Cover refinement of numerical manifold method for crack propagation simulation

Shikou, Yang; Ma, Guowei; Ren, Xuhua; Ren, Feng

doi:10.1016/j.enganabound.2014.03.005

Cited by 43 publications

(4 citation statements)

References 40 publications

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“…In the presence of singularities such as crack tips, Yang et al developed a procedure for local refinement [22]. Zhang et al solved thermo-mechanical fracture problems in two-dimensional setting [23], where the singularity of temperature as well as displacement is reflected.…”

Section: Introductionmentioning

confidence: 99%

Complementarity problem arising from static growth of multiple cracks and MLS-based numerical manifold method

Zheng

Liu

2015

Computer Methods in Applied Mechanics and Engineering

142

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Section: Introductionmentioning

confidence: 99%

Complementarity problem arising from static growth of multiple cracks and MLS-based numerical manifold method

Zheng

Liu

2015

Computer Methods in Applied Mechanics and Engineering

142

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“…As a more general scheme, a manifold-based mass lumping scheme was recently presented by Yang et al 26 in the context of partition of unity (PU) method, 27 specifically the numerical manifold method (NMM), 28 which has been successfully applied to structures, [29][30][31][32][33][34] cracks, [35][36][37][38][39][40][41] fluids, [42][43][44] and large deformation. 45,46 The manifold-based mass lumping scheme is a rigorous and unified approach.…”

Section: Introductionmentioning

confidence: 99%

A new family of high‐order triangular weight functions for mass lumping in vibration analysis

Fan

Huang

Wang

2023

Numerical Meth Engineering

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In the conventional finite element method, only a few types of elements can directly use the weight functions to generate a proper, diagonally lumped mass matrix (LMM), which satisfies mass conservation and positive definiteness. This study proposes a new set of weight functions that can be efficiently constructed and used for generating a proper LMM based on classical 6‐, 9‐, and 10‐node triangular elements. Furthermore, we prove that these new elements are all complete and consistent, which ensures the convergence of the numerical solution. Finally, some modal and forced/free vibration analyses are conducted to demonstrate the computational accuracy and validation of the proposed LMM.

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“…Considering the crack surface contact, the stability analysis of the rock slope was studied based on the Mohr-Coulomb criterion with a tensile cutoff (Ning Y. J. et al, 2011;An et al, 2014). Based on a cover refinement method, Yang et al (2014) modeled cracks with contact. The second type is that the crack tips are allowed to stay at any position of physical patch.…”

Section: Introductionmentioning

confidence: 99%

MLS-Based Numerical Manifold Method for Modeling the Cracked Rock Considering the Contact of the Crack Surface

Zheng

et al. 2022

Front. Earth Sci.

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To simulate the moving boundary problems, the moving least square–based numerical manifold method, abbreviated as MLS-based NMM, was proposed. The MLS-based NMM has been applied successfully to open crack problems, which exhibits the high accuracy and strong robustness. In this study, we extend the MLS-based NMM to simulate the cracked rock considering the contact of the crack surface. Simultaneously, in order to simulate the progressive failure of the cracked rock, an improved strength-based criterion is proposed. The criterion is based on the Mohr–Coulomb criterion and maximum tensile stress criterion. Because rock can be regarded as a quasi-brittle material, a characteristic distance is used to calculate the crack tip stress and correct the crack propagation direction which avoids the phenomenon of “Zig-zag” for the crack propagation path based on the fracture mechanics criterion. The proposed strength-based criterion can acquire the crack tip stress and propagation direction and also realize the automatic determination of the crack propagation length in each step of the crack growth. A Brazilian disc problem and a rectangular plate problem are adopted to verify the numerical model. At last, the numerical model is applied to study the progressive failure process of the rock slope. The results indicate that the proposed method can deal with the crack propagation in the rock and the opening/sliding of rock blocks along discontinuities in a natural way.

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Cover refinement of numerical manifold method for crack propagation simulation

Cited by 43 publications

References 40 publications

Complementarity problem arising from static growth of multiple cracks and MLS-based numerical manifold method

Complementarity problem arising from static growth of multiple cracks and MLS-based numerical manifold method

A new family of high‐order triangular weight functions for mass lumping in vibration analysis

MLS-Based Numerical Manifold Method for Modeling the Cracked Rock Considering the Contact of the Crack Surface

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