Alex Hansen

Origin of the universal roughness exponent of brittle fracture surfaces:stress-weighted percolation in the damage zone.

We suggest that the observed large-scale universal roughness of brittle fracture surfaces is due to the fracture propagation being a damage coalescence process described by a stress-weighted percolation phenomenon in a self-generated quadratic damage gradient. We use the quasistatic 2D fuse model as a paradigm of a mode I fracture model. We measure for this model, which exhibits a correlated percolation process, the correlation length exponent nu approximately 1.35 and conjecture it to be equal to that of classical percolation, 4/3. We then show that the roughness exponent in the 2D fuse model is zeta=2nu/(1+2nu)=8/11. This is in accordance with the numerical value zeta=0.75. Using the value for 3D percolation, nu=0.88, we predict the roughness exponent in the 3D fuse model to be zeta=0.64, in close agreement with the previously published value of 0.62+/-0.05. We furthermore predict zeta=4/5 for 3D brittle fractures, based on a recent calculation giving nu=2. This is in full accordance with the value zeta=0.80 found experimentally.

Fourier acceleration of iterative processes in disordered systems

Technical details are given on how to use Fourier acceleration with iterative processes such as relaxation and conjugate gradient methods. These methods are often used to solve large linear systems of equations, but become hopelessly slow very rapidly as the size of the set of equations to be solved increases. Fourier acceleration is a method designed to alleviate these problems and result in a very fast algorithm. The method is explained for the Jacobi relaxation and conjugate gradient methods and is applied to two models: the random resistor network and the random central-force network. In the first model, acceleration works very well; in the second, little is gained. We discuss reasons for this. We also include a discussion of stopping criteria.

Burst avalanches in bundles of fibers: Local versus global load-sharing

Abstract Bursts in bundles of many parallel fibers with stochastically distributed failure thresholds are studied. The distribution of the sizes Δ of burst avalanches has a power-law behavior, ∞Δ-ξ. When the load is shared equally among surviving fibers, the power-law exponent is ξ=2.5. When, however, the increased stresses that result from a fiber failure are concentrated to the nearest-neighbor fibers, the exponent is considerably higher, for randomly distributed thresholds ξ=4.5.

Roughness of Interfacial Crack Fronts: Stress-Weighted Percolation in the Damage Zone

We study numerically the roughness exponent zeta of an in-plane fracture front slowly propagating along a heterogeneous interface embedded in an elastic body, using a model based on the evolution of a process zone rather than a fracture line. We find zeta=0.60+/-0.05. For the first time, simulation results are in close agreement with experimental results. We then show that the roughness exponent is related to the correlation length exponent nu of a stress-weighted percolation problem through zeta=nu/(1+nu). A numerical study of the stress-weighted percolation problem yields nu=1.54 giving zeta=0.61 in close agreement with our numerical results and with experimental observations.

Are stress distributions along faults the signature of asperity squeeze

[1] We propose a possible model for the origin of the spatial fluctuations of the stress field along faults and test our model in the case of the Nojima fault, Japan where unique estimates of the absolute stress field have been obtained. The model consists of two parts: an up-scaling of the fault morphology measured at laboratory scales and a numerical computation using a boundary element approach of the influence on the stress field along the fault of an elastic squeeze of the fault asperities. Accordingly, fluctuations of the stress field along the fault would be dominated by quenched fault properties rather than dynamical stress fluctuations produced during earthquakes. Citation: Schmittbuhl, J., G. Chambon, A. Hansen, and M. Bouchon (2006), Are stress distributions along faults the signature of asperity squeeze?, Geophys. Res. Lett., 33, L13307, doi:10.1029/2006GL025952.

Fracture roughness scaling: A case study on planar cracks

Using a multi-resolution technique, we analyze large in-plane fracture fronts moving slowly between two sintered Plexiglas plates. We find that the roughness of the front exhibits two distinct regimes separated by a crossover length scale

Statistical mechanics of warm and cold unfolding in proteins

\delta^*

Heterogeneous interfacial failure between two elastic blocks.

. Below

Some Physical Properties of Self-Affine Rough Surfaces

\delta^*

Rupture of heterogeneous media in the limit of infinite disorder

, we observe a multi-affine regime and the measured roughness exponent