24 research outputs found
Statistical properties of fracture in a random spring model
Using large scale numerical simulations we analyze the statistical properties
of fracture in the two dimensional random spring model and compare it with its
scalar counterpart: the random fuse model. We first consider the process of
crack localization measuring the evolution of damage as the external load is
raised. We find that, as in the fuse model, damage is initially uniform and
localizes at peak load. Scaling laws for the damage density, fracture strength
and avalanche distributions follow with slight variations the behavior observed
in the random fuse model. We thus conclude that scalar models provide a
faithful representation of the fracture properties of disordered systems.Comment: 12 pages, 17 figures, 1 gif figur
A Fast and Efficient Algorithm for Slater Determinant Updates in Quantum Monte Carlo Simulations
We present an efficient low-rank updating algorithm for updating the trial
wavefunctions used in Quantum Monte Carlo (QMC) simulations. The algorithm is
based on low-rank updating of the Slater determinants. In particular, the
computational complexity of the algorithm is O(kN) during the k-th step
compared with traditional algorithms that require O(N^2) computations, where N
is the system size. For single determinant trial wavefunctions the new
algorithm is faster than the traditional O(N^2) Sherman-Morrison algorithm for
up to O(N) updates. For multideterminant configuration-interaction type trial
wavefunctions of M+1 determinants, the new algorithm is significantly more
efficient, saving both O(MN^2) work and O(MN^2) storage. The algorithm enables
more accurate and significantly more efficient QMC calculations using
configuration interaction type wavefunctions
Effect of Disorder and Notches on Crack Roughness
We analyze the effect of disorder and notches on crack roughness in two
dimensions. Our simulation results based on large system sizes and extensive
statistical sampling indicate that the crack surface exhibits a universal local
roughness of and is independent of the initial notch size
and disorder in breaking thresholds. The global roughness exponent scales as
and is also independent of material disorder. Furthermore, we
note that the statistical distribution of crack profile height fluctuations is
also independent of material disorder and is described by a Gaussian
distribution, albeit deviations are observed in the tails.Comment: 6 pages, 6 figure
An Efficient Block Circulant Preconditioner For Simulating Fracture Using Large Fuse Networks
{\it Critical slowing down} associated with the iterative solvers close to
the critical point often hinders large-scale numerical simulation of fracture
using discrete lattice networks. This paper presents a block circlant
preconditioner for iterative solvers for the simulation of progressive fracture
in disordered, quasi-brittle materials using large discrete lattice networks.
The average computational cost of the present alorithm per iteration is , where the stiffness matrix is partioned into
-by- blocks such that each block is an -by- matrix, and
represents the operational count associated with solving a block-diagonal
matrix with -by- dense matrix blocks. This algorithm using the block
circulant preconditioner is faster than the Fourier accelerated preconditioned
conjugate gradient (PCG) algorithm, and alleviates the {\it critical slowing
down} that is especially severe close to the critical point. Numerical results
using random resistor networks substantiate the efficiency of the present
algorithm.Comment: 16 pages including 2 figure
Role of disorder in the size-scaling of material strength
We study the sample size dependence of the strength of disordered materials
with a flaw, by numerical simulations of lattice models for fracture. We find a
crossover between a regime controlled by the fluctuations due to disorder and
another controlled by stress-concentrations, ruled by continuum fracture
mechanics. The results are formulated in terms of a scaling law involving a
statistical fracture process zone. Its existence and scaling properties are
only revealed by sampling over many configurations of the disorder. The scaling
law is in good agreement with experimental results obtained from notched paper
samples.Comment: 4 pages 5 figure
Fracture Strength of Disordered Media: Universality, Interactions, and Tail Asymptotics
We study the asymptotic properties of fracture strength distributions of disordered elastic media by a combination of renormalization group, extreme value theory, and numerical simulation. We investigate the validity of the “weakest-link hypothesis” in the presence of realistic long-ranged interactions in the random fuse model. Numerical simulations indicate that the fracture strength is well-described by the Duxbury-Leath-Beale (DLB) distribution which is shown to flow asymptotically to the Gumbel distribution. We explore the relation between the extreme value distributions and the DLB-type asymptotic distributions and show that the universal extreme value forms may not be appropriate to describe the nonuniversal low-strength tail.Peer reviewe
Morphology of two dimensional fracture surface
We consider the morphology of two dimensional cracks observed in experimental
results obtained from paper samples and compare these results with the
numerical simulations of the random fuse model (RFM). We demonstrate that the
data obey multiscaling at small scales but cross over to self-affine scaling at
larger scales. Next, we show that the roughness exponent of the random fuse
model is recovered by a simpler model that produces a connected crack, while a
directed crack yields a different result, close to a random walk. We discuss
the multiscaling behavior of all these models.Comment: slightly revise
Size effects in statistical fracture
We review statistical theories and numerical methods employed to consider the
sample size dependence of the failure strength distribution of disordered
materials. We first overview the analytical predictions of extreme value
statistics and fiber bundle models and discuss their limitations. Next, we
review energetic and geometric approaches to fracture size effects for
specimens with a flaw. Finally, we overview the numerical simulations of
lattice models and compare with theoretical models.Comment: review article 19 pages, 5 figure