Phase‐field modeling and simulation of fracture in brittle materials with strongly anisotropic surface energy

International Journal for Numerical Methods in Engineering - Tập 102 Số 3-4 - Trang 711-727 - 2015
Bin Li1, Christian Peco1, Daniel Millán1, Irene Arias1, Marino Arroyo1
1Laboratori de Càlcul Numèric (LaCaN) Universitat Politècnica de Catalunya‐BarcelonaTech (UPC) Barcelona Spain

Tóm tắt

SummaryCrack propagation in brittle materials with anisotropic surface energy is important in applications involving single crystals, extruded polymers, or geological and organic materials. Furthermore, when this anisotropy is strong, the phenomenology of crack propagation becomes very rich, with forbidden crack propagation directions or complex sawtooth crack patterns. This problem interrogates fundamental issues in fracture mechanics, including the principles behind the selection of crack direction. Here, we propose a variational phase‐field model for strongly anisotropic fracture, which resorts to the extended Cahn‐Hilliard framework proposed in the context of crystal growth. Previous phase‐field models for anisotropic fracture were formulated in a framework only allowing for weak anisotropy. We implement numerically our higher‐order phase‐field model with smooth local maximum entropy approximants in a direct Galerkin method. The numerical results exhibit all the features of strongly anisotropic fracture and reproduce strikingly well recent experimental observations. Copyright © 2014 John Wiley & Sons, Ltd.

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Tài liệu tham khảo

10.1080/14786435808565804

10.1016/0022-5096(72)90013-0

10.1016/0020-7683(92)90068-5

Argon AS, 2002, Cleavage cracking resistance of large‐angle grain boundaries in Fe‐3 wt% Si alloy, Philosophical Magazine A, 82, 3333

10.1103/PhysRevLett.84.5347

10.1103/PhysRevLett.76.3594

10.1103/PhysRevLett.110.144301

10.1130/0016-7606(1961)72[985:ESOSFI]2.0.CO;2

10.1002/(SICI)1099-1484(199801)3:1<1::AID-CFM38>3.0.CO;2-7

10.1016/S1365-1609(97)80029-9

10.1016/j.ijrmms.2007.04.005

10.1007/BF00349031

10.1209/epl/i2003-10254-4

10.1016/S0022-5096(98)00002-7

10.1016/j.jmps.2009.05.009

10.1103/PhysRevLett.95.235501

10.1016/j.jmps.2008.10.012

10.1023/A:1007565624473

10.1098/rsta.1921.0006

Freund LB, 1998, Dynamic Fracture Mechanics

Cotterell B, 1965, On brittle fracture paths, International Journal of Fracture Mechanics, 1, 96, 10.1007/BF00186747

10.1007/BF00155254

10.1007/BF00130464

10.1007/BF00035493

10.1115/1.3656897

10.1016/0020-7683(92)90210-K

10.1016/S0022-5096(99)00028-9

10.1002/nme.1534

10.1002/nme.4443

10.1016/j.jcp.2013.04.046

10.1016/S0022-5096(98)00034-9

10.1007/s10659-007-9107-3

10.1007/s10704-010-9562-x

10.1016/j.cma.2014.01.016

10.1016/0167-2789(93)90120-P

10.1016/S0167-2789(97)00177-2

10.1016/S0167-2789(00)00222-0

10.1098/rspa.2008.0385

10.1063/1.1744102

10.1080/01418610110038420

10.1103/PhysRevE.85.041603

10.1007/s10853-008-3196-7

10.1177/1056789510386852

10.1007/s00161-011-0228-3

BordenMJ.Isogeometric analysis of phase‐field models for dynamic brittle and ductile fracture Ph.D. Thesis Computational Science Engineering and Mathematics University of Texas at Austin Austin USA August 2012.

10.1103/PhysRev.82.87

10.1016/j.tsf.2008.08.143

10.1016/j.jcrysgro.2004.10.069

10.1002/nme.2793

10.1016/j.jcp.2013.04.038

10.1016/j.cma.2011.11.022

10.1016/j.cma.2011.09.004

10.1016/j.cad.2012.10.018

10.1016/j.cma.2013.05.015

10.4171/IFB/171

Huang K, 2005, Lectures on Statistical Physics and Protein Folding, 10.1142/5741

10.1007/BF00665906

10.1093/oso/9780195074475.001.0001

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International Journal for Numerical Methods in Engineering

Tập 102 Số 3-4

711-727

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