A simple beam model for the shear failure of interfaces

We propose a novel model for the shear failure of a glued interface between two solid blocks. We model the interface as an array of elastic beams which experience stretching and bending under shear load and break if the two deformation modes exceed randomly distributed breaking thresholds. The two breaking modes can be independent or combined in the form of a von Mises type breaking criterion. Assuming global load sharing following the beam breaking, we obtain analytically the macroscopic constitutive behavior of the system and describe the microscopic process of the progressive failure of the interface. We work out an efficient simulation technique which allows for the study of large systems. The limiting case of very localized interaction of surface elements is explored by computer simulations.Comment: 11 pages, 13 figure

Quantitative analysis of numerical estimates for the permeability of porous media from lattice-Boltzmann simulations

During the last decade, lattice-Boltzmann (LB) simulations have been improved to become an efficient tool for determining the permeability of porous media samples. However, well known improvements of the original algorithm are often not implemented. These include for example multirelaxation time schemes or improved boundary conditions, as well as different possibilities to impose a pressure gradient. This paper shows that a significant difference of the calculated permeabilities can be found unless one uses a carefully selected setup. We present a detailed discussion of possible simulation setups and quantitative studies of the influence of simulation parameters. We illustrate our results by applying the algorithm to a Fontainebleau sandstone and by comparing our benchmark studies to other numerical permeability measurements in the literature.Comment: 14 pages, 11 figure

Continuous Damage Fiber Bundle Model for Strongly Disordered Materials

We present an extension of the continuous damage fiber bundle model to describe the gradual degradation of highly heterogeneous materials under an increasing external load. Breaking of a fiber in the model is preceded by a sequence of partial failure events occurring at random threshold values. In order to capture the subsequent propagation and arrest of cracks, furthermore, the disorder of the number of degradation steps of material constituents, the failure thresholds of single fibers are sorted into ascending order and their total number is a Poissonian distributed random variable over the fibers. Analytical and numerical calculations showed that the failure process of the system is governed by extreme value statistics, which has a substantial effect on the macroscopic constitutive behaviour and on the microscopic bursting activity as well.Comment: 10 pages, 13 figure

Searching for optimal variables in real multivariate stochastic data

By implementing a recent technique for the determination of stochastic eigendirections of two coupled stochastic variables, we investigate the evolution of fluctuations of NO2 concentrations at two monitoring stations in the city of Lisbon, Portugal. We analyze the stochastic part of the measurements recorded at the monitoring stations by means of a method where the two concentrations are considered as stochastic variables evolving according to a system of coupled stochastic differential equations. Analysis of their structure allows for transforming the set of measured variables to a set of derived variables, one of them with reduced stochasticity. For the specific case of NO2 concentration measures, the set of derived variables are well approximated by a global rotation of the original set of measured variables. We conclude that the stochastic sources at each station are independent from each other and typically have amplitudes of the order of the deterministic contributions. Such findings show significant limitations when predicting such quantities. Still, we briefly discuss how predictive power can be increased in general in the light of our methods