A 3D benchmark problem for crack propagation in brittle fracture

Hug, Lisa; Kollmannsberger, Stefan; Yosibash, Zohar; Rank, Ernst

doi:10.1016/j.cma.2020.112905

Cited by 19 publications

(12 citation statements)

References 45 publications

(69 reference statements)

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“…On the other hand, the realized (actual) flows are an outcome of an optimized transmission process that maximizes the global throughput subject to the redundancies of, and the capacities of member segments or bonds along, the percolating paths through the specimen. Results here are consistent with recent experiments on ceramics 3,4 , metallic glasses 6 and graphite 39 . www.nature.com/scientificreports/ 2.…”

Section: Resultssupporting

confidence: 93%

Early prediction of macrocrack location in concrete, rocks and other granular composite materials

Tordesillas

Kahagalage

Ras

et al. 2020

Sci Rep

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Heterogeneous quasibrittle composites like concrete, ceramics and rocks comprise grains held together by bonds. The question on whether or not the path of the crack that leads to failure can be predicted from known microstructural features, viz. bond connectivity, size, fracture surface energy and strength, remains open. Many fracture criteria exist. The most widely used are based on a postulated stress and/or energy extremal. Since force and energy share common transmission paths, their flow bottleneck may be the precursory failure mechanism to reconcile these optimality criteria in one unified framework. We explore this in the framework of network flow theory, using microstructural data from 3D discrete element models of concrete under uniaxial tension. We find the force and energy bottlenecks emerge in the same path and provide an early and accurate prediction of the ultimate macrocrack path $${\mathcal {C}}$$ C . Relative to all feasible crack paths, the Griffith’s fracture surface energy and the Francfort–Marigo energy functional are minimum in $${\mathcal {C}}$$ C ; likewise for the critical strain energy density if bonds are uniformly sized. Redundancies in transmission paths govern prefailure dynamics, and predispose $${\mathcal {C}}$$ C to cascading failure during which the concomitant energy release rate and normal (Rankine) stress become maximum along $${\mathcal {C}}$$ C .

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Section: Resultssupporting

confidence: 93%

Early prediction of macrocrack location in concrete, rocks and other granular composite materials

Tordesillas

Kahagalage

Ras

et al. 2020

Sci Rep

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“…These discretization techniques are used in tandem to perform numerical simulations on domains with complex geometries. Noteworthy application areas include the analysis of bone-implant systems [48], the simulation of metal additive manufacturing processes [49] and the modeling of crack growth in brittle structures by means of a phase-field approach [50].…”

Section: The Finite Cell Methods and Multi-level Hp-refinementmentioning

confidence: 99%

Hierarchical multigrid approaches for the finite cell method on uniform and multi-level hp-refined grids

Jomo,

Oztoprak,

de Prenter

et al. 2020

Preprint

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This contribution presents a hierarchical multigrid approach for the solution of large-scale finite cell problems on both uniform grids and multi-level hp-discretizations. The proposed scheme leverages the hierarchical nature of the basis functions utilized in the finite cell method and the multi-level hp-method, which is attributed to the use of high-order integrated Legendre basis functions and overlay meshes, to yield a simple and elegant multigrid scheme. This simplicity is reflected in the fact that all restriction and prolongation operators reduce to binary matrices that do not need to be explicitly constructed. The coarse spaces are constructed over the different polynomial orders and refinement levels of the immersed discretization. Elementwise and patchwise additive Schwarz smoothing techniques are used to mitigate the influence of the cut cells leading to convergence rates that are independent of the cut configuration, mesh size and in certain scenarios even the polynomial order. The multigrid approach is applied to second-order problems arising from the Poisson equation and linear elasticity. A series of numerical examples demonstrate the applicability of the scheme for solving large immersed systems with multiple millions and even billions of unknowns on massively parallel machines.

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“…ey adopted the fourth-order Runge-Kutta method and finite difference method for the integration in time and the spatial differential operator, respectively, with a cosine initial condition. Hug et al [16] proposed a benchmark problem for brittle fracture.…”

Section: Introductionmentioning

confidence: 99%

Benchmark Problems for the Numerical Schemes of the Phase‐Field Equations

Hwang

Lee

Kwak

et al. 2022

Discrete Dynamics in Nature and Society

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In this study, we present benchmark problems for the numerical methods of the phase-field equations. To find appropriate benchmark problems, we first perform a linear stability analysis and then take a growth mode solution as the benchmark problem, which is closely related to the dynamics of the original governing equations. As concrete examples, we perform convergence tests of the numerical methods of the Allen–Cahn (AC) and Cahn–Hilliard (CH) equations using the proposed benchmark problems. The one- and two-dimensional computational experiments confirm the accuracy and efficiency of the proposed scheme as the benchmark problems.

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A 3D benchmark problem for crack propagation in brittle fracture

Cited by 19 publications

References 45 publications

Early prediction of macrocrack location in concrete, rocks and other granular composite materials

Early prediction of macrocrack location in concrete, rocks and other granular composite materials

Hierarchical multigrid approaches for the finite cell method on uniform and multi-level hp-refined grids

Benchmark Problems for the Numerical Schemes of the Phase‐Field Equations

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