A novel approach to compute the spatial gradients of enriching functions in the X-FEM with a hybrid representation of cracks

doi:10.1016/j.cma.2023.116419

CORC > 力学研究所 > 中国科学院力学研究所 > 非线性力学国家重点实验室

	A novel approach to compute the spatial gradients of enriching functions in the X-FEM with a hybrid representation of cracks
	Liu, Chuanqi; Wei, Yujie
刊名	COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
	2023-12-01
卷号	417 页码:21
关键词	X-FEM Level sets Hybrid representation WENO
ISSN号	0045-7825
DOI	10.1016/j.cma.2023.116419
通讯作者	Liu, Chuanqi(chuanqil@imech.ac.cn)
英文摘要	The eXtended Finite Element Method (X-FEM) is a versatile technique to model discontinuities by enriching the trial functions with a prior solution. In the X-FEM, a crack can be explicitly represented by a set of triangles or implicit signed distances, i.e., level set functions, of the points of interest from the crack surface and the crack front. In the explicit representations, it is crucial to accurately evaluate surface normal, conormal, and tangent vectors along crack fronts for computations of the gradients of the enriching functions. The solution is very sensitive to these directional vectors, especially for non-planar 3D cracks. We here propose a novel approach to compute these gradients without evaluating the directional vectors. Level set functions are first set up in a hexahedral grid independent of the background mesh in the X-FEM. We can thus implement the Weight Essentially Non-Oscillatory (WENO) scheme to compute the gradients of level sets. The gradients of the enriching functions at any integration point can therefore be computed by interpolations and chain rules. We compare the implementation procedures of the explicit representation and the proposed hybrid representation in detail. A three-dimensional lens crack problem is studied to demonstrate the accuracy of the proposed method, especially for coarse meshes.(c) 2023 Elsevier B.V. All rights reserved.
资助项目	National Natural Science Foundation of China (NSFC)[11988102] ; National Natural Science Foundation of China (NSFC)[11790291] ; NSFC[12172368] ; One Hundred Talents Program of Chinese Academy of Sciences (CAS)
WOS关键词	FINITE-ELEMENT-METHOD ; STRESS INTENSITY FACTORS ; LEVEL SETS ; SURFACE REPRESENTATION ; ENRICHMENT FUNCTIONS ; ORDER ENRICHMENT ; PROPAGATION ; GROWTH ; IMPROVEMENTS ; UPDATE
WOS研究方向	Engineering ; Mathematics ; Mechanics
语种	英语
WOS记录号	WOS:001075882100001
资助机构	National Natural Science Foundation of China (NSFC) ; NSFC ; One Hundred Talents Program of Chinese Academy of Sciences (CAS)
内容类型	期刊论文
源URL	[http://dspace.imech.ac.cn/handle/311007/93075]
专题	力学研究所_非线性力学国家重点实验室
通讯作者	Liu, Chuanqi
作者单位	Chinese Acad Sci, Inst Mech, State Key Lab Nonlinear Mech, Beijing 100090, Peoples R China
推荐引用方式 GB/T 7714	Liu, Chuanqi,Wei, Yujie. A novel approach to compute the spatial gradients of enriching functions in the X-FEM with a hybrid representation of cracks[J]. COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING,2023,417:21.
APA	Liu, Chuanqi,&Wei, Yujie.(2023).A novel approach to compute the spatial gradients of enriching functions in the X-FEM with a hybrid representation of cracks.COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING,417,21.
MLA	Liu, Chuanqi,et al."A novel approach to compute the spatial gradients of enriching functions in the X-FEM with a hybrid representation of cracks".COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING 417(2023):21.