Skip to main content
Disciplines
Automotive Business IT + Informatics Construction + Real Estate Electrical Engineering + Electronics Energy + Sustainability Insurance + Risk Finance + Banking Management + Leadership Marketing + Sales Mechanical Engineering + Materials
Events
DE
EN
Books
Journals
Topic Page
Marketing
Start single access now
Access for companies
EXTENDED SEARCH
Log in
Top
Computational Mechanics
Published in: Computational Mechanics 6/2016

22-09-2016 | Original Paper

A novel two-stage discrete crack method based on the screened Poisson equation and local mesh refinement

Authors: P. Areias, T. Rabczuk, J. César de Sá

Published in: Computational Mechanics | Issue 6/2016

Log in

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

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.
previous article On stochastic FEM based computational homogenization of magneto-active heterogeneous materials with random microstructure
next article Partition of unity isogeometric analysis of two dimensional elliptic singular perturbation problems

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

inform now
Literature
1.
Moës N, Dolbow J, Belytschko T (1999) A finite element method for crack growth without remeshing. Int J Numer Methods Eng 46:131–150CrossRefMATH
2.
Oliver J (1995) Continuum modelling of strong discontinuities in solid mechanics using damage models. Comput Mech 17:49–61CrossRefMATH
3.
Henshell RD, Shaw KG (1975) Crack tip elements are unnecessary. Int J Numer Methods Eng 9:1727–1742CrossRefMATH
4.
Lasry D, Belytschko T (1988) Localization limiters in transient problems. Int J Solids Struct 24:581–597CrossRefMATH
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):321–334CrossRef
6.
Colombo D, Giglio M (2006) A methodology for automatic crack propagation modelling in planar and shell fe models. Eng Fract Mech 73:490–504CrossRef
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 81:119–129CrossRef
8.
Loehnert S, Belytschko T (2007) A multiscale projection method for macro/microcrack simulations. Int J Numer Methods Eng 71:1466–1482MathSciNetCrossRefMATH
9.
Moës N, Belytschko T (2002) Extended finite element method for cohesive crack growth. Eng Fract Mech 69:813–833CrossRef
10.
Nguyen-Xuan H, Liu GR, Nourbakhshnia N, Chen L (2012) A novel singular ES-FEM for crack growth simulation. Eng Fract Mech 84:41–66CrossRef
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 69:661–686CrossRef
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 193:3523–3540MathSciNetCrossRefMATH
14.
Areias P, Rabczuk T (2013) Finite strain fracture of plates and shells with configurational forces and edge rotations. Int J Numer Methods Eng 94:1099–1122MathSciNetCrossRef
15.
Miehe C, Gürses E (2007) A robust algorithm for configurational-force-driven brittle crack propagation with \(r-\)adaptive mesh alignment. Int J Numer Methods Eng 72:127–155MathSciNetCrossRefMATH
16.
Duflot M, Nguyen-Dang H (2004) A meshless method with enriched weight functions for fatigue. Int J Numer Methods Eng 59:1945–1961CrossRefMATH
17.
Barbieri E, Petrinic N (2014) Three-dimensional crack propagation with distance-based discontinuous kernels in meshfree methods. Comput Mech 53(2):325–342MathSciNetCrossRefMATH
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)
19.
Paulus CJ, Untereiner L, Courtecuisse H, Cotin S, Cazier D (2015) Virtual cutting of deformable objects based on efficient topological operations. Vis Comput 31:831–841CrossRef
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):3887–3908CrossRefMATH
21.
El Khaoulani R, Bouchard PO (2012) An anisotropic mesh adaptation strategy for damage and failure in ductile materials. Finite Elem Anal Des 59:1–10MathSciNetCrossRef
22.
Teng X, Wierzbicki T (2006) Evaluation of six fracture models in high velocity perforation. Eng Fract Mech 73:1653–1678CrossRef
23.
Oliver J (1989) A consistent characteristic length for smeared cracking models. Int J Numer Methods Eng 28:461–474CrossRefMATH
24.
Etse G, Willam K (1999) Failure analysis of elastoviscoplastic material models. J Eng Mech 125:60–69CrossRef
25.
Schreyer HL, Chen Z (1986) One-dimensional softening with localization. J Appl Mech 53:791–797CrossRef
26.
27.
28.
Fetter AL, Walecka JD (2003) Theoretical mechanics of particles and continua. Courier Dover, New YorkMATH
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
31.
Peerlings RHJ, de Borst R, Brekelmans WAM, de Vree JHP (1996) Gradient enhanced damage for quasi-brittle materials. Int J Numer Methods Eng 39:3391–3403CrossRefMATH
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
33.
Areias PMA, César de Sá JMA, Conceição CA (2003) A gradient model for finite strain elastoplasticity coupled with damage. Finite Elem Anal Des 39:1191–1235CrossRef
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 18:939–962CrossRefMATH
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 160:133–153CrossRefMATH
36.
37.
Korelc J (2002) Multi-language and multi-environment generation of nonlinear finite element codes. Eng Comput 18(4):312–327CrossRef
38.
Belytschko T, Liu WK, Moran B (2000) Nonlinear finite elements for continua and structures. Wiley, New YorkMATH
39.
Frey PJ, George P-L (2000) Mesh generation: application to finite elements. Hermes Science, OxfordMATH
40.
Areias P, Garção J, Pires EB, Barbosa JI (2011) Exact corotational shell for finite strains and fracture. Comput Mech 48:385–406MathSciNetCrossRefMATH
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
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
43.
Dumstorff P, Meschke G (2007) Crack propagation criteria. Int J Numer Anal Met 31:239–259CrossRefMATH
44.
Erdogan F, Sih GC (1963) On the crack extension in plates under plane loading and transverse shear. J Bas Eng 85:519–527CrossRef
45.
Areias P, Msekh MA, Rabczuk T (2016) Damage and fracture algorithm using the screened poisson equation and local remeshing. Eng Fract Mech 158:116–143CrossRef
46.
Carol I, Prat PC, López CM (1997) Normal/shear cracking model: application to discrete crack analysis. J Eng Mech 123:765–773CrossRef
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
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 35:54–71CrossRefMATH
50.
Dias-da-Costa D, Alfaiate J, Sluys LJ, Júlio E (2009) A discrete strong discontinuity approach. Eng Fract Mech 76(9):1176–1201CrossRefMATH
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 63:760–788CrossRefMATH
53.
Bocca P, Carpinteri A, Valente S (1991) Mixed mode fracture of concrete. Int J Solids Struct 27(9):1139–1153CrossRef
54.
Rabczuk T, Belytschko T (2004) Cracking particles: a simplified meshfree method for arbitrary evolving cracks. Int J Numer Methods Eng 61:2316–2343CrossRefMATH
55.
Ruprecht D, Müller H (1998) A scheme for edge-based adaptive tetrahedron subdivision. In: Hege H-C, Polthier K (eds) Mathematical visualization: algorithms., Applications and numericsSpringer, Berlin, pp 61–70CrossRef
Metadata
Title
A novel two-stage discrete crack method based on the screened Poisson equation and local mesh refinement
Authors
P. Areias
T. Rabczuk
J. César de Sá
Publication date
22-09-2016
Publisher
Springer Berlin Heidelberg
Published in
Computational Mechanics / Issue 6/2016
Print ISSN: 0178-7675
Electronic ISSN: 1432-0924
DOI
https://doi.org/10.1007/s00466-016-1328-5

Other articles of this Issue 6/2016

Computational Mechanics 6/2016 Go to the issue

Original Paper

A virtual element method for contact

Original Paper

A pseudo-compressible variational multiscale solver for turbulent incompressible flows

Original Paper

Higher-order hybrid stress triangular Mindlin plate element

Original Paper

On stochastic FEM based computational homogenization of magneto-active heterogeneous materials with random microstructure

Original paper

Computation of the effective nonlinear mechanical response of lattice materials considering geometrical nonlinearities

Original Paper

Partition of unity isogeometric analysis of two dimensional elliptic singular perturbation problems