A linearly-independent higher-order extended numerical manifold method and its application to multiple crack growth simulation

doi:10.1016/j.jrmge.2019.02.007

CORC > 武汉岩土力学研究所 > 中科院武汉岩土力学所 > 岩土力学所知识全产出 > 期刊论文

	A linearly-independent higher-order extended numerical manifold method and its application to multiple crack growth simulation
	Xu, Dongdong ; Wu, Aiqing ; Li, Cong
刊名	JOURNAL OF ROCK MECHANICS AND GEOTECHNICAL ENGINEERING
	2019
卷号	11 期号:6 页码:1256-1263
关键词	Numerical manifold method (NMM) Physical cover Multiple crack propagation Linear independence Nodal stress continuity
ISSN号	1674-7755
DOI	10.1016/j.jrmge.2019.02.007
英文摘要	The numerical manifold method (NMM) can be viewed as an inherent continuous-discontinuous numerical method, which is based on two cover systems including mathematical and physical covers. Higher-order NMM that adopts higher-order polynomials as its local approximations generally shows higher-precision than zero-order NMM whose local approximations are constants. Therefore, higher-order NMM will be an excellent choice for crack propagation problem which requires higher stress accuracy. In addition, it is crucial to improve the stress accuracy around the crack tip for determining the direction of crack growth according to the maximum circumferential stress criterion in fracture mechanics. Thus, some other enriched local approximations are introduced to model the stress singularity at the crack tip. Generally, higher-order NMM, especially first-order NMM wherein local approximations are first-order polynomials, has the linear dependence problems as other partition of unit (PUM) based numerical methods does. To overcome this problem, an extended NMM is developed based on a new local approximation derived from the triangular plate element in the finite element method (FEM), which has no linear dependence issue. Meanwhile, the stresses at the nodes of mathematical mesh (the nodal stresses in FEM) are continuous and the degrees of freedom defined on the physical patches are physically meaningful. Next, the extended NMM is employed to solve multiple crack propagation problems. It shows that the fracture mechanics requirement and mechanical equilibrium can be satisfied by the trial-and-error method and the adjustment of the load multiplier in the process of crack propagation. Four numerical examples are illustrated to verify the feasibility of the proposed extended NMM. The numerical examples indicate that the crack growths simulated by the extended NMM are in good accordance with the reference solutions. Thus the effectiveness and correctness of the developed NMM have been validated. (C) 2019 Institute of Rock and Soil Mechanics, Chinese Academy of Sciences. Production and hosting by Elsevier B.V.
WOS研究方向	Engineering
语种	英语
WOS记录号	WOS:000500915400010
内容类型	期刊论文
源URL	[http://119.78.100.198/handle/2S6PX9GI/14807]
专题	岩土力学所知识全产出_期刊论文
作者单位	1.Minist Water Resources, Key Lab Geotech Mech & Engn, Changjiang River Sci Res Inst, Wuhan, Hubei, Peoples R China; 2.Chinese Acad Sci, Inst Rock & Soil Mech, State Key Lab Geomech & Geotech Engn, Wuhan, Hubei, Peoples R China
推荐引用方式 GB/T 7714	Xu, Dongdong,Wu, Aiqing,Li, Cong. A linearly-independent higher-order extended numerical manifold method and its application to multiple crack growth simulation[J]. JOURNAL OF ROCK MECHANICS AND GEOTECHNICAL ENGINEERING,2019,11(6):1256-1263.
APA	Xu, Dongdong,Wu, Aiqing,&Li, Cong.(2019).A linearly-independent higher-order extended numerical manifold method and its application to multiple crack growth simulation.JOURNAL OF ROCK MECHANICS AND GEOTECHNICAL ENGINEERING,11(6),1256-1263.
MLA	Xu, Dongdong,et al."A linearly-independent higher-order extended numerical manifold method and its application to multiple crack growth simulation".JOURNAL OF ROCK MECHANICS AND GEOTECHNICAL ENGINEERING 11.6(2019):1256-1263.