An asynchronous variational integrator for the phase field approach to dynamic fracture
dc.contributor.author | Niu, Zongwu | |
dc.contributor.author | Ziaei-Rad, Vahid | |
dc.contributor.author | Wu, Zongyuan | |
dc.contributor.author | Shen, Yongxing | |
dc.date.accessioned | 2023-01-11T16:21:50Z | |
dc.date.available | 2024-02-11 11:21:47 | en |
dc.date.available | 2023-01-11T16:21:50Z | |
dc.date.issued | 2023-01-30 | |
dc.identifier.citation | Niu, Zongwu; Ziaei-Rad, Vahid ; Wu, Zongyuan; Shen, Yongxing (2023). "An asynchronous variational integrator for the phase field approach to dynamic fracture." International Journal for Numerical Methods in Engineering 124(2): 434-457. | |
dc.identifier.issn | 0029-5981 | |
dc.identifier.issn | 1097-0207 | |
dc.identifier.uri | https://hdl.handle.net/2027.42/175398 | |
dc.description.abstract | The phase field approach is widely used to model fracture behaviors due to the absence of the need to track the crack topology and the ability to predict crack nucleation and branching. In this work, the asynchronous variational integrator (AVI) is adapted for the phase field approach of dynamic brittle fracture. The AVI is derived from Hamilton’s principle and allows each element in the mesh to have its own local time step that may be different from others’. While the displacement field is explicitly updated, the phase field is implicitly solved, with upper and lower bounds strictly and conveniently enforced. In particular, two important variants of the phase field approach, the AT1 and AT2 models, are equally easily implemented. Several benchmark problems are used to study the performances of both the AT1 and AT2 models, and the results show that the AVI for the phase field approach significantly speeds up the computational efficiency and successfully captures the complicated dynamic fracture behavior. | |
dc.publisher | John Wiley & Sons, Inc. | |
dc.subject.other | dynamic fracture | |
dc.subject.other | phase field approach | |
dc.subject.other | computational efficiency | |
dc.subject.other | asynchronous variational integrators | |
dc.title | An asynchronous variational integrator for the phase field approach to dynamic fracture | |
dc.type | Article | |
dc.rights.robots | IndexNoFollow | |
dc.subject.hlbsecondlevel | Engineering (General) | |
dc.subject.hlbsecondlevel | Mechanical Engineering | |
dc.subject.hlbtoplevel | Engineering | |
dc.description.peerreviewed | Peer Reviewed | |
dc.description.bitstreamurl | http://deepblue.lib.umich.edu/bitstream/2027.42/175398/1/nme7127_am.pdf | |
dc.description.bitstreamurl | http://deepblue.lib.umich.edu/bitstream/2027.42/175398/2/nme7127.pdf | |
dc.identifier.doi | 10.1002/nme.7127 | |
dc.identifier.source | International Journal for Numerical Methods in Engineering | |
dc.identifier.citedreference | Schlüter A, Kuhn C, Müller R. Phase field approximation of dynamic brittle fracture. Proc Appl Math Mech. 2014; 14 ( 1 ): 143 - 144. doi: 10.1002/pamm.201410059 | |
dc.identifier.citedreference | Wu JY. Robust numerical implementation of non-standard phase-field damage models for failure in solids. Comput Methods Appl Mech Eng. 2018; 340: 767 - 797. doi: 10.1016/j.cma.2018.06.007 | |
dc.identifier.citedreference | Farrell P, Maurini C. Linear and nonlinear solvers for variational phase-field models of brittle fracture. Int J Numer Methods Eng. 2017; 109 ( 5 ): 648 - 667. doi: 10.1002/nme.5300 | |
dc.identifier.citedreference | Knuth DE. The Art of Computer Programming. Addison Wesley; 1998. | |
dc.identifier.citedreference | Song JH, Wang H, Belytschko T. A comparative study on finite element methods for dynamic fracture. Comput Mech. 2008; 42: 239 - 250. doi: 10.1007/s00466-007-0210-x | |
dc.identifier.citedreference | Ramulu M, Kobayashi AS. Mechanics of crack curving and branching – A dynamic fracture analysis. Int J Fract. 1985; 27: 187 - 201. doi: 10.1007/BF00017967 | |
dc.identifier.citedreference | Sharon E, Fineberg J. Microbranching instability and the dynamic fracture of brittle materials. Phys Rev B Condens Matter. 1996; 54 ( 10 ): 7128 - 7139. doi: 10.1103/physrevb.54.7128 | |
dc.identifier.citedreference | Liu G, Li Q, Msekh MA, Zuo Z. Abaqus implementation of monolithic and staggered schemes for quasi-static and dynamic fracture phase-field model. Comput Mater Sci. 2016; 121: 35 - 47. doi: 10.1016/j.commatsci.2016.04.009 | |
dc.identifier.citedreference | Bobaru F, Zhang G. Why do cracks branch? A peridynamic investigation of dynamic brittle fracture. Int J Fract. 2015; 196: 59 - 98. doi: 10.1007/s10704-015-0056-8 | |
dc.identifier.citedreference | Mandal TK, Nguyen VP, Wu JY. Evaluation of variational phase-field models for dynamic brittle fracture. Eng Fract Mech. 2020; 235: 107169. doi: 10.1016/j.engfracmech.2020.107169 | |
dc.identifier.citedreference | Kalthoff JF. Shadow optical analysis of dynamic shear fracture. Opt Eng. 1988; 27 ( 10 ): 835 - 840. doi: 10.1117/12.7976772 | |
dc.identifier.citedreference | Kalthoff JF. Modes of dynamic shear failure in solids. Int J Fract. 2000; 101 ( 1 ): 1 - 31. doi: 10.1023/A:1007647800529 | |
dc.identifier.citedreference | Wang H, Xu Y, Huang D. A non-ordinary state-based peridynamic formulation for thermo-visco-plastic deformation and impact fracture. Int J Mech Sci. 2019; 159: 336 - 344. doi: 10.1016/j.ijmecsci.2019.06.008 | |
dc.identifier.citedreference | Chu D, Li X, Liu Z. Study the dynamic crack path in brittle material under thermal shock loading by phase field modeling. Int J Fract. 2017; 208: 115 - 130. doi: 10.1007/s10704-017-0220-4 | |
dc.identifier.citedreference | Zhou S, Rabczuk T, Zhuang X. Phase field modeling of quasi-static and dynamic crack propagation: COMSOL implementation and case studies. Adv Eng Softw. 2018; 122: 31 - 49. doi: 10.1016/j.advengsoft.2018.03.012 | |
dc.identifier.citedreference | Zhang Y, Ren H, Areias P, Zhuang X, Rabczuk T. Quasi-static and dynamic fracture modeling by the nonlocal operator method. Eng Anal Bound Elem. 2021; 133: 120 - 137. doi: 10.1016/j.enganabound.2021.08.020 | |
dc.identifier.citedreference | Park K, Paulino GH, Celes W, Espinha R. Adaptive mesh refinement and coarsening for cohesive zone modeling of dynamic fracture. Int J Numer Methods Eng. 2012; 92 ( 1 ): 1 - 35. doi: 10.1002/nme.3163 | |
dc.identifier.citedreference | Tangella RG, Kumbhar P, Annabattula RK. Hybrid phase field modelling of dynamic brittle fracture and implementation in FEniCS. In: Krishnapillai SRV, Ha SK, eds. Composite Materials for Extreme Loading. Springer; 2022: 15 - 24. | |
dc.identifier.citedreference | Reddy SSK, Amirtham R, Reddy JN. Modeling fracture in brittle materials with inertia effects using the phase field method. Mech Adv Mater Struct. 2021. doi: 10.1080/15376494.2021.2010289 | |
dc.identifier.citedreference | Bourdin B, Francfort GA, Marigo JJ. The variational approach to fracture. J Elast. 2008; 91: 5 - 148. doi: 10.1007/s10659-007-9107-3 | |
dc.identifier.citedreference | Bleyer J, Roux-Langlois C, Molinari JF. Dynamic crack propagation with a variational phase-field model: limiting speed, crack branching and velocity-toughening mechanisms. Int J Fract. 2017; 204: 79 - 100. doi: 10.1007/s10704-016-0163-1 | |
dc.identifier.citedreference | Yin BB, Zhang LW. Phase field method for simulating the brittle fracture of fiber reinforced composites. Eng Fract Mech. 2019; 211: 321 - 340. doi: 10.1016/j.engfracmech.2019.02.033 | |
dc.identifier.citedreference | Sumi Y, Wang ZN. A finite-element simulation method for a system of growing cracks in a heterogeneous material. Mech Mater. 1998; 28 ( 1 ): 197 - 206. doi: 10.1016/S0167-6636(97)00048-3 | |
dc.identifier.citedreference | Yao Y, Keer LM. Cohesive fracture mechanics based numerical analysis to BGA packaging and lead free solders under drop impact. Microelectron Reliab. 2013; 53 ( 4 ): 629 - 637. doi: 10.1016/j.microrel.2012.12.007 | |
dc.identifier.citedreference | Lew A, Marsden JE, Ortiz M, West M. Asynchronous variational integrators. Arch Ration Mech Anal. 2003; 167 ( 2 ): 85 - 146. doi: 10.1007/s00205-002-0212-y | |
dc.identifier.citedreference | Zhang R, Zhang X, Kang T, He F. Dynamic fracture propagation model for oriented perforation steering fracturing in low permeability reservoir based on microelement method. J Nat Gas Sci Eng. 2020; 74: 103105. doi: 10.1016/j.jngse.2019.103105 | |
dc.identifier.citedreference | Chen S, Zang M, Wang D, Yoshimura S, Yamada T. Numerical analysis of impact failure of automotive laminated glass: a review. Compos Part B. 2017; 122: 47 - 60. doi: 10.1016/j.compositesb.2017.04.007 | |
dc.identifier.citedreference | Freund LB. Dynamic Fracture Mechanics. Cambridge University Press; 1998. | |
dc.identifier.citedreference | Ravi-Chandar K. Dynamic Fracture. Elsevier; 2004. | |
dc.identifier.citedreference | Fineberg J, Bouchbinder E. Recent developments in dynamic fracture: some perspectives. Int J Fract. 2015; 196 ( 1-2 ): 33 - 57. doi: 10.1007/s10704-015-0038-x | |
dc.identifier.citedreference | Sun Y, Edwards MG, Chen B, Li C. A state-of-the-art review of crack branching. Eng Fract Mech. 2021; 257: 108036. doi: 10.1016/j.engfracmech.2021.108036 | |
dc.identifier.citedreference | Rabczuk T. Computational methods for fracture in brittle and quasi-brittle solids: state-of-the-art review and future perspectives. International Scholarly Research Notices. 2013; 2013: 1 - 38. doi: 10.1155/2013/849231 | |
dc.identifier.citedreference | Réthoré J, Gravouil A, Combescure A. An energy-conserving scheme for dynamic crack growth using the eXtended finite element method. Int J Numer Methods Eng. 2005; 63 ( 5 ): 631 - 659. doi: 10.1002/nme.1283 | |
dc.identifier.citedreference | Nguyen VP. Discontinuous Galerkin/extrinsic cohesive zone modeling: implementation caveats and applications in computational fracture mechanics. Eng Fract Mech. 2014; 128: 37 - 68. doi: 10.1016/j.engfracmech.2014.07.003 | |
dc.identifier.citedreference | Liu Y, Filonova V, Hu N, et al. A regularized phenomenological multiscale damage model. Int J Numer Methods Eng. 2014; 99 ( 12 ): 867 - 887. doi: 10.1002/nme.4705 | |
dc.identifier.citedreference | Zhang Y, Zhuang X. Cracking elements method for dynamic brittle fracture. Theor Appl Fract Mech. 2019; 102: 1 - 9. doi: 10.1016/j.tafmec.2018.09.015 | |
dc.identifier.citedreference | Song JH, Areias PMA, Belytschko T. A method for dynamic crack and shear band propagation with phantom nodes. Int J Numer Methods Eng. 2006; 67 ( 6 ): 868 - 893. doi: 10.1002/nme.1652 | |
dc.identifier.citedreference | Li T, Marigo JJ, Guilbaud D, Potapov S. Gradient damage modeling of brittle fracture in an explicit dynamics context. Int J Numer Methods Eng. 2016; 108 ( 11 ): 1381 - 1405. doi: 10.1002/nme.5262 | |
dc.identifier.citedreference | Moreau K, Moës N, Picart D, Stainier L. Explicit dynamics with a non-local damage model using the thick level set approach. Int J Numer Methods Eng. 2015; 102 ( 3-4 ): 808 - 838. doi: 10.1002/nme.4824 | |
dc.identifier.citedreference | Bourdin B, Francfort GA, Marigo JJ. Numerical experiments in revisited brittle fracture. J Mech Phys Solids. 2000; 48 ( 4 ): 797 - 826. doi: 10.1016/S0022-5096(99)00028-9 | |
dc.identifier.citedreference | Francfort GA, Marigo JJ. Revisiting brittle fracture as an energy minimization problem. J Mech Phys Solids. 1998; 46 ( 8 ): 1319 - 1342. doi: 10.1016/S0022-5096(98)00034-9 | |
dc.identifier.citedreference | Amiri F, Millán D, Shen Y, Rabczuk T, Arroyo M. Phase-field modeling of fracture in linear thin shells. Theor Appl Fract Mech. 2014; 69: 102 - 109. doi: 10.1016/j.tafmec.2013.12.002 | |
dc.identifier.citedreference | Lai W, Gao J, Li Y, Arroyo M, Shen Y. Phase field modeling of brittle fracture in an Euler-Bernoulli beam accounting for transverse part-through cracks. Comput Methods Appl Mech Eng. 2020; 361: 112787. doi: 10.1016/j.cma.2019.112787 | |
dc.identifier.citedreference | Mollaali M, Ziaei-Rad V, Shen Y. Numerical modeling of CO2 fracturing by the phase field approach. J Nat Gas Sci Eng. 2019; 70: 102905. doi: 10.1016/j.jngse.2019.102905 | |
dc.identifier.citedreference | Shen Y, Mollaali M, Li Y, Ma W, Jiang J. Implementation details for the phase field approaches to fracture. J Shanghai Jiaotong Univ (Sci). 2018; 23 ( 1 ): 166 - 174. doi: 10.1007/s12204-018-1922-0 | |
dc.identifier.citedreference | Borden MJ, Verhoosel CV, Scott MA, Hughes TJ, Landis CM. A phase-field description of dynamic brittle fracture. Comput Methods Appl Mech Eng. 2012; 217-220: 77 - 95. doi: 10.1016/j.cma.2012.01.008 | |
dc.identifier.citedreference | Nguyen VP, Wu JY. Modeling dynamic fracture of solids with a phase-field regularized cohesive zone model. Comput Methods Appl Mech Eng. 2018; 340: 1000 - 1022. doi: 10.1016/j.cma.2018.06.015 | |
dc.identifier.citedreference | Hao S, Shen Y, Cheng JB. Phase field formulation for the fracture of a metal under impact with a fluid formulation. Eng Fract Mech. 2022; 261: 108142. doi: 10.1016/j.engfracmech.2021.108142 | |
dc.identifier.citedreference | Hao S, Chen Y, Cheng JB, Shen Y. A phase field model for high-speed impact based on the updated Lagrangian formulation. Finite Elem Anal Des. 2022; 199: 103652. doi: 10.1016/j.finel.2021.103652 | |
dc.identifier.citedreference | Tian F, Tang X, Xu T, Yang J, Li L. A hybrid adaptive finite element phase-field method for quasi-static and dynamic brittle fracture. Int J Numer Methods Eng. 2019; 120 ( 9 ): 1108 - 1125. doi: 10.1002/nme.6172 | |
dc.identifier.citedreference | Ziaei-Rad V, Shen Y. Massive parallelization of the phase field formulation for crack propagation with time adaptivity. Comput Methods Appl Mech Eng. 2016; 312: 224 - 253. doi: 10.1016/j.cma.2016.04.013 | |
dc.identifier.citedreference | Li Y, Lai W, Shen Y. Variational h-adaption method for the phase field approach to fracture. Int J Fract. 2019; 217: 83 - 103. doi: 10.1007/s10704-019-00372-y | |
dc.identifier.citedreference | Engwer C, Pop IS, Wick T. Dynamic and weighted stabilizations of the L-scheme applied to a phase-field model for fracture propagation; 2021: 1177 - 1184; Springer International Publishing, Cham. | |
dc.identifier.citedreference | Lew A, Marsden JE, Ortiz M, West M. Variational time integrators. Int J Numer Methods Eng. 2004; 60 ( 1 ): 153 - 212. doi: 10.1002/nme.958 | |
dc.identifier.citedreference | Fong W, Darve E, Lew A. Stability of asynchronous variational integrators. J Comput Phys. 2008; 227 ( 18 ): 8367 - 8394. doi: 10.1016/j.jcp.2008.05.017 | |
dc.identifier.citedreference | Focardi M, Mariano PM. Convergence of asynchronous variational integrators in linear elastodynamics. Int J Numer Methods Eng. 2008; 75 ( 7 ): 755 - 769. doi: 10.1002/nme.2271 | |
dc.identifier.citedreference | Ryckman RA, Lew AJ. An explicit asynchronous contact algorithm for elastic body-rigid wall interaction. Int J Numer Methods Eng. 2012; 89 ( 7 ): 869 - 896. doi: 10.1002/nme.3266 | |
dc.identifier.citedreference | Liu P, Yang JZ, Yuan C. Extended synchronous variational integrators for wave propagations on non-uniform meshes. Commun Comput Phys. 2020; 28 ( 2 ): 691 - 722. doi: 10.4208/cicp.OA-2019-0167 | |
dc.identifier.citedreference | Thomaszewski B, Pabst S, Straßer W. Asynchronous cloth simulation. Proceedings of the 2008 International Conference on Computer Graphics and Virtual Reality; 2008. | |
dc.identifier.citedreference | Pham K, Amor H, Marigo JJ, Maurini C. Gradient damage models and their use to approximate brittle fracture. Int J Damage Mech. 2011; 20 ( 4 ): 618 - 652. doi: 10.1177/1056789510386852 | |
dc.identifier.citedreference | Ren HL, Zhuang X, Anitescu C, Rabczuk T. An explicit phase field method for brittle dynamic fracture. Comput Struct. 2019; 217: 45 - 56. doi: 10.1016/j.compstruc.2019.03.005 | |
dc.identifier.citedreference | Suh HS, Sun W. Asynchronous phase field fracture model for porous media with thermally non-equilibrated constituents. Comput Methods Appl Mech Eng. 2021; 387: 114182. doi: 10.1016/j.cma.2021.114182 | |
dc.identifier.citedreference | Miehe C, Hofacker M, Welschinger F. A phase field model for rate-independent crack propagation: robust algorithmic implementation based on operator splits. Comput Methods Appl Mech Eng. 2010; 199 ( 45 ): 2765 - 2778. doi: 10.1016/j.cma.2010.04.011 | |
dc.identifier.citedreference | Amor H, Marigo JJ, Maurini C. Regularized formulation of the variational brittle fracture with unilateral contact: numerical experiments. J Mech Phys Solids. 2009; 57 ( 8 ): 1209 - 1229. doi: 10.1016/j.jmps.2009.04.011 | |
dc.identifier.citedreference | Liu Y, Cheng C, Ziaei-Rad V, Shen Y. A micromechanics-informed phase field model for brittle fracture accounting for unilateral constraint. Eng Fract Mech. 2021; 241: 107358. doi: 10.1016/j.engfracmech.2020.107358 | |
dc.identifier.citedreference | Wu JY, Nguyen VP, Zhou H, Huang Y. A variationally consistent phase-field anisotropic damage model for fracture. Comput Methods Appl Mech Eng. 2020; 358: 112629. doi: 10.1016/j.cma.2019.112629 | |
dc.identifier.citedreference | Marsden JE, West M. Discrete mechanics and variational integrators. Acta Numer. 2001; 10 ( 10 ): 357 - 514. doi: 10.1017/S096249290100006X | |
dc.identifier.citedreference | Gerasimov T, De Lorenzis L. On penalization in variational phase-field models of brittle fracture. Comput Methods Appl Mech Eng. 2019; 354: 990 - 1026. doi: 10.1016/j.cma.2019.05.038 | |
dc.identifier.citedreference | Geelen RJM, Liu Y, Hu T, Tupek MR, Dolbow JE. A phase-field formulation for dynamic cohesive fracture. Comput Methods Appl Mech Eng. 2019; 348: 680 - 711. doi: 10.1016/j.cma.2019.01.026 | |
dc.working.doi | NO | en |
dc.owningcollname | Interdisciplinary and Peer-Reviewed |
Files in this item
Remediation of Harmful Language
The University of Michigan Library aims to describe library materials in a way that respects the people and communities who create, use, and are represented in our collections. Report harmful or offensive language in catalog records, finding aids, or elsewhere in our collections anonymously through our metadata feedback form. More information at Remediation of Harmful Language.
Accessibility
If you are unable to use this file in its current format, please select the Contact Us link and we can modify it to make it more accessible to you.