A Three-Dimensional Adaptive Finite Element Method for Phase-Field Models of Fracture

QIU Shasha; LIU Xingze; NING Wenjie; YAO Weian; DUAN Qinglin

doi:10.21656/1000-0887.440299

Volume 45 Issue 4

Apr. 2024

Turn off MathJax

Article Contents

Article Navigation > Applied Mathematics and Mechanics > 2024 > 45(4): 391-399

QIU Shasha, LIU Xingze, NING Wenjie, YAO Weian, DUAN Qinglin. A Three-Dimensional Adaptive Finite Element Method for Phase-Field Models of Fracture[J]. Applied Mathematics and Mechanics, 2024, 45(4): 391-399. doi: 10.21656/1000-0887.440299

Citation:

PDF( 6379 KB)

A Three-Dimensional Adaptive Finite Element Method for Phase-Field Models of Fracture

doi: 10.21656/1000-0887.440299

1.
State Key Laboratory of Structural Analysis, Optimization and CAE Software for Industrial Equipment, Dalian University of Technology, Dalian, Liaoning 116024, P.R.China
2.
DUT-BSU Joint Institute, Dalian University of Technology, Dalian, Liaoning 116024, P.R.China

Received Date: 2023-10-03
Rev Recd Date: 2024-03-14
Publish Date: 2024-04-01

Abstract

Abstract

A robust predictor-corrector algorithm was developed and a 3D adaptive finite element analysis for the fracture phase-field model was established. This model can deal with complex fracture problems conveniently, avoiding extra tracking of crack paths and without mesh-dependency. However, the 3D phase-field modeling usually requires extremely fine meshes, which brings reduction of the solving efficiency. Aimed at this problem, the predictor-corrector adaptive mesh refinement algorithm was developed based on a staggered solution scheme, to achieve high-precision analysis of crack propagation in 3D structures. Numerical examples show that, the developed method can accurately and reasonably describe crack propagation in structures, and the meshes can be adaptively refined along the crack propagation paths.
- fracture mechanics,
- phase-field model,
- adaptive refinement,
- finite element method,
- 3D crack

FullText(HTML)

References(15)

References

[1]	唐红梅, 周福川, 陈松, 等. 高烈度下双裂缝主控结构面危岩的断裂破坏机制分析[J]. 应用数学和力学, 2021, 42(6): 645-655. doi: 10.21656/1000-0887.410187 TANG Hongmei, ZHOU Fuchuan, CHEN Song, et al. Analysis of the fracture failure mechanism of dangerous rocks with double crack main control structural planes under high intensity[J]. Applied Mathematics and Mechanics, 2021, 42(6): 645-655. (in Chinese) doi: 10.21656/1000-0887.410187
[2]	肖刘. 某型飞机机翼断裂分析[J]. 装备制造技术, 2013, 5: 132-133. https://www.cnki.com.cn/Article/CJFDTOTAL-GXJX201305051.htm XIAO Liu. Analysis of wing fracture of a certain type of aircraft[J]. Equipment Manufacturing Technology, 2013, 5: 132-133. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-GXJX201305051.htm
[3]	GRIFFITH A A. The phenomena of rupture and flow in solids[J]. Philosophical Transactions of the Royal Society A: Mathematical Physical and Engineering Sciences, 1920, A221(4): 163-198.
[4]	FRANCFORT G A, MARIGO J J. Revisiting brittle fracture as an energy minimization problem[J]. Journal of the Mechanics & Physics of Solids, 1998, 46(8): 1319-1342.
[5]	BOURDIN B, FRANCFORT G A, MARIGO J J. Numerical experiments in revisited brittle fracture[J]. Journal of the Mechanics & Physics of Solids, 2000, 48(4): 797-826.
[6]	MIEHE C, HOFACKER M, WELSCHINGER F. A phase field model for rate-independent crack propagation: robust algorithmic implementation based on operator splits[J]. Computer Methods in Applied Mechanics and Engineering, 2010, 199(45/48): 2765-2778.
[7]	AMBATI M, GERASIMOV T, LORENZIS L D. A review on phase-field models of brittle fracture and a new fast hybrid formulation[J]. Computational Mechanics, 2015, 55(2): 383-405. doi: 10.1007/s00466-014-1109-y
[8]	WU J Y, HUANG Y, ZHOU H, et al. Three-dimensional phase-field modeling of mode Ⅰ+Ⅱ/Ⅲ failure in solids[J]. Computer Methods in Applied Mechanics and Engineering, 2021, 373: 113537. doi: 10.1016/j.cma.2020.113537
[9]	MOLNAR G, GRAVOUIL A. 2D and 3D Abaqus implementation of a robust staggered phase-field solution for modeling brittle fracture[J]. Finite Elements in Analysis and Design, 2017, 130: 27-38. doi: 10.1016/j.finel.2017.03.002
[10]	BURKE S, ORTNER C, SULI E. An adaptive finite element approximation of a variational model of brittle fracture[J]. SIAM Journal on Numerical Analysis, 2010, 48(3): 980-1012. doi: 10.1137/080741033
[11]	ARTINA M, FORNASIER M, MICHELETTI S, et al. Anisotropic mesh adaptation for crack detection in brittle materials[J]. SIAM Journal on Scientific Computing, 2015, 37(4): B633-B659. doi: 10.1137/140970495
[12]	HIRSHIKESH, JANSARI C, KANNAN K, et al. Adaptive phase field method for quasi-static brittle fracture based on recovery based error indicator and quadtree decomposition[J]. Engineering Fracture Mechanics, 2019, 220: 106599. doi: 10.1016/j.engfracmech.2019.106599
[13]	HEISTER T, WHEELER M F, WICK T. A primal-dual active set method and predictor-corrector mesh adaptivity for computing fracture propagation using a phase-field approach[J]. Computer Methods in Applied Mechanics and Engineering, 2015, 290: 466-495. doi: 10.1016/j.cma.2015.03.009
[14]	LEE S, WHEELER M F, WICK T. Pressure and fluid-driven fracture propagation in porous media using an adaptive finite element phase field model[J]. Computer Methods in Applied Mechanics and Engineering, 2016, 305: 111-132. doi: 10.1016/j.cma.2016.02.037
[15]	MOËS N, STOLZ C, BERNARD P E, et al. A level set based model for damage growth: the thick level set approach[J]. International Journal for Numerical Methods in Engineering, 2011, 86(3): 358-380. doi: 10.1002/nme.3069