Computational homogenization for adhesive and cohesive failure in quasi-brittle solids

International Journal for Numerical Methods in Engineering

Volumn 83, Issue 8-9, 2010, Pages 1155-1179

  Verhoosel, Clemens V ^a   Remmers, Joris J C ^a   Gutiérrez, Miguel A ^b   de Borst, René ^a  

^a EINDHOVEN UNIVERSITY OF TECHNOLOGY   (Netherlands)

^b DELFT UNIVERSITY OF TECHNOLOGY   (Netherlands)

Author keywords

Computational homogenization; Finite elements; Fracture; Multiscale; Partition of unity method

Indexed keywords

COHESIVE FAILURES; COMPUTATIONAL HOMOGENIZATION; DISCRETE-FRACTURE MODELS; FINITE ELEMENT; FRACTURE MODEL; HOMOGENIZATION PROCEDURE; HOMOGENIZATION SCHEME; MACRO SCALE; MICRO MODELS; MICRO-STRUCTURAL; MULTISCALE FRAMEWORK; MULTISCALE SCHEMES; MULTISCALES; NUMERICAL SIMULATION; PARTITION OF UNITY METHODS; PERIODIC MICROSTRUCTURE; QUASI-BRITTLE SOLIDS;

BRITTLENESS; COMPUTATIONAL METHODS; COMPUTER SIMULATION; HOMOGENIZATION METHOD;

FRACTURE;

EID: 77955569487     PISSN: 00295981     EISSN: 10970207     Source Type: Journal    
DOI: 10.1002/nme.2854     Document Type: Article

References (34)

1. Voigt W. Über die beziehung zwischen den beiden elasticitätsconstanten isotroper körper. Annalen der Physik 1889; 274:573-587.
2. Reuss A. Berechnung der fließgrenze von mischkristallen auf grund der plastizitätsbedingung für einkristalle. Zeitschrift für Angewandte Mathematik und Mechanik 1929; 9:49-58.
3. Eshelby JD. The determination of the elastic field of an ellipsoidal inclusion, and related problems. Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences 1957; 241:376-396.
4. Suquet PM. Local and global aspects in the mathematical theory of plasticity. In Plasticity Today: Modelling, Methods and Applications, Sawczuk A, Bianchi G (eds). Elsevier: London, 1985; 279-310.
5. 2 elastoviscoplastic analysis of composite structures. Computational Materials Science 1999; 16(1-4):344-354.
6. Kouznetsova VG, Geers MGD, Brekelmans WAM. Multi-scale constitutive modelling of heterogeneous materials with a gradient-enhanced computational homogenization scheme. International Journal for Numerical Methods in Engineering 2002; 54(8):1235-1260.
7. 2) to describe the response of highly non-linear structures using generalized continua. Computer Methods in Applied Mechanics and Engineering 2003; 192(28-30):3233-3244.
8. Matouš K, Kulkarni MG, Geubelle PH. Multiscale cohesive failure modeling of heterogeneous adhesives. Journal of Mechanics and Physics of Solids 2008; 56(4):1511-1533.
9. Hirschberger CB, Sukumar N, Steinmann P. Computational homogenization of material layers with micromorphic mesostructure. Philosophical Magazine 2008; 88(30):3603-3631.
10. Belytschko T, Loehnert S, Song JH. Multiscale aggregating discontinuities: a method for circumventing loss of material stability. International Journal for Numerical Methods in Engineering 2008; 73(6):869-894.
11. Hettich T, Hund A, Ramm E. Modeling of failure in composites by X-FEM and level sets within a multiscale framework. Computer Methods in Applied Mechanics and Engineering 2008; 197(5):414-424.
12. Verhoosel CV, Remmers JJC, Gutiérrez MA. A partition of unity-based multiscale approach for modeling failure in piezoelectric components. International Journal for Numerical Methods in Engineering 2009; DOI: 10.1002/nme.2792.
13. Gitman IM, Askes H, Sluys LJ. Representative volume: existence and size determination. Engineering Fracture Mechanics 2007; 74(16):2518-2534.
14. Camacho GT, Ortiz M. Computational modelling of impact damage in brittle materials. International Journal of Solids and Structures 1996; 33(20-22):2899-2938.
15. Wells GN, Sluys LJ. A new method for modelling cohesive cracks using finite elements. International Journal for Numerical Methods in Engineering 2001; 50(12):2667-2682.
16. Moës N, Belytschko T. Extended finite element method for cohesive crack growth. Engineering Fracture Mechanics 2002; 69(7):813-833.
17. Wells GN, de Borst R, Sluys LJ. A consistent geometrically non-linear approach for delamination. International Journal for Numerical Methods in Engineering 2002; 54(9):1333-1355.
18. Peerlings RHJ, de Borst R, Brekelmans WAM, Geers MGD. Localisation issues in local and nonlocal continuum approaches to fracture. European Journal of Mechanics-A/Solids 2002; 21(2):175-189.
19. Hill R. Elastic properties of reinforced solids: some theoretical principles. Journal of the Mechanics and Physics of Solids 1963; 11(5):357-372.
20. Kouznetsova VG, Brekelmans WAM, Baaijens FPT. An approach to micro-macro modeling of heterogeneous materials. Computational Mechanics 2001; 27(1):37-48.
21. Cid Alfaro MV, Suiker ASJ, Verhoosel CV, de Borst R. Computational homogenization of cracking processes in thin fibre-expoxy layers. European Journal of Mechanics-A/Solids 2009; DOI: 10.1016/j.euromechsol.2009. 09.006.
22. Gitman IM, Askes H, Sluys LJ. Coupled-volume multi-scale modelling of quasi-brittle material. European Journal of Mechanics-A/Solids 2008; 27(3):302-327.
23. Papoulia KD, Sam CH, Vavasis SA. Time continuity in cohesive finite element modeling. International Journal for Numerical Methods in Engineering 2003; 58(5):679-701.
24. Verhoosel CV, Remmers JJC, Gutiérrez MA. A dissipation-based arc-length method for robust simulation of brittle and ductile failure. International Journal for Numerical Methods in Engineering 2009; 77(9):1290-1321.
25. Terada K, Hori M, Kyoya T, Kikuchi N. Simulation of the multi-scale convergence in computational homogenization approaches. International Journal of Solids and Structures 2004; 37(16):2285-2311.
26. Zohdi TI. Homogenization methods and multiscale modelling. Encyclopedia of Computational Mechanics, Volume 2: Solids and Structures. Wiley: Chichester, 2004; 335-373.
27. Xu XP, Needleman A. Void nucleation by inclusion debonding in a crystal matrix. Modelling and Simulation in Materials Science and Engineering 1993; 1(2):111-132.
28. Tijssens MGA, Sluys LJ, van der Giessen E. Simulation of fracture of cementitious composites with explicit modeling of microstructural features. Engineering Fracture Mechanics 2001; 68(11):1245-1263.
29. Remmers JJC, de Borst R, Needleman A. A cohesive segments method for the simulation of crack growth. Computational Mechanics 2003; 31(1-2):69-77.
30. Jirásek M. Embedded crack models for concrete fracture. In Proceedings of Computational Modelling of Concrete Structures, de Borst R, Bicanic N, Mang H, Meschke G (eds). Balkema: Rotterdam, 1998; 291-300.
31. Jirásek M. Comparative study on finite elements with embedded discontinuities. Computer Methods in Applied Mechanics and Engineering 2000; 188(1-3):307-330.
32. Turon A, Camanho PP, Costa J, Renart J. Accurate simulation of delamination growth under mixed-mode loading using cohesive elements: definition of interlaminar strengths and elastic stiffness. Composite Structures, DOI: 10.1016/j.compstruct.2010.01.012.
33. Bathe KJ. Finite Element Procedures. Prentice-Hall: Upper Saddle River, 1996.
34. Remmers JJC, de Borst R. Delamination buckling of fibre-metal laminates. Composites Science and Technology 2001; 61(15):2207-2213.