3D crack propagation by the numerical manifold method

Shikou, Yang; Cao, Maosen; Ren, Xiaobing; Ma, Guowei; Zhang, Jixun; Wang, Haijun

doi:10.1016/j.compstruc.2017.09.008

Cited by 38 publications

(6 citation statements)

References 50 publications

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“…The phase field method often requires very refined meshes in order to represent high aspect ratio fractures. XFEMs avoid re-meshing by representing fractures as a shape function discontinuity, but often require re-meshing in order to resolve stresses and fracture propagation in initially coarsely discretised regions of the model [31,32].…”

Section: Introductionmentioning

confidence: 99%

Growth of three-dimensional fractures, arrays, and networks in brittle rocks under tension and compression

Thomas

Paluszny

Zimmerman

2020

Computers and Geotechnics

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Concurrent growth of multiple fractures in brittle rock is a complex process due to mechanical interaction effects. Fractures can amplify or shield stress on other fracture tips, and stress field perturbations change continuously during fracture growth. A three-dimensional, finite-element based, quasi-static growth algorithm is validated for mixed mode fracture growth in linear elastic media, and is used to investigate concurrent fracture growth in arrays and networks.Growth is governed by fracture tip stress intensity factors, which quantify the energy contributing to fracture extension, and are validated against analytical solutions for fractures under compression and tension, demonstrating that growth is accurate even in coarsely meshed domains. Isolated fracture geometries are compared to wing cracks grown in experiments on brittle media. A novel formulation of a Paris-type extension criterion is introduced to handle concurrent fracture growth. Fracture and volume-based growth rate exponents are shown to modify fracture interaction patterns. A geomechanical discrete fracture network is generated and examined during its growth, whose properties are the direct result of the imposed anisotropic stress field and mutual fracture interaction. Two-dimensional cut-plane views of the network demonstrate how fractures would appear in outcrops, and show the variability in fracture traces arising during interaction and growth.

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Section: Introductionmentioning

confidence: 99%

Growth of three-dimensional fractures, arrays, and networks in brittle rocks under tension and compression

Thomas

Paluszny

Zimmerman

2020

Computers and Geotechnics

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“…An et al 11 summarized constructions of local approximations for diverse discontinuities. Tsay et al, 12 Ning et al, 13 Zheng et al, 7 Yang et al, 14 Wu et al, 15‐17 and Yang et al 18 performed crack propagation modeling and simulations. Modeling of weak discontinuities such as material interfaces has also been investigated 19 .…”

Section: Introductionmentioning

confidence: 99%

Smoothed numerical manifold method with physical patch‐based smoothing domains for linear elasticity

Liu

Zhang

Sun

et al. 2020

Numerical Meth Engineering

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Smoothed finite element method with the node-based strain smoothing domains (NS-FEM) is remarkable for the upper-bound feature and insensitivity to the volumetric locking. As a mesh-based methodology, its application is limited by the burdensome meshing for which elements align with the physical domain. We extend the strain smoothing in NS-FEM to the numerical manifold method (NMM) with unfitted meshes, and propose a novel methodology named physical patch-based smoothed NMM. Benchmark problems demonstrate the optimal convergence, stability in term of the condition number, upper-bound property, suppression of the volumetric locking, as well as the stress stability.

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“…Numerical simulation is a new technique that has been developed in recent years, which can directly reflect the internal mechanisms of rock fracture, which is regarded as the “third method” of scientific studies. The finite element method (FEM) [ 10 ] is one of the earliest methods that was used in rock damage simulations; however, it relies heavily on mesh grids. Mesh refinements should be carried out for the discontinuous properties such as cracks or holes.…”

Section: Introductionmentioning

confidence: 99%

Shear Damage Simulations of Rock Masses Containing Fissure-Holes Using an Improved SPH Method

Yang

Ren

et al. 2023

Materials

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Fissures and holes widely exist in rock mechanics engineering, and, at present, their failure mechanisms under complex compress and shear stress states have not been well recognized. In our work, a fracture mark, ξ, is introduced, and the kernel function of the smoothed-particle hydrodynamics (SPH) is then re-written, thus realizing the fracture modelling of the rock media. Then, the numerical models containing the fissures and holes are established, and their progressive failure processes under the compress and shear stress states are simulated, with the results showing that: (1) the improved SPH method can reflect the dynamic crack propagation processes of the rock masses, and the numerical results are in good agreement with the previous experimental results. Meanwhile, the improved SPH method can get rid of the traditional mesh re-division problems, which can be well-applied to rock failure modeling; (2) the hole shapes, fissure angles, fissure lengths, fissure numbers, and confining pressure all have great impacts on the final failure modes and peak strengths of the model; and (3) in practical engineering, the rock masses are in the 3D stress state, therefore, developing a high performance 3D SPH program and applying it to engineering in practice will be of great significance.

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3D crack propagation by the numerical manifold method

Cited by 38 publications

References 50 publications

Growth of three-dimensional fractures, arrays, and networks in brittle rocks under tension and compression

Growth of three-dimensional fractures, arrays, and networks in brittle rocks under tension and compression

Smoothed numerical manifold method with physical patch‐based smoothing domains for linear elasticity

Shear Damage Simulations of Rock Masses Containing Fissure-Holes Using an Improved SPH Method

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