Journal of Applied and Computational Mechanics
An Efficient Implementation of Phase Field Method with Explicit Time Integration
Document Type : Research Paper
Authors
Department of Civil Engineering, University of Cincinnati, Cincinnati, OH, 45220, USA
Abstract
The phase field method integrates the Griffith theory and damage mechanics approach to predict crack initiation, propagation, and branching within one framework. No crack tracking topology is needed, and complex crack shapes can be captures without user intervention. In this paper, a detailed description of how the phase field method is implemented with explicit dynamics into LS-DYNA is provided. The displacement field and the damage field are solved in a staggered approach and the phase field equation is solved every Nth time step (N is refered to as calculation cycle) to save computational time. An N value smaller than 1/400 of the total time step numbers is suggested. Several simulations are presented to demonstrate the feasibility of this solving scheme.
Keywords
Main Subjects
[1] T. Rabczuk, T. Belytschko, Cracking particles: A simplified meshfree method for arbitrary evolving cracks, International Journal for Numerical Methods in Engineering, 61(13), 2004, 2316-2343.
[2] T. Rabczuk, G. Zi, S. Bordas, N.X. Hung, A simple and robust three-dimensional cracking-particle method without enrichment, Computer Methods in Applied Mechanics and Engineering, 199(37–40), 2010, 2437-2455.
[3] H.L. Ren, X.Y. Zhuang, C. Anitescu, T. Rabczuk. An explicit phase field method for brittle dynamic fracture, Computers and Structures, 217, 2019, 45-56.
[4] H. Ren, X. Zhuang, T. Rabczuk, Dual-horizon peridynamics: A stable solution to varying horizons, Computer Methods in Applied Mechanics and Engineering, 318, 2017, 762-782.
[5] W. J. Boettinger, J. A. Warren, C. Beckermann, A. Karma, Phase-Field Simulation of Solidification, Annual Review of Materials Research, 32(1), 2002, 163–194.
[6] G. A. Francfort, J.-J. Marigo, Revisiting brittle fracture as an energy minimization problem, Journal of the Mechanics and Physics of Solids, 46(8), 1998, 1319-1342.
[7] B. Bourdin, G. A. Francfort, J.-J. Marigo, The Variational Approach to Fracture, Journal of Elasticity, 91(1–3), 2008, 5–148.
[8] B. Bourdin, G. Francfort, J.-J. Marigo, Numerical experiments in revisited brittle fracture, Journal of the Mechanics and Physics of Solids, 48(4), 2000, 797-826.
[9] C. Miehe, F. Welschinger, M. Hofacker, Thermodynamically consistent phase-field models of fracture: Variational principles and multi-field FE implementations, International Journal for Numerical Methods in Engineering, 83(10), 2010, 1273–1311.
[10] A. Tabiei, W. Zhang, Cohesive element approach for dynamic crack propagation: Artificial compliance and mesh dependency, Engineering Fracture Mechanics, 180, 2017, 23-42.
[11] A. Tabiei, J. Wu, Development of the DYNA3D simulation code with automated fracture procedure for brick elements, International Journal for Numerical Methods in Engineering, 57(14), 2003, 1979–2006.
[12] X. F. Hu, B. Y. Chen, M. Tirvaudey, V. B. C. Tana, T. E.Tay, Integrated XFEM-CE analysis of delamination migration in multi-directional composite laminates, Composites Part A: Applied Science and Manufacturing, 90, 2016, 161-173.
[13] H. Ulmer, M. Hofacker, C. Miehe, Phase Field Modeling of Brittle and Ductile Fracture, Gesellschaft fur Angewandte Mathematik und Mechanik, 13(1), 2013, 533-536.
[14] M. Hofacker, C. Miehe, A phase field model of dynamic fracture: Robust field updates for the analysis of complex crack patterns, International Journal for Numerical Methods in Engineering, 93(3), 2013, 276–301.
[15] M. J. Borden, T. J. R. Hugh, C. M. Landis, C. V. Verhoosel, A higher-order phase-field model for brittle fracture: Formulation and analysis within the isogeometric analysis framework, Computer Methods in Applied Mechanics and Engineering, 273, 2014, 100-118.
[16] C. Hesch, K. Weinberg, Thermodynamically consistent algorithms for a finite-deformation phase-field approach to fracture, International Journal for Numerical Methods in Engineering, 99(12), 2014, 906-924.
[17] C. V. Verhoosel, R. de Borst, A phase-field model for cohesive fracture, International Journal for Numerical Methods in Engineering, 96(1), 2013, 43-62.
[18] S. Zhou, X. Zhuang, T. Rabczuk, A phase-field modeling approach of fracture propagation in poroelastic media, Engineering Geology, 240, 2018, 189-203.
[19] M. A. Msekh, N. H. Cuong, G. Zi, P. Areias, X. Zhuang, T. Rabczuk, Fracture properties prediction of clay/epoxy nanocomposites with interphase zones using a phase field model, Engineering Fracture Mechanics, 188, 2018, 287-299.
[20] G. Molnár and A. Gravouil, 2D and 3D Abaqus implementation of a robust staggered phase-field solution for modeling brittle fracture, Finite Elements in Analysis and Design, 130, 2017, 27-38.
[21] G. Liu, Q. Li, M. A. Msekh, Z. Zuo, Abaqus implementation of monolithic and staggered schemes for quasi-static and dynamic fracture phase-field model, Computational Materials Science, 121, 2016, 35–47.
[22] E. G. Kakouris, S. P. Triantafyllou, Phase-field material point method for brittle fracture, International Journal for Numerical Methods in Engineering, 112(12), 2017, 1750-1776.
[23] C. Miehe, M. Hofacker, F. Welschinger, A phase field model for rate-independent crack propagation: Robust algorithmic implementation based on operator splits, Computer Methods in Applied Mechanics and Engineering, 199(45–48), 2010, 2765-2778.
[24] C. Miehe, F. Welschinger, M. Hofacker, Thermodynamically consistent phase‐field models of fracture: Variational principles and multi-field FE implementations, International Journal for Numerical Methods in Engineering, 83(10), 2010, 1273-1311.
[25] W. Zhang, A. Tabiei, D. French, Comparison Between Discontinuous Galerkin Method and Cohesive Element Method: On the Convergence and Dynamic Wave Propagation Issue, International Journal of Computational Methods in Engineering Science and Mechanics, 19(5), 2018, 363-373.
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