Implementation Details for the Phase Field Approaches to Fracture

doi:10.1007/s12204-018-1922-0

Journal of Shanghai Jiao Tong University (Science) ›› 2018, Vol. 23 ›› Issue (1): 166-174.doi: 10.1007/s12204-018-1922-0

Previous Articles Next Articles

Implementation Details for the Phase Field Approaches to Fracture

SHEN Yongxing1,2* (沈泳星), MOLLAALI Mostafa1,2, LI Yihuan1,2 (李毅环),MA Weixin1,2 (马维馨), JIANG Jiahao3 (蒋家皓)

(1. State Key Laboratory of Metal Matrix Composites, Shanghai Jiao Tong University, Shanghai 200240, China; 2. University of Michigan - Shanghai Jiao Tong University Joint Institute, Shanghai Jiao Tong University, Shanghai 200240, China; 3. Department of Mechanical Engineering, University of Michigan, Ann Arbor, Michigan, USA)
(1. State Key Laboratory of Metal Matrix Composites, Shanghai Jiao Tong University, Shanghai 200240, China; 2. University of Michigan - Shanghai Jiao Tong University Joint Institute, Shanghai Jiao Tong University, Shanghai 200240, China; 3. Department of Mechanical Engineering, University of Michigan, Ann Arbor, Michigan, USA)

Online:2018-02-01 Published:2018-02-01
Contact: SHEN Yongxing(沈泳星) E-mail: yongxing.shen@sjtu.edu.cn

Abstract

Abstract: Phase field description of fracture is a very promising approach for simulating crack initiation, propagation, merging and branching. This method greatly reduces the implementation complexity, compared with discrete descriptions of cracks. In this work, we provide an overview of phase field models for quasistatic and dynamic cases. Afterward, we present useful vectors and matrices for the implementation of this method in two and three dimensions.

Key words: phase field approach to fracture| variational fracture| brittle fracture| dynamic fracture| variational integrator

摘要： Phase field description of fracture is a very promising approach for simulating crack initiation, propagation, merging and branching. This method greatly reduces the implementation complexity, compared with discrete descriptions of cracks. In this work, we provide an overview of phase field models for quasistatic and dynamic cases. Afterward, we present useful vectors and matrices for the implementation of this method in two and three dimensions.

关键词: phase field approach to fracture| variational fracture| brittle fracture| dynamic fracture| variational integrator

CLC Number:

O241.82

SHEN Yongxing1,2* (沈泳星), MOLLAALI Mostafa1,2, LI Yihuan1,2 (李毅环),MA Weixin1,2 (马维馨), JIANG Jiahao3 (蒋家皓). Implementation Details for the Phase Field Approaches to Fracture[J]. Journal of Shanghai Jiao Tong University (Science), 2018, 23(1): 166-174.

References

[1] LANDAU L D, LIFSHITZ E M. Statistical physics [M].Oxford: Pergamon Press, 1980. [2] ARANSON I, KALATSKY V, VINOKUR V. Continuum field description of crack propagation [J]. Physical Review Letters, 2000, 85(1): 118. [3] KARMA A, KESSLER D A, LEVINE H. Phase-field model of mode iii dynamic fracture [J]. Physical Review Letters, 2001, 87(4): 045501. [4] HENRY H, LEVINE H. Dynamic instabilities of fracture under biaxial strain using a phase field model [J].Physical Review Letters, 2004, 93(10): 105504. [5] AMBATI M, GERASIMOV T, DE LORENZIS L. A review on phase-field models of brittle fracture and a new fast hybrid formulation [J]. Computational Mechanics,2015, 55(2): 383-405. [6] FRANCFORT G A, MARIGO J J. Revisiting brittle fracture as an energy minimization problem [J].Journal of the Mechanics and Physics of Solids, 1998,46(8): 1319-1342. [7] BOURDIN B, FRANCFORT G A, MARIGO J J. Numerical experiments in revisited brittle fracture [J].Journal of the Mechanics and Physics of Solids, 2000,48(4): 797-826. [8] BOURDIN B. Numerical implementation of the variational formulation for quasi-static brittle fracture [J].Interfaces and Free Boundaries, 2007, 9(3): 411-430. [9] BOURDIN B, MARIGO J J, MAURINI C, et al. Morphogenesis and propagation of complex cracks induced by thermal shocks [J]. Physical Review Letters, 2014,112: 014301. [10] TANN′ EE, LI T, BOURDINB, et al. Crack nucleation in variational phase-field models of brittle fracture [J].Journal of the Mechanics and Physics of Solids, 2018,110: 80-99. [11] BORDEN M J, HUGHES T J, LANDIS C M, et al. A higher-order phase-field model for brittle fracture: Formulation and analysis within the isogeometric analysis framework [J]. Computer Methods in Applied Mechanics and Engineering, 2014, 273: 100-118. [12] BORDEN M J. Isogeometric analysis of phase-field models for dynamic brittle and ductile fracture [D].Austin: University of Texas at Austin, 2012. [13] SARGADO J M, KEILEGAVLEN E, BERRE I, et al.High-accuracy phasefield models for brittle fracture based on a new family of degradation functions [J].Journal of the Mechanics and Physics of Solids,2017. https://doi.org/10.1016/j.jmps.2017.10.015(published online). [14] AMOR H, MARIGO J J, MAURINI C. Regularized formulation of the variational brittle fracture with unilateral contact: Numerical experiments [J]. Journal of the Mechanics and Physics of Solids, 2009, 57: 1209-1229. [15] MIEHE C, WELSCHINGER F, HOFACKER M.Thermodynamically consistent phase-field models of fracture: Variational principles and multi-field FE implementations[J]. International Journal for Numerical Methods in Engineering, 2010, 83: 1273-1311. [16] GERASIMOV T, DE LORENZIS L. A line search assisted monolithic approach for phase-field computing of brittle fracture [J]. Computer Methods in Applied Mechanics and Engineering, 2016, 312: 276-303. [17] WHEELER M, WICK T, WOLLNER W. An augmented-Lagrangian method for the phasefield approach for pressurized fractures [J]. Computer Methods in Applied Mechanics and Engineering, 2014, 271: 69-85. [18] ZIAEI-RAD V, SHEN Y. Massive parallelization of the phase field formulation for crack propagation with time adaptivity [J]. Computer Methods in Applied Mechanics and Engineering, 2016, 312, 224-253.

Implementation Details for the Phase Field Approaches to Fracture

Implementation Details for the Phase Field Approaches to Fracture

Knowledge

Abstract

Cite this article

share this article

References

Related Articles 3

Recommended Articles

Metrics

Comments

[1]	WANG Man (王曼), ZHANG Xiaomin (张晓敏), LONG Peng (龙鹏), JIANG Yu (蒋渝). Torsion Failure Analysis of Galvanized Steel Wires for Transmission and Distribution Lines Based on ANSYS Numerical Simulation [J]. Journal of Shanghai Jiao Tong University (Science), 2019, 24(5): 632-639.
[2]	GONG Neng-Ping, LUO Yu-Fan, GAO Yuan. Experimental Study on the Effect of Loading Rate for Dynamic Fracture Toughness of Rock [J]. Journal of Shanghai Jiaotong University, 2012, 46(10): 1570-1572.
[3]	KE Chang-Ren-1, 2 , JIANG Jun-Ling-2, GE Xiu-Run-1, 3 . Numerical Simulation of Heterogeneous Rock Dynamic Fracture Based on Virtual Internal Bond Model [J]. Journal of Shanghai Jiaotong University, 2012, 46(01): 142-145.