, reminiscent of
dynamical systems.Comment: plain TeX, (33 pages), 17 figures, some uufiled and included, the
remaining available at ftp://ftp.sns.ias.edu/pub/kamien/ or by request to
[email protected]
Collective pinning of the vortex lattice by columnar defects in layered superconductors
The mixed phase of layered superconductors with no magnetic screening is
studied through a partial duality analysis of the corresponding frustrated XY
model in the presence of random columnar pins. A small fraction of pinned
vortex lines is assumed. Thermally induced plastic creep of the vortex lattice
within isolated layers results in an intermediate Bose glass phase that
exhibits weak superconductivity across layers in the limit of weak Josephson
coupling. The correlation volume of the vortex lattice is estimated in the
strongly-coupled Bose-glass regime at lower temperature. In the absence of
additional point pins, no peak effect in the critical current density is
predicted to occur on this basis as a function of the Josephson coupling. Also,
the phase transition observed recently inside of the vortex-liquid phase of
high-temperature superconductors pierced by sparse columnar defects is argued
to be a sign of dimensional cross-over.Comment: 16 pages, 1 figure, account of transition to ``nanoliquid'' in BSCCO,
to appear in PR
Depinning and plasticity of driven disordered lattices
We review in these notes the dynamics of extended condensed matter systesm,
such as vortex lattices in type-II superconductors and charge density waves in
anisotropic metals, driven over quenched disorder. We focus in particular on
the case of strong disorder, where topological defects are generated in the
driven lattice. In this case the repsonse is plastic and the depinning
transition may become discontinuous and hysteretic.Comment: 21 pages, 6 figures. Proceedings the XIX Sitges Conference on
Jamming, Yielding, and Irreversible Deformations in Condensed Matter, Sitges,
Barcelona, Spain, June 14-18, 200
Vortices in a Thin Film Superconductor with a Spherical Geometry
We report results from Monte Carlo simulations of a thin film superconductor
in a spherical geometry within the lowest Landau level approximation. We
observe the absence of a phase transition to a low temperature vortex solid
phase with these boundary conditions; the system remains in the vortex liquid
phase for all accessible temperatures. The correlation lengths are measured for
phase coherence and density modulation. Both lengths display identical
temperature dependences, with an asymptotic scaling form consistent with a
continuous zero temperature transition. This contrasts with the first order
freezing transition which is seen in the alternative quasi-periodic boundary
conditions. The high temperature perturbation theory and the ground states of
the spherical system suggest that the thermodynamic limit of the spherical
geometry is the same as that on the flat plane. We discuss the advantages and
drawbacks of simulations with different geometries, and compare with current
experimental conclusions. The effect of having a large scale inhomogeneity in
the applied field is also considered.Comment: This replacment contains substantial revisions: the new article is
twice as long with new and different results on the thermodynamic limit on
the sphere plus a full discussion on the alternative boundary conditions used
in simulations in the LLL approximation. 19 pages, 12 encapsulated PostScript
figures, 1 JPEG figure, uses RevTeX (with epsf
Spatial fluctuations in transient creep deformation
We study the spatial fluctuations of transient creep deformation of materials
as a function of time, both by Digital Image Correlation (DIC) measurements of
paper samples and by numerical simulations of a crystal plasticity or discrete
dislocation dynamics model. This model has a jamming or yielding phase
transition, around which power-law or Andrade creep is found. During primary
creep, the relative strength of the strain rate fluctuations increases with
time in both cases - the spatially averaged creep rate obeys the Andrade law
, while the time dependence of the spatial
fluctuations of the local creep rates is given by . A similar scaling for the fluctuations is found in the logarithmic
creep regime that is typically observed for lower applied stresses. We review
briefly some classical theories of Andrade creep from the point of view of such
spatial fluctuations. We consider these phenomenological, time-dependent creep
laws in terms of a description based on a non-equilibrium phase transition
separating evolving and frozen states of the system when the externally applied
load is varied. Such an interpretation is discussed further by the data
collapse of the local deformations in the spirit of absorbing state/depinning
phase transitions, as well as deformation-deformation correlations and the
width of the cumulative strain distributions. The results are also compared
with the order parameter fluctuations observed close to the depinning
transition of the 2 Linear Interface Model or the quenched Edwards-Wilkinson
equation.Comment: 27 pages, 18 figure
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