Investigation of 3D crack propagation problems via fast BEM formulations

Kolk, K.; Weber, W.; Kühn, G.

doi:10.1007/s00466-005-0695-0

Cited by 29 publications

(18 citation statements)

References 16 publications

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“…In the coupled method, the fast marching method maintains the location and motion of the crack front via signed distance functions, whereas the X-FEM is used to compute the local front velocity. In keeping with standard level set notation, we use in three dimensions are: finite element methods [12,13], boundary element-based techniques [14][15][16][17][18][19], and boundary integral equations [20,21]. Gao and Rice [22] and Lai et al [23] used perturbation analysis to study planar and non-planar cracks, whereas Lazarus and coworkers [24][25][26] conducted planar crack growth simulations.…”

Section: Introductionmentioning

confidence: 99%

Three‐dimensional non‐planar crack growth by a coupled extended finite element and fast marching method

Sukumar

Chopp

Béchet

et al. 2008

Numerical Meth Engineering

114

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SUMMARYA numerical technique for non-planar three-dimensional linear elastic crack growth simulations is proposed. This technique couples the extended finite element method and the fast marching method.In crack modeling using the extended finite element method, the framework of partition of unity is used to enrich the standard finite element approximation by a discontinuous function and the twodimensional asymptotic crack-tip displacement fields. The initial crack geometry is represented by two level set functions, and subsequently signed distance functions are used to maintain the location of the crack and to compute the enrichment functions that appear in the displacement approximation.Crack modeling is performed without the need to mesh the crack, and crack propagation is simulated * Correspondence to: N. Sukumar,

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Section: Introductionmentioning

confidence: 99%

Three‐dimensional non‐planar crack growth by a coupled extended finite element and fast marching method

Sukumar

Chopp

Béchet

et al. 2008

Numerical Meth Engineering

114

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“…Additionally, the number of degrees of freedom (DOF) increases during the simulation and the limits for the storage capacity of the system matrix and the solution time of the linear system of equations are easily reached. Therefore, a fast BEM formulation in terms of the ACA, cf., [2,13], will be applied and explained in Sect. 2.2.2.…”

Section: Statement Of the Bvpmentioning

confidence: 99%

The advanced simulation of fatigue crack growth in complex 3D structures

Kolk¹,

Kühn²

2006

Arch Appl Mech

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An advanced incremental crack growth algorithm for the three-dimensional (3D) simulation of fatigue crack growth in complex 3D structures with linear elastic material behavior is presented. To perform the crack growth simulation as effectively as possible an accurate stress analysis is done by the boundaryelement method (BEM) in terms of the 3D dual BEM. The question concerning a reliable 3D crack growth criterion is answered based on experimental observations. All criteria under consideration are numerically realized by a predictor-corrector procedure. The agreement between numerically determined and experimentally observed crack fronts will be shown on both fracture specimens and an industrial application.

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“…There are also various papers on three-dimensional crack propagation, e.g. Mi and Aliabadi (1994), Kolk et al (2005), Meng et al (2013). Comprehensive lists of references on three-dimensional fracture problems could be found in the books by Cruse (1988) and Aliabadi (2002).…”

Section: Literature Reviewmentioning

confidence: 99%

Geomechanical Simulation of Fluid-Driven Fractures

Makhnenko¹,

Nikolskiy²,

Mogilevskaya³

et al. 2012

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The project supported graduate students working on experimental and numerical modeling of rock fracture, with the following objectives: (a) perform laboratory testing of fluid-saturated rock; (b) develop predictive models for simulation of fracture; and (c) establish educational frameworks for geologic sequestration issues related to rock fracture. These objectives were achieved through (i) using a novel apparatus to produce faulting in a fluid-saturated rock; (ii) modeling fracture with a boundary element method; and (iii) developing curricula for training geoengineers in experimental mechanics, numerical modeling of fracture, and poroelasticity.4 EXECUTIVE SUMMARYCarbon storage technologies offer a means of reducing CO 2 emissions and mitigating climate change. These new technologies will require a workforce educated in geomechanics. To this end, the project supported graduate students working on geomechanical simulation of fluid-driven fractures with the following objectives:1. Measure elastic and inelastic response of fluid-saturated rock 2. Develop predictive models for simulation of fluid-driven fractures 1. Deformation and damage of a porous, fluid-saturated rock under drained and undrained conditions were investigated. A plane-strain apparatus was modified in order to conduct tests with water-saturated rock specimens and to measure the pore pressure within the rock. Transducers within the apparatus were calibrated at the various loading states and the compliances of the system were determined. Plane strain compression and conventional triaxial compression tests were performed at different confining pressures under air-dry, drained, and undrained conditions. The behavior of the rock was evaluated within the framework of linear poroelasticity. Dilatant hardening and contractant softening was investigated from undrained experiments, where pore pressure was measured throughout the failure process. The parameters that govern the inelastic deformation of fluid-saturated rock, i.e. dilatancy angle β, friction coefficient µ, poroelastic coefficient K eff , shear modulus G, and inelastic hardening modulus H, were calculated for the drained response. The constitutive model predicts the undrained inelastic response of the rock fairly well, almost up to the peak load if compared with the undrained test that had the same effective mean stress at the onset of inelasticity. Knowledge of dilatant hardening behavior is essential for the proper assessment of underground structures, such as long-term CO 2 storage facilities.2. The boundary element method (BEM) is based on the boundary integral representation equivalent to the differential equation governing a specific physical problem. Such representation is possible when the so-called fundamental solution of the governing differential equation is available. The fundamental solution satisfies the differential equation everywhere in the domain except one point where it is singular. In the case of linear isotropic and homogeneous elasticity, the fundamental solution...

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Investigation of 3D crack propagation problems via fast BEM formulations

Cited by 29 publications

References 16 publications

Three‐dimensional non‐planar crack growth by a coupled extended finite element and fast marching method

Three‐dimensional non‐planar crack growth by a coupled extended finite element and fast marching method

The advanced simulation of fatigue crack growth in complex 3D structures

Geomechanical Simulation of Fluid-Driven Fractures

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