36 research outputs found
Scaling of Fracture Strength in Disordered Quasi-Brittle Materials
This paper presents two main results. The first result indicates that in
materials with broadly distributed microscopic heterogeneities, the fracture
strength distribution corresponding to the peak load of the material response
does not follow the commonly used Weibull and (modified) Gumbel distributions.
Instead, a {\it lognormal} distribution describes more adequately the fracture
strengths corresponding to the peak load of the response. Lognormal
distribution arises naturally as a consequence of multiplicative nature of
large number of random distributions representing the stress scale factors
necessary to break the subsequent "primary" bond (by definition, an increase in
applied stress is required to break a "primary" bond) leading up to the peak
load. Numerical simulations based on two-dimensional triangular and diamond
lattice topologies with increasing system sizes substantiate that a {\it
lognormal} distribution represents an excellent fit for the fracture strength
distribution at the peak load. The second significant result of the present
study is that, in materials with broadly distributed microscopic
heterogeneities, the mean fracture strength of the lattice system behaves as
, and scales as as the lattice system size, , approaches
infinity.Comment: 24 pages including 11 figure
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
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
Crack avalanches in the three dimensional random fuse model
We analyze the scaling of avalanche precursors in the three dimensional
random fuse model by numerical simulations. We find that both the integrated
and non-integrated avalanche size distributions are in good agreement with the
results of the global load sharing fiber bundle model, which represents the
mean-field limit of the model.Comment: 6 pages, 2 figures, submitted for the proceedings of the conference
"Physics Survey of Irregular Systems", in honor of Bernard Sapova
Role of the sample thickness in planar crack propagation
We study the effect of the sample thickness in planar crack front propagation in a disordered elastic medium using the random fuse model. We employ different loading conditions and we test their stability with respect to crack growth. We show that the thickness induces characteristic lengths in the stress enhancement factor in front of the crack and in the stress transfer function parallel to the crack. This is reflected by a thickness-dependent crossover scale in the crack front morphology that goes from from multiscaling to self-affine with exponents, in agreement with line depinning models and experiments. Finally, we compute the distribution of crack avalanches, which is shown to depend on the thickness and the loading mode.Peer reviewe
Crack roughness and avalanche precursors in the random fuse model
We analyze the scaling of the crack roughness and of avalanche precursors in
the two dimensional random fuse model by numerical simulations, employing large
system sizes and extensive sample averaging. We find that the crack roughness
exhibits anomalous scaling, as recently observed in experiments. The roughness
exponents (, ) and the global width distributions are found
to be universal with respect to the lattice geometry. Failure is preceded by
avalanche precursors whose distribution follows a power law up to a cutoff
size. While the characteristic avalanche size scales as , with a
universal fractal dimension , the distribution exponent differs
slightly for triangular and diamond lattices and, in both cases, it is larger
than the mean-field (fiber bundle) value
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
Sub-matrix updates for the Continuous-Time Auxiliary Field algorithm
We present a sub-matrix update algorithm for the continuous-time auxiliary
field method that allows the simulation of large lattice and impurity problems.
The algorithm takes optimal advantage of modern CPU architectures by
consistently using matrix instead of vector operations, resulting in a speedup
of a factor of and thereby allowing access to larger systems and
lower temperature. We illustrate the power of our algorithm at the example of a
cluster dynamical mean field simulation of the N\'{e}el transition in the
three-dimensional Hubbard model, where we show momentum dependent self-energies
for clusters with up to 100 sites
Fracture roughness in three-dimensional beam lattice systems
We study the scaling of three-dimensional crack roughness using large-scale beam lattice systems. Our results for prenotched samples indicate that the crack surface is statistically isotropic, with the implication that experimental findings of anisotropy of fracture surface roughness in directions parallel and perpendicular to crack propagation is not due to the scalar or vectorial elasticity of the model. In contrast to scalar fuse lattices, beam lattice systems do not exhibit anomalous scaling or an extra dependence of roughness on system size. The local and global roughness exponents (ζloc and ζ, respectively) are equal to each other, and the three-dimensional crack roughness exponent is estimated to be ζloc=ζ=0.48±0.03. This closely matches the roughness exponent observed outside the fracture process zone. The probability density distribution p[Δh(ℓ)] of the height differences Δh(ℓ)=[h(x+ℓ)−h(x)] of the crack profile follows a Gaussian distribution, in agreement with experimental results.Peer reviewe
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