×

zbMATH — the first resource for mathematics

Phase-field modelling of ductile fracture: a variational gradient-extended plasticity-damage theory and its micromorphic regularization. (English) Zbl 1353.74065
Summary: This work outlines a novel variational-based theory for the phase-field modelling of ductile fracture in elastic-plastic solids undergoing large strains. The phase-field approach regularizes sharp crack surfaces within a pure continuum setting by a specific gradient damage modelling. It is linked to a formulation of gradient plasticity at finite strains. The framework includes two independent length scales which regularize both the plastic response as well as the crack discontinuities. This ensures that the damage zones of ductile fracture are inside of plastic zones, and guarantees on the computational side a mesh objectivity in post-critical ranges.

MSC:
74R10 Brittle fracture
74M25 Micromechanics of solids
74C10 Small-strain, rate-dependent theories of plasticity (including theories of viscoplasticity)
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Lemaitre J , Chaboche J . 1990 Mechanics of solid materials . Cambridge, UK: Cambridge University Press. · Zbl 0743.73002 · doi:10.1017/CBO9781139167970
[2] DOI: 10.1177/1056789509103482 · doi:10.1177/1056789509103482
[3] DOI: 10.1016/j.ijplas.2010.04.001 · doi:10.1016/j.ijplas.2010.04.001
[4] DOI: 10.1103/PhysRevLett.87.045501 · doi:10.1103/PhysRevLett.87.045501
[5] DOI: 10.1016/j.jmps.2008.10.012 · Zbl 1421.74089 · doi:10.1016/j.jmps.2008.10.012
[6] DOI: 10.1016/S0022-5096(98)00034-9 · Zbl 0966.74060 · doi:10.1016/S0022-5096(98)00034-9
[7] Bourdin B , Francfort G , Marigo JJ . 2008 The variational approach to fracture . Berlin, Germany: Springer. · Zbl 1176.74018 · doi:10.1007/978-1-4020-6395-4
[8] DOI: 10.1002/cpa.3160420503 · Zbl 0691.49036 · doi:10.1002/cpa.3160420503
[9] DOI: 10.1002/cpa.3160430805 · Zbl 0722.49020 · doi:10.1002/cpa.3160430805
[10] DOI: 10.1002/nme.2861 · Zbl 1202.74014 · doi:10.1002/nme.2861
[11] DOI: 10.1177/1056789510386852 · doi:10.1177/1056789510386852
[12] Borden, A phase-field description of dynamic brittle fracture, Comput. Methods Appl. Mech. Eng. 217–220 pp 77– (2012) · Zbl 1253.74089 · doi:10.1016/j.cma.2012.01.008
[13] DOI: 10.1002/nme.4553 · Zbl 1352.74029 · doi:10.1002/nme.4553
[14] DOI: 10.1002/pamm.201310258 · doi:10.1002/pamm.201310258
[15] DOI: 10.1016/j.mechmat.2013.12.005 · doi:10.1016/j.mechmat.2013.12.005
[16] DOI: 10.1007/s00466-015-1151-4 · Zbl 1329.74018 · doi:10.1007/s00466-015-1151-4
[17] DOI: 10.1016/j.cma.2014.11.017 · doi:10.1016/j.cma.2014.11.017
[18] Miehe C , Aldakheel F , Raina A . Submitted. Phase-field modelling of ductile fracture at finite strains: a variational gradient-extended plasticity-damage theory. Int. J. Plast .
[19] DOI: 10.1016/j.jmps.2010.11.001 · Zbl 1270.74022 · doi:10.1016/j.jmps.2010.11.001
[20] DOI: 10.1016/j.cma.2013.03.014 · Zbl 1295.74013 · doi:10.1016/j.cma.2013.03.014
[21] Maugin, Internal variables and dissipative structures, J. Non-Equilib. Thermodyn. 15 pp 173– (1990) · doi:10.1515/jnet.1990.15.2.173
[22] Capriz G . 1989 Continua with microstructure . Berlin, Germany: Springer. · Zbl 0676.73001 · doi:10.1007/978-1-4612-3584-2
[23] Mariano, Multifield theories in mechanics of solids, Adv. Appl. Mech. 38 pp 1– (2001) · doi:10.1016/S0065-2156(02)80102-8
[24] FrĂ©mond M . 2002 Non-smooth thermomechanics . Berlin, Germany: Springer. · Zbl 0990.80001 · doi:10.1007/978-3-662-04800-9
[25] DOI: 10.1061/(ASCE)0733-9399(2009)135:3(117) · doi:10.1061/(ASCE)0733-9399(2009)135:3(117)
[26] DOI: 10.1016/S0020-7683(97)00175-3 · Zbl 0935.74022 · doi:10.1016/S0020-7683(97)00175-3
[27] DOI: 10.1016/S0045-7825(02)00438-3 · Zbl 1083.74518 · doi:10.1016/S0045-7825(02)00438-3
[28] DOI: 10.1016/j.cma.2014.01.016 · Zbl 1296.74098 · doi:10.1016/j.cma.2014.01.016
[29] DOI: 10.1016/j.cma.2013.07.015 · Zbl 1295.74014 · doi:10.1016/j.cma.2013.07.015
[30] DOI: 10.1002/nme.4486 · Zbl 1352.74408 · doi:10.1002/nme.4486
[31] DOI: 10.1016/j.ijsolstr.2004.05.072 · Zbl 1121.74330 · doi:10.1016/j.ijsolstr.2004.05.072
[32] DOI: 10.1002/(SICI)1097-0207(19961015)39:19<3391::AID-NME7>3.0.CO;2-D · Zbl 0882.73057 · doi:10.1002/(SICI)1097-0207(19961015)39:19<3391::AID-NME7>3.0.CO;2-D
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.