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A novel two-stage discrete crack method based on the screened Poisson equation and local mesh refinement. (English) Zbl 1398.74293

Summary: We propose an alternative crack propagation algorithm which effectively circumvents the variable transfer procedure adopted with classical mesh adaptation algorithms. The present alternative consists of two stages: a mesh-creation stage where a local damage model is employed with the objective of defining a crack-conforming mesh and a subsequent analysis stage with a localization limiter in the form of a modified screened Poisson equation which is exempt of crack path calculations. In the second stage, the crack naturally occurs within the refined region. A staggered scheme for standard equilibrium and screened Poisson equations is used in this second stage. Element subdivision is based on edge split operations using a constitutive quantity (damage). To assess the robustness and accuracy of this algorithm, we use five quasi-brittle benchmarks, all successfully solved.

MSC:

74S05 Finite element methods applied to problems in solid mechanics
74R10 Brittle fracture
74S30 Other numerical methods in solid mechanics (MSC2010)
74R99 Fracture and damage
74R20 Anelastic fracture and damage

Software:

Mathematica
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Full Text: DOI

References:

[1] Moës N, Dolbow J, Belytschko T (1999) A finite element method for crack growth without remeshing. Int J Numer Methods Eng 46:131-150 · Zbl 0955.74066 · doi:10.1002/(SICI)1097-0207(19990910)46:1<131::AID-NME726>3.0.CO;2-J
[2] Oliver J (1995) Continuum modelling of strong discontinuities in solid mechanics using damage models. Comput Mech 17:49-61 · Zbl 0840.73051 · doi:10.1007/BF00356478
[3] Henshell RD, Shaw KG (1975) Crack tip elements are unnecessary. Int J Numer Methods Eng 9:1727-1742 · Zbl 0306.73064 · doi:10.1002/nme.1620090302
[4] Lasry D, Belytschko T (1988) Localization limiters in transient problems. Int J Solids Struct 24:581-597 · Zbl 0636.73021 · doi:10.1016/0020-7683(88)90059-5
[5] Bittencourt TN, Wawrzynek PA, Ingraffea AR, Sousa JL (1996) Quasi-automatic simulation of crack propagation for 2D LEFM problems. Eng Fract Mech 55(2):321-334 · doi:10.1016/0013-7944(95)00247-2
[6] Colombo D, Giglio M (2006) A methodology for automatic crack propagation modelling in planar and shell fe models. Eng Fract Mech 73:490-504 · doi:10.1016/j.engfracmech.2005.08.007
[7] Karihaloo BL, Xiao QZ (2003) Modelling of stationary and growing cracks in FE framework without remeshing: a state-of-the-art review. Comput Struct 81:119-129 · doi:10.1016/S0045-7949(02)00431-5
[8] Loehnert S, Belytschko T (2007) A multiscale projection method for macro/microcrack simulations. Int J Numer Methods Eng 71:1466-1482 · Zbl 1194.74436 · doi:10.1002/nme.2001
[9] Moës N, Belytschko T (2002) Extended finite element method for cohesive crack growth. Eng Fract Mech 69:813-833 · doi:10.1016/S0013-7944(01)00128-X
[10] Nguyen-Xuan H, Liu GR, Nourbakhshnia N, Chen L (2012) A novel singular ES-FEM for crack growth simulation. Eng Fract Mech 84:41-66 · doi:10.1016/j.engfracmech.2012.01.001
[11] Pierard O, Jin Y, Wyart E, Dompierre B, Bechet E (2016) Simulation of contact on crack lips and its influence on fatigue life prediction. In: Carpintieri A, Fatemi A, Navarro C (eds) International Conference on Multiaxial Fatigue and Fracture, ICMFF11, Seville. Fracture and structural integrity
[12] Alfaiate J, Wells GN, Sluys LJ (2002) On the use of embedded discontinuity elements with crack path continuity for mode-I and mixed-mode fracture. Eng Fract Mech 69:661-686 · doi:10.1016/S0013-7944(01)00108-4
[13] Hansbo A, Hansbo P (2004) A finite element method for the simulation of strong and weak discontinuities in solid mechanics. Comput Methods Appl Mech Eng 193:3523-3540 · Zbl 1068.74076 · doi:10.1016/j.cma.2003.12.041
[14] Areias P, Rabczuk T (2013) Finite strain fracture of plates and shells with configurational forces and edge rotations. Int J Numer Methods Eng 94:1099-1122 · Zbl 1352.74316 · doi:10.1002/nme.4477
[15] Miehe C, Gürses E (2007) A robust algorithm for configurational-force-driven brittle crack propagation with \[r-\] r-adaptive mesh alignment. Int J Numer Methods Eng 72:127-155 · Zbl 1194.74444 · doi:10.1002/nme.1999
[16] Duflot M, Nguyen-Dang H (2004) A meshless method with enriched weight functions for fatigue. Int J Numer Methods Eng 59:1945-1961 · Zbl 1060.74664 · doi:10.1002/nme.948
[17] Barbieri E, Petrinic N (2014) Three-dimensional crack propagation with distance-based discontinuous kernels in meshfree methods. Comput Mech 53(2):325-342 · Zbl 1398.74451 · doi:10.1007/s00466-013-0910-3
[18] Peng X, Atroshchenko E, Kerfriden P, Bordas SPA (2016) Isogeometric boundary element methods for three dimensional static fracture and fatigue crack growth. Comput Methods Appl Mech Eng (in press) · Zbl 1439.74370
[19] Paulus CJ, Untereiner L, Courtecuisse H, Cotin S, Cazier D (2015) Virtual cutting of deformable objects based on efficient topological operations. Vis Comput 31:831-841 · doi:10.1007/s00371-015-1123-x
[20] Bouchard PO, Bay F, Chastel Y (2003) Numerical modeling of crack propagation—implementation, techniques and comparison of different criteria. Comp Methods Appl Mech Eng 192(35-36):3887-3908 · Zbl 1054.74724 · doi:10.1016/S0045-7825(03)00391-8
[21] El Khaoulani R, Bouchard PO (2012) An anisotropic mesh adaptation strategy for damage and failure in ductile materials. Finite Elem Anal Des 59:1-10 · doi:10.1016/j.finel.2012.04.006
[22] Teng X, Wierzbicki T (2006) Evaluation of six fracture models in high velocity perforation. Eng Fract Mech 73:1653-1678 · doi:10.1016/j.engfracmech.2006.01.009
[23] Oliver J (1989) A consistent characteristic length for smeared cracking models. Int J Numer Methods Eng 28:461-474 · Zbl 0676.73066 · doi:10.1002/nme.1620280214
[24] Etse G, Willam K (1999) Failure analysis of elastoviscoplastic material models. J Eng Mech 125:60-69 · doi:10.1061/(ASCE)0733-9399(1999)125:1(60)
[25] Schreyer HL, Chen Z (1986) One-dimensional softening with localization. J Appl Mech 53:791-797 · doi:10.1115/1.3171860
[26] Areias P. Simplas. http://home.uevora.pt/ pmaa/SimplasWebsite/Simplas.html · Zbl 1194.74444
[27] Lemaitre J (1996) A course on damage mechanics, 2nd edn. Springer, New York · Zbl 0852.73003 · doi:10.1007/978-3-642-18255-6
[28] Fetter AL, Walecka JD (2003) Theoretical mechanics of particles and continua. Courier Dover, New York · Zbl 1191.70001
[29] Ogden RW (1997) Non-linear elastic deformations. Dover Publications, New York
[30] Mazars J (1984) Application de la mécanique de l’endommagement au comportement non linéaire et à la rupture du béton de structure. Thèse de Doctorat d’Etat, Université Paris VI, Paris · Zbl 1230.74177
[31] Peerlings RHJ, de Borst R, Brekelmans WAM, de Vree JHP (1996) Gradient enhanced damage for quasi-brittle materials. Int J Numer Methods Eng 39:3391-3403 · Zbl 0882.73057 · doi:10.1002/(SICI)1097-0207(19961015)39:19<3391::AID-NME7>3.0.CO;2-D
[32] Areias P, Dias-da-Costa D, Alfaiate J, Júlio E (2009) Arbitrary bi-dimensional finite strain cohesive crack propagation. Comput Mech 45(1):61-75 · Zbl 1398.74272
[33] Areias PMA, César de Sá JMA, Conceição CA (2003) A gradient model for finite strain elastoplasticity coupled with damage. Finite Elem Anal Des 39:1191-1235 · doi:10.1016/S0168-874X(02)00164-6
[34] de Borst R, Pamin J, Geers MGD (1999) On coupled gradient-dependent plasticity and damage theories with a view to localization analysis. Eur J Mech A 18:939-962 · Zbl 0968.74007 · doi:10.1016/S0997-7538(99)00114-X
[35] Geers MGD, de Borst R, Brekelmans WAM, Peerlings RHJ (1998) Strain-based transient-gradient damage model for failure analysis. Comput Methods Appl Mech Eng 160:133-153 · Zbl 0938.74006 · doi:10.1016/S0045-7825(98)80011-X
[36] Wolfram Research Inc. Mathematica (2007) · Zbl 1360.74133
[37] Korelc J (2002) Multi-language and multi-environment generation of nonlinear finite element codes. Eng Comput 18(4):312-327 · doi:10.1007/s003660200028
[38] Belytschko T, Liu WK, Moran B (2000) Nonlinear finite elements for continua and structures. Wiley, New York · Zbl 0959.74001
[39] Frey PJ, George P-L (2000) Mesh generation: application to finite elements. Hermes Science, Oxford · Zbl 0968.65009
[40] Areias P, Garção J, Pires EB, Barbosa JI (2011) Exact corotational shell for finite strains and fracture. Comput Mech 48:385-406 · Zbl 1360.74133 · doi:10.1007/s00466-011-0588-3
[41] Winkler BJ (2001) Traglastuntersuchungen von unbewehrten und bew. Betonstrukturen auf der Grundlage eines objektiven Werkstoffgesetzes für Beton. PhD thesis, University of Innsbruck, Innrain 52, 6020 Innsbruck · Zbl 1352.74316
[42] Most T, Bucher C (2006) Energy-based simulation of concrete cracking using an improved mixed-mode cohesive crack model within a meshless discretization. Int J Numer Anal Met 31:285-305 · Zbl 1115.74060
[43] Dumstorff P, Meschke G (2007) Crack propagation criteria. Int J Numer Anal Met 31:239-259 · Zbl 1159.74038 · doi:10.1002/nag.560
[44] Erdogan F, Sih GC (1963) On the crack extension in plates under plane loading and transverse shear. J Bas Eng 85:519-527 · doi:10.1115/1.3656897
[45] Areias P, Msekh MA, Rabczuk T (2016) Damage and fracture algorithm using the screened poisson equation and local remeshing. Eng Fract Mech 158:116-143 · doi:10.1016/j.engfracmech.2015.10.042
[46] Carol I, Prat PC, López CM (1997) Normal/shear cracking model: application to discrete crack analysis. J Eng Mech 123:765-773 · doi:10.1061/(ASCE)0733-9399(1997)123:8(765)
[47] Schlangen E (1993) Experimental and numerical analysis of fracture processes in concrete. PhD thesis, Delft
[48] Alfaiate J, Simone A, Sluys LJ (2003) A new approach to strong embedded discontinuities. In: Bicanic N, de Borst R, Mang H, Meschke G (eds) Computational Modelling of Concrete Structures, EURO-C 2003. St. Johann im Pongau · Zbl 1059.74548
[49] Areias PMA, César de Sá JMA, Conceição António CA, Carneiro JASAO, Teixeira VMP (2004) Strong displacement discontinuities and Lagrange multipliers in the analysis of finite displacement fracture problems. Comput Mech 35:54-71 · Zbl 1109.74350 · doi:10.1007/s00466-004-0603-z
[50] Dias-da-Costa D, Alfaiate J, Sluys LJ, Júlio E (2009) A discrete strong discontinuity approach. Eng Fract Mech 76(9):1176-1201 · Zbl 1230.74177 · doi:10.1016/j.engfracmech.2009.01.011
[51] Arrea M, Ingraffea RA (1982) Mixed-mode crack propagation in mortar and concrete. Technical Report Report 81-13, Cornell University, Department of Structural Engineering
[52] Areias PMA, Belytschko T (2005) Analysis of three-dimensional crack initiation and propagation using the extended finite element method. Int J Numer Methods Eng 63:760-788 · Zbl 1122.74498 · doi:10.1002/nme.1305
[53] Bocca P, Carpinteri A, Valente S (1991) Mixed mode fracture of concrete. Int J Solids Struct 27(9):1139-1153 · Zbl 0755.46012 · doi:10.1016/0020-7683(91)90115-V
[54] Rabczuk T, Belytschko T (2004) Cracking particles: a simplified meshfree method for arbitrary evolving cracks. Int J Numer Methods Eng 61:2316-2343 · Zbl 1075.74703 · doi:10.1002/nme.1151
[55] Ruprecht, D.; Müller, H.; Hege, H-C (ed.); Polthier, K. (ed.), A scheme for edge-based adaptive tetrahedron subdivision, 61-70 (1998), Berlin · Zbl 0940.68148 · doi:10.1007/978-3-662-03567-2_5
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