1,051 research outputs found
Fibers on a graph with local load sharing
We study a random fiber bundle model with tips of the fibers placed on a
graph having co-ordination number 3. These fibers follow local load sharing
with uniformly distributed threshold strengths of the fibers. We have studied
the critical behaviour of the model numerically using a finite size scaling
method and the mean field critical behaviour is established. The avalanche size
distribution is also found to exhibit a mean field nature in the asymptotic
limit.Comment: 9 pages, 6 figures, To appear in International Journal of Modern
Physics
Dynamic model of fiber bundles
A realistic continuous-time dynamics for fiber bundles is introduced and
studied both analytically and numerically. The equation of motion reproduces
known stationary-state results in the deterministic limit while the system
under non-vanishing stress always breaks down in the presence of noise.
Revealed in particular is the characteristic time evolution that the system
tends to resist the stress for considerable time, followed by sudden complete
rupture. The critical stress beyond which the complete rupture emerges is also
obtained
Onset of Localization in Heterogeneous Interfacial Failure
We study numerically the failure of an interface joining two elastic
materials under load using a fiber bundle model connected to an elastic half
space. We find that the breakdown process follows the equal load sharing fiber
bundle model without any detectable spatial correlations between the positions
of the failing fibers until localization sets in. The onset of localization is
an instability, not a phase transition. Depending on the elastic constant
describing the elastic half space, localization sets in before or after the
critical load causing the interface to fail completely, is reached. There is a
crossover between failure due to localization or failure without spatial
correlations when tuning the elastic constant, not a phase transition. Contrary
to earlier claims based on models different from ours, we find that a finite
fraction of fibers must fail before the critical load is attained, even in the
extreme localization regime, i.e.\ for very small elastic constant. We
furthermore find that the critical load remains finite for all values of the
elastic constant in the limit of an infinitely large system.Comment: 4 pages, 5 figure
Failure properties of loaded fiber bundles having a lower cutoff in fiber threshold distribution
Presence of lower cutoff in fiber threshold distribution may affect the
failure properties of a bundle of fibers subjected to external load. We
investigate this possibility both in a equal load sharing (ELS) fiber bundle
model and in local load sharing (LLS) one. We show analytically that in ELS
model, the critical strength gets modified due to the presence of lower cutoff
and it becomes bounded by an upper limit. Although the dynamic exponents for
the susceptibility and relaxation time remain unchanged, the avalanche size
distribution shows a permanent deviation from the mean-fiels power law. In the
LLS model, we analytically estimate the upper limit of the lower cutoff above
which the bundle fails at one instant. Also the system size variation of
bundle's strength and the avalanche statistics show strong dependence on the
lower cutoff level.Comment: 7 pages and 7 figure
Breakdown of disordered media by surface loads
We model an interface layer connecting two parts of a solid body by N
parallel elastic springs connecting two rigid blocks. We load the system by a
shear force acting on the top side. The springs have equal stiffness but are
ruptured randomly when the load reaches a critical value. For the considered
system, we calculate the shear modulus, G, as a function of the order
parameter, \phi, describing the state of damage, and also the ``spalled''
material (burst) size distribution. In particular, we evaluate the relation
between the damage parameter and the applied force and explore the behaviour in
the vicinity of material breakdown. Using this simple model for material
breakdown, we show that damage, caused by applied shear forces, is analogous to
a first-order phase transition. The scaling behaviour of G with \phi is
explored analytically and numerically, close to \phi=0 and \phi=1 and in the
vicinity of \phi_c, when the shear load is close but below the threshold force
that causes material breakdown. Our model calculation represents a first
approximation of a system subject to wear induced loads.Comment: 15 pages, 7 figure
Dynamic model for failures in biological systems
A dynamic model for failures in biological organisms is proposed and studied
both analytically and numerically. Each cell in the organism becomes dead under
sufficiently strong stress, and is then allowed to be healed with some
probability. It is found that unlike the case of no healing, the organism in
general does not completely break down even in the presence of noise. Revealed
is the characteristic time evolution that the system tends to resist the stress
longer than the system without healing, followed by sudden breakdown with some
fraction of cells surviving. When the noise is weak, the critical stress beyond
which the system breaks down increases rapidly as the healing parameter is
raised from zero, indicative of the importance of healing in biological
systems.Comment: To appear in Europhys. Let
A random fiber bundle with many discontinuities in the threshold distribution
We study the breakdown of a random fiber bundle model (RFBM) with
-discontinuities in the threshold distribution using the global load sharing
scheme. In other words, different classes of fibers identified on the
basis of their threshold strengths are mixed such that the strengths of the
fibers in the class are uniformly distributed between the values
and where . Moreover, there
is a gap in the threshold distribution between and class. We
show that although the critical stress depends on the parameter values of the
system, the critical exponents are identical to that obtained in the recursive
dynamics of a RFBM with a uniform distribution and global load sharing. The
avalanche size distribution (ASD), on the other hand, shows a non-universal,
non-power law behavior for smaller values of avalanche sizes which becomes
prominent only when a critical distribution is approached. We establish that
the behavior of the avalanche size distribution for an arbitrary is
qualitatively similar to a RFBM with a single discontinuity in the threshold
distribution (), especially when the density and the range of threshold
values of fibers belonging to strongest ()-th class is kept identical in
all the cases.Comment: 6 pages, 4 figures, Accepted in Phys. Rev.
Crossover Behavior in Burst Avalanches of Fiber Bundles: Signature of Imminent Failure
Bundles of many fibers, with statistically distributed thresholds for
breakdown of individual fibers and where the load carried by a bursting fiber
is equally distributed among the surviving members, are considered. During the
breakdown process, avalanches consisting of simultaneous rupture of several
fibers occur, with a distribution D(Delta) of the magnitude Delta of such
avalanches. We show that there is, for certain threshold distributions, a
crossover behavior of D(Delta) between two power laws D(Delta) proportional to
Delta^(-xi), with xi=3/2 or xi=5/2. The latter is known to be the generic
behavior, and we give the condition for which the D(Delta) proportional to
Delta^(-3/2) behavior is seen. This crossover is a signal of imminent
catastrophic failure in the fiber bundle. We find the same crossover behavior
in the fuse model.Comment: 4 pages, 4 figure
Energy bursts in fiber bundle models of composite materials
As a model of composite materials, a bundle of many fibers with
stochastically distributed breaking thresholds for the individual fibers is
considered. The bundle is loaded until complete failure to capture the failure
scenario of composite materials under external load. The fibers are assumed to
share the load equally, and to obey Hookean elasticity right up to the breaking
point. We determine the distribution of bursts in which an amount of energy
is released. The energy distribution follows asymptotically a universal power
law , for any statistical distribution of fiber strengths. A similar
power law dependence is found in some experimental acoustic emission studies of
loaded composite materials.Comment: 5 pages, 4 fig
A thermodynamical fiber bundle model for the fracture of disordered materials
We investigate a disordered version of a thermodynamic fiber bundle model
proposed by Selinger, Wang, Gelbart, and Ben-Shaul a few years ago. For simple
forms of disorder, the model is analytically tractable and displays some new
features. At either constant stress or constant strain, there is a non
monotonic increase of the fraction of broken fibers as a function of
temperature. Moreover, the same values of some macroscopic quantities as stress
and strain may correspond to different microscopic cofigurations, which can be
essential for determining the thermal activation time of the fracture. We argue
that different microscopic states may be characterized by an experimentally
accessible analog of the Edwards-Anderson parameter. At zero temperature, we
recover the behavior of the irreversible fiber bundle model.Comment: 18 pages, 10 figure
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