Fracturing the optimal paths

Optimal paths play a fundamental role in numerous physical applications ranging from random polymers to brittle fracture, from the flow through porous media to information propagation. Here for the first time we explore the path that is activated once this optimal path fails and what happens when this new path also fails and so on, until the system is completely disconnected. In fact numerous applications can be found for this novel fracture problem. In the limit of strong disorder, our results show that all the cracks are located on a single self-similar connected line of fractal dimension $D_{b} \approx 1.22$. For weak disorder, the number of cracks spreads all over the entire network before global connectivity is lost. Strikingly, the disconnecting path (backbone) is, however, completely independent on the disorder.Comment: 4 pages,4 figure

From invasion percolation to flow in rock fracture networks

The main purpose of this work is to simulate two-phase flow in the form of immiscible displacement through anisotropic, three-dimensional (3D) discrete fracture networks (DFN). The considered DFNs are artificially generated, based on a general distribution function or are conditioned on measured data from deep geological investigations. We introduce several modifications to the invasion percolation (MIP) to incorporate fracture inclinations, intersection lines, as well as the hydraulic path length inside the fractures. Additionally a trapping algorithm is implemented that forbids any advance of the invading fluid into a region, where the defending fluid is completely encircled by the invader and has no escape route. We study invasion, saturation, and flow through artificial fracture networks, with varying anisotropy and size and finally compare our findings to well studied, conditioned fracture networks.Comment: 18 pages, 10 figure

Estimating Flow Rates through Fracture Networks using Combinatorial Optimization

To enable fast uncertainty quantification of fluid flow in a discrete fracture network (DFN), we present two approaches to quickly compute fluid flow in DFNs using combinatorial optimization algorithms. Specifically, the presented Hanan Shortest Path Maxflow (HSPM) and Intersection Shortest Path Maxflow (ISPM) methods translate DFN geometries and properties to a graph on which a max flow algorithm computes a combinatorial flow, from which an overall fluid flow rate is estimated using a shortest path decomposition of this flow. The two approaches are assessed by comparing their predictions with results from explicit numerical simulations of simple test cases as well as stochastic DFN realizations covering a range of fracture densities. Both methods have a high accuracy and very low computational cost, which can facilitate much-needed in-depth analyses of the propagation of uncertainty in fracture and fracture-network properties to fluid flow rates

3d numerical model of a confined fracture tests in concrete

The paper deals with the numerical simulation of a confined fracture test in concrete. The test is part of the experimental work carried out at ETSECCPB-UPC in order to elucidate the existence of a second mode of fracture under shear and high compression, and evaluate the associated fracture energy. The specimen is a short cylinder with also cylindrical coaxial notches similar the one proposed by Luong (1990), which is introduced in a largecapacity triaxial cell, protected with membranes and subject to different levels of confining pressure prior to vertical loading. In the experiments, the main crack follows the preestablished cylindrical notch path, which is in itself a significant achievement. The loaddisplacement curves for various confining pressures also seem to follow the expected trend according to the underlying conceptual model. The FE model developed includes zerothickness interface elements with fracture-based constitutive laws, which are pre-inserted along the cylindrical ligament and the potential radial crack plane. The results reproduce reasonably well the overall force-displacement curves of the test for various confinement levels, and make it possible to identify the fracture parameters including the fracture energies in modes I and IIa

A fracture-controlled path-following technique for phase-field modeling of brittle fracture

In the phase-field description of brittle fracture, the fracture-surface area can be expressed as a functional of the phase field (or damage field). In this work we study the applicability of this explicit expression as a (non-linear) path-following constraint to robustly track the equilibrium path in quasi-static fracture propagation simulations, which can include snap-back phenomena. Moreover, we derive a fracture-controlled staggered solution procedure by systematic decoupling of the path-following controlled elasticity and phase-field problems. The fracture-controlled monolithic and staggered solution procedures are studied for a series of numerical test cases. The numerical results demonstrate the robustness of the new approach, and provide insight in the advantages and disadvantages of the monolithic and staggered procedures

Quasicontinuum simulation of fracture at the atomic scale

We study the problem of atomic scale fracture using the recently developed quasicontinuum method in which there is a systematic thinning of the atomic-level degrees of freedom in regions where they are not needed. Fracture is considered in two distinct settings. First, a study is made of cracks in single crystals, and second, we consider a crack advancing towards a grain boundary (GB) in its path. In the investigation of single crystal fracture, we evaluate the competition between simple cleavage and crack-tip dislocation emission. In addition, we examine the ability of analytic models to correctly predict fracture behaviour, and find that the existing analytical treatments are too restrictive in their treatment of nonlinearity near the crack tip. In the study of GB-crack interactions, we have found a number of interesting deformation mechanisms which attend the advance of the crack. These include the migration of the GB, the emission of dislocations from the GB, and deflection of the crack front along the GB itself. In each case, these mechanisms are rationalized on the basis of continuum mechanics arguments

Porous LSCF/Dense 3YSZ Interface Fracture Toughness Measured by Single Cantilever Beam Wedge Test

Sandwich specimens were prepared by firing a thin inter-layer of porous La0.6Sr0.4Co0.2Fe0.8O3-d (LSCF) to bond a thin tetragonal yttria-stabilised zirconia (YSZ) beam to a thick YSZ substrate. Fracture of the joint was evaluated by introducing a wedge between the two YSZ adherands so that the stored energy in the thin YSZ cantilever beam drives a stable crack in the adhesive bond and allows the critical energy release rate for crack extension (fracture toughness) to be measured. The crack path in most specimens showed a mixture of adhesive failure (at the YSZ-LSCF interface) and cohesive failure (within the LSCF). It was found that the extent of adhesive fracture increased with firing temperature and decreased with LSCF layer thickness. The adhesive failures were mainly at the interface between the LSCF and the thin YSZ beam and FEM modelling revealed that this is due to asymmetric stresses in the LSCF. Within the firing temperature range of 1000-1150C, the bonding fracture toughness appears to have a strong dependence on firing temperature. However, the intrinsic adhesive fracture toughness of the LSCF/YSZ interface was estimated to be 11 Jm2 and was not firing temperature dependent within the temperature range investigated.Comment: 13 figures, 1 table, journal paper publishe