A novel approach to compute the spatial gradients of enriching functions in the X-FEM with a hybrid representation of cracks
文献类型：期刊论文
| 作者 | Liu, Chuanqi; Wei, Yujie ; Wei YJ(魏宇杰); Wei YJ(魏宇杰)
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| 刊名 | COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
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| 出版日期 | 2023-12-01 |
| 卷号 | 417页码:21 |
| ISSN号 | 0045-7825 |
| 关键词 | X-FEM Level sets Hybrid representation WENO |
| 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. |
| WOS关键词 | FINITE-ELEMENT-METHOD ; STRESS INTENSITY FACTORS ; LEVEL SETS ; SURFACE REPRESENTATION ; ENRICHMENT FUNCTIONS ; ORDER ENRICHMENT ; PROPAGATION ; GROWTH ; IMPROVEMENTS ; UPDATE |
| 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) |
| 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,Wei YJ,et al. 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,魏宇杰,&魏宇杰.(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. |
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来源：力学研究所
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