A finite element method with mesh-separation-based approximation technique and its application in modeling crack propagation with adaptive mesh refinement

SUMMARYThis paper presents a FEM with mesh‐separation‐based approximation technique that separates a standard element into three geometrically independent elements. A dual mapping scheme is introduced to couple them seamlessly and to derive the element approximation. The novel technique makes it ver...

Full description

Saved in:
Bibliographic Details
Published in:International journal for numerical methods in engineering 2014-08, Vol.99 (7), p.487-521
Main Authors: Ling, Daosheng, Bu, Lingfang, Tu, Fubin, Yang, Qingda, Chen, Yunmin
Format: Article
Language:English
Subjects:
adaptive mesh refinement
Approximation
approximation technique
Discontinuity
FEM
Finite element method
Fracture mechanics
hanging node
Mathematical analysis
Mathematical models
Mesh generation
Meshless methods
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:SUMMARYThis paper presents a FEM with mesh‐separation‐based approximation technique that separates a standard element into three geometrically independent elements. A dual mapping scheme is introduced to couple them seamlessly and to derive the element approximation. The novel technique makes it very easy for mesh generation of problems with complex or solution‐dependent, varying geometry. It offers a flexible way to construct displacement approximations and provides a unified framework for the FEM to enjoy some of the key advantages of the Hansbo and Hansbo method, the meshfree methods, the semi‐analytical FEMs, and the smoothed FEM. For problems with evolving discontinuities, the method enables the devising of an efficient crack‐tip adaptive mesh refinement strategy to improve the accuracy of crack‐tip fields. Both the discontinuities due to intra‐element cracking and the incompatibility due to hanging nodes resulted from the element refinement can be treated at the elemental level. The effectiveness and robustness of the present method are benchmarked with several numerical examples. The numerical results also demonstrate that a high precision integral scheme is critical to pass the crack patch test, and it is essential to apply local adaptive mesh refinement for low fracture energy problems. Copyright © 2014 John Wiley & Sons, Ltd.
ISSN:0029-5981
1097-0207
DOI:10.1002/nme.4689