5,264 research outputs found
Shear band dynamics from a mesoscopic modeling of plasticity
The ubiquitous appearance of regions of localized deformation (shear bands)
in different kinds of disordered materials under shear is studied in the
context of a mesoscopic model of plasticity. The model may or may not include
relaxational (aging) effects. In the absence of relaxational effects the model
displays a monotonously increasing dependence of stress on strain-rate, and
stationary shear bands do not occur. However, in start up experiments transient
(although long lived) shear bands occur, that widen without bound in time. I
investigate this transient effect in detail, reproducing and explaining a t^1/2
law for the thickness increase of the shear band that has been obtained in
atomistic numerical simulations. Relaxation produces a negative sloped region
in the stress vs. strain-rate curve that stabilizes the formation of shear
bands of a well defined width, which is a function of strain-rate. Simulations
at very low strain-rates reveal a non-trivial stick-slip dynamics of very thin
shear bands that has relevance in the study of seismic phenomena. In addition,
other non-stationary processes, such as stop-and-go, or strain-rate inversion
situations display a phenomenology that matches very well the results of recent
experimental studies.Comment: 10 pages, 10 figure
Heterogeneities in amorphous systems under shear
The last decade has seen major progresses in studies of elementary mechanisms
of deformation in amorphous materials. Here, we start with a review of
physically-based theories of plasticity, going back to the identification of
"shear-transformations" as early as the 70's. We show how constructive
criticism of the theoretical models permits to formulate questions concerning
the role of structural disorder, mechanical noise, and long-ranged elastic
interactions. These questions provide the necessary context to understand what
has motivated recent numerical studies. We then summarize their results, show
why they had to focus on athermal systems, and point out the outstanding
questions.Comment: Chapter of "Dynamical Heterogeneities in glasses, colloids and
granular materials", Eds.: L. Berthier, G. Biroli, J-P Bouchaud, L.
Cipelletti and W. van Saarloos (Oxford University Press, to appear), more
info at http://w3.lcvn.univ-montp2.fr/~lucacip/DH_book.ht
On the critical nature of plastic flow: one and two dimensional models
Steady state plastic flows have been compared to developed turbulence because
the two phenomena share the inherent complexity of particle trajectories, the
scale free spatial patterns and the power law statistics of fluctuations. The
origin of the apparently chaotic and at the same time highly correlated
microscopic response in plasticity remains hidden behind conventional
engineering models which are based on smooth fitting functions. To regain
access to fluctuations, we study in this paper a minimal mesoscopic model whose
goal is to elucidate the origin of scale free behavior in plasticity. We limit
our description to fcc type crystals and leave out both temperature and rate
effects. We provide simple illustrations of the fact that complexity in rate
independent athermal plastic flows is due to marginal stability of the
underlying elastic system. Our conclusions are based on a reduction of an
over-damped visco-elasticity problem for a system with a rugged elastic energy
landscape to an integer valued automaton. We start with an overdamped one
dimensional model and show that it reproduces the main macroscopic
phenomenology of rate independent plastic behavior but falls short of
generating self similar structure of fluctuations. We then provide evidence
that a two dimensional model is already adequate for describing power law
statistics of avalanches and fractal character of dislocation patterning. In
addition to capturing experimentally measured critical exponents, the proposed
minimal model shows finite size scaling collapse and generates realistic shape
functions in the scaling laws.Comment: 72 pages, 40 Figures, International Journal of Engineering Science
for the special issue in honor of Victor Berdichevsky, 201
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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