An Adaptive Domain Decomposition Preconditioner for Crack Propagation Problems Modeled by Xfem

Waisman, Haim; Berger-Vergiat, Luc

doi:10.1615/intjmultcompeng.2013006012

Cited by 35 publications

(21 citation statements)

References 54 publications

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“…In practical XFEM realizations, the stress and strain are computed in a Cartesian coordinate system, so both quantities need to be transformed into a polar coordinate system shown in Equations (49) and (50). The transformation relation for displacements is given in Equation (41) and for stresses is given as:…”

Section: Numerical Formulation Of Irwin's Integralmentioning

confidence: 99%

A High‐order extended finite element method for extraction of mixed‐mode strain energy release rates in arbitrary crack settings based on Irwin's integral

Lan

Waisman

Harari

2013

Numerical Meth Engineering

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SUMMARYAn analytical formulation based on Irwin's integral and combined with the extended finite element method is proposed to extract mixed-mode components of strain energy release rates in linear elastic fracture mechanics. The proposed formulation extends our previous work to cracks in arbitrary orientations and is therefore suited for crack propagation problems. In essence, the approach employs high-order enrichment functions and evaluates Irwin's integral in closed form, once the linear system is solved and the algebraic degrees of freedom are determined.Several benchmark examples are investigated including off-center cracks, inclined cracks, and two crack growth problems. On all these problems, the method is shown to work well, giving accurate results. Moreover, because of its analytical nature, no special post-processing is required. Thus, we conclude that this method may provide a good and simple alternative to the popular J-integral method. In addition, it may circumvent some of the limitations of the J-integral in 3D modeling and in problems involving branching and coalescence of cracks.

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Section: Numerical Formulation Of Irwin's Integralmentioning

confidence: 99%

A High‐order extended finite element method for extraction of mixed‐mode strain energy release rates in arbitrary crack settings based on Irwin's integral

Lan

Waisman

Harari

2013

Numerical Meth Engineering

Self Cite

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“…[42]. Multigrid methods, either as iterative methods or as a preconditioners, have been studied in many application areas: for the Helmholtz equation when analyzing frequency responses of an structure [14], for plasticity problems [85] or recently in fracture mechanics with the XFEM method [83]. In contrast, direct solvers are not as popular as iterative solvers.…”

Section: Algebraic Solversmentioning

confidence: 99%

Alya: Computational Solid Mechanics for Supercomputers

Casoni

Jérusalem

Samaniego

et al. 2014

Arch Computat Methods Eng

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While solid mechanics codes are now conventional tools both in industry and research, the increasingly more exigent requirements of both sectors are fuelling the need for more computational power and more advanced algorithms. For obvious reasons, commercial codes are lagging behind academic codes often dedicated either to the implementation of one new technique, or the upscaling of current conventional codes to tackle massively large scale computational problems. Only in a few cases, both approaches have been followed simultaneously. In this article, a solid mechanics simulation strategy for parallel supercomputers based on a hybrid approach is presented. Hybrid parallelization exploits the thread-level parallelism of multicore architectures, com- bining MPI tasks with OpenMP threads. This paper describes the proposed strategy, programmed in Alya, a parallel multiphysics code. Hybrid parallelization is specially well suited for the current trend of supercomputers, namely large clusters of multicores. The strategy is assessed through transient non-linear solid mechanics problems, both for explicit and implicit schemes, running on thousands of cores. In order to demonstrate the flexibility of the proposed strategy under advance algorithmic evolution of computational mechanics, a non-local parallel overset meshes method (Chimera-like) is implemented and the conservation of the scalability is demonstrated.

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“…However, in most applications, modeling the crack propagation at the scale of constituents up to the macroscale is, in general, not tractable. In the recent years, a few attempts have been devoted to multiscale modeling of damage from microscale crack propagation, including, among many others: FE 2 -approaches considering separated scales and microscale nonlinear damage, 1,2 extended FE 2 techniques with discontinuities at the macroscale, [3][4][5][6] domain decompositions methods embedding discontinuities, [7][8][9] or more recently methodologies enabling the identification of regularized damage models at the macroscale from microscale calculations. 10,11 In the mentioned works, only deterministic geometries and crack paths were considered.…”

Section: Introductionmentioning

confidence: 99%

Stochastic multiscale modeling of crack propagation in random heterogeneous media

Hun

Guilleminot

Yvonnet

et al. 2019

Numerical Meth Engineering

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Summary A stochastic approach to model crack propagation in random heterogeneous media, using mesoscopic representations of elastic and fracture properties, is presented. In order to obtain reference results, Monte‐Carlo simulations are first conducted on microstructural samples in which a pre‐existing crack is propagated by means of a phase‐field approach. These computations are used to estimate the subscale‐induced randomness on the macroscopic response of the domain. Mesoscopic descriptors are then introduced to investigate scale transition. Elasticity tensor random fields are specifically defined, at that stage, through a moving‐window upscaling approach. The mesoscopic fracture toughness, which is assumed homogeneous and deterministic, is identified by solving an inverse problem involving the macroscopic peak force. A stochastic model is subsequently constructed in which the mesoscopic elasticity is described as a non‐Gaussian random field. This model allows the multiscale‐informed elastic counterpart in the phase‐field formulation to be sampled without resorting to computational homogenization. The results obtained with the sample‐based and model‐based mesoscopic descriptions are finally compared with those corresponding to the full‐scale microscopic model. It is shown, in particular, that the mesoscopic elasticity‐phase‐field formulation associated with statically uniform boundary conditions enables the accurate predictions of the mean elastic response and mean peak force.

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An Adaptive Domain Decomposition Preconditioner for Crack Propagation Problems Modeled by Xfem

Cited by 35 publications

References 54 publications

A High‐order extended finite element method for extraction of mixed‐mode strain energy release rates in arbitrary crack settings based on Irwin's integral

A High‐order extended finite element method for extraction of mixed‐mode strain energy release rates in arbitrary crack settings based on Irwin's integral

Alya: Computational Solid Mechanics for Supercomputers

Stochastic multiscale modeling of crack propagation in random heterogeneous media

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