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.

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.

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 (ζ(loc) and ζ, respectively) are equal to each other, and the three-dimensional crack roughness exponent is estimated to be ζ(loc)=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.

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 wave functions 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 kth step compared to traditional algorithms that require O(N(2)) computations, where N is the system size. For single determinant trial wave functions 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 wave functions 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 wave functions.

Crack roughness in the two-dimensional random threshold beam model.

We study the scaling of two-dimensional crack roughness using large scale beam lattice systems. Our results indicate that the crack roughness obtained using beam lattice systems does not exhibit anomalous scaling in sharp contrast to the simulation results obtained using scalar fuse lattices. The local and global roughness exponents (zetaloc and zeta, respectively) are equal to each other, and the two-dimensional crack roughness exponent is estimated to be zetaloc = zeta = 0.64+/-0.02 . Removal of overhangs (jumps) in the crack profiles eliminates even the minute differences between the local and global roughness exponents. Furthermore, removing these jumps in the crack profile completely eliminates the multiscaling observed in other studies. We find that the probability density distribution p[Deltah(l)] of the height differences Deltah(l)=[h(x+l)-h(x)] of the crack profile obtained after removing the jumps in the profiles follows a Gaussian distribution even for small window sizes (l) .

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 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 revealed only by sampling over many configurations of the disorder. The scaling law is in good agreement with experimental results obtained from notched paper samples.

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 zeta(loc)=0.71 and is independent of the initial notch size and disorder in breaking thresholds. The global roughness exponent scales as zeta=0.87 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.

A continuous damage random thresholds model for simulating the fracture behavior of nacre.

This study investigates the fracture properties of nacre using a discrete lattice model based on continuous damage random threshold fuse network. The discrete lattice topology of the model is based on nacre's unique brick and mortar microarchitecture. The mechanical behavior of each of the bonds in the discrete lattice model is governed by the characteristic modular damage evolution of the organic matrix and the mineral bridges between the aragonite platelets. The numerical results obtained using this simple discrete lattice model are in very good agreement with the previously obtained experimental results, such as nacre's stiffness, tensile strength, and work of fracture. The analysis indicates that nacre's superior toughness is a direct consequence of ductility (maximum shear strain) of the organic matrix in terms of repeated unfolding of protein molecules, and its fracture strength is a result of its ordered brick and mortar architecture with significant overlap of the platelets, and shear strength of the organic matrix.