A finite element method with mesh‐separation‐based approximation technique and its application in modeling crack propagation with adaptive mesh refinement
Abstract
This 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.
Document Details
- Document Type
- Pub Defense Publication
- Publication Date
- Jun 17, 2014
- Source ID
- 10.1002/nme.4689
Entities
People
- Daosheng Ling
- Fubin Tu
- Lingfang Bu
- Qingda Yang
- Yunmin Chen
Organizations
- Army Research Office
- National Natural Science Foundation of China
- Program 973
- University of Miami
- Zhejiang University