Time-dependent deformation and failure of granite based on the virtual crack incorporated numerical manifold method

Yu, Xian-yang; Xu, Tao; Heap, Michael; Baud, Patrick; Reuschlé, Thierry; Heng, Zhen; Zhu, Wancheng; Wang, Xingwei

doi:10.1016/j.compgeo.2021.104070

Cited by 21 publications

(1 citation statement)

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“…Great progress has been made in its theory and application. It has been successfully applied to solving problems of solid mechanics, 17,18 geomechanics, 3,17,[19][20][21][22][23][24][25][26][27][28][29][30][31][32][33] fracture, 4,7,19,[34][35][36][37][38][39][40][41][42][43][44][45][46] heat conduction, 47 electromagnetics, 48 and structure analyses. 5,49,50 NMM was also coupled with other methods to further improve the performance.…”

Section: Introductionmentioning

confidence: 99%

Preconditioned smoothed numerical manifold methods with unfitted meshes

Liu,

Guan,

Tong

et al. 2023

Numerical Meth Engineering

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The numerical manifold method (NMM) has been widely utilized to solve problems involving complicated boundaries, cracks, and interfaces. Recently, strain or gradient smoothing techniques have been incorporated into NMM to improve its performance. The resulting smoothed NMMs (SNMMs) normally possess enhanced numerical properties, for example, higher accuracy, convergence, and efficiency. A challenging issue rooted in NMM and other enhanced finite element methods using unfitted meshes is the ill‐conditioning induced by extremely small cut element. In this study, we investigate the behaviors of SNMMs in the case of small cut element. It is demonstrated that the cut‐induced ill‐conditionings also exist for two types of SNMMs, namely, edge‐based SNMM and physical‐patch‐based SNMM. Furthermore, a preconditioner based on the normalization of basis functions is proposed to resolve the ill‐conditioning. Several benchmark problems demonstrate the performances of SNMMs regarding accuracy, convergence, and stability.

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