An enhanced continuous-discontinuous multiscale method for modeling mode-I cohesive failure in random heterogeneous quasi-brittle materials

Engineering Fracture Mechanics

Volumn 79, Issue , 2012, Pages 78-102

  Nguyen, Vinh Phu ^a   Stroeven, Martijn ^a   Sluys, Lambertus Johannes ^a  

^a DELFT UNIVERSITY OF TECHNOLOGY   (Netherlands)

Author keywords

Computational homogenization; Fully coupled multiscale; Multiscale cohesive law; Random heterogeneous quasi brittle materials; Representative volume element (RVE)

Indexed keywords

COMPUTATIONAL HOMOGENIZATION; FULLY-COUPLED; MULTISCALE COHESIVE LAW; QUASIBRITTLE MATERIAL; REPRESENTATIVE VOLUME ELEMENTS;

BRITTLE FRACTURE; COMPUTATION THEORY; CRACKS; HOMOGENIZATION METHOD; NUMERICAL METHODS;

BRITTLENESS;

EID: 84855188555     PISSN: 00137944     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.engfracmech.2011.10.005     Document Type: Article

References (59)

1. Belytschko T., Song J.H. Coarse-graining of multiscale crack propagation. Int J Numer Methods Engng 2010, 81(5):537-563.
2. Guidault P.A., Allix O., Champaney L., Navarro J.P. A two-scale approach with homogenization for the computation of cracked structures. Comput Struct 2007, 85(17-18):1360-1371.
3. Hettich T., Hund A., Ramm E. Modeling of failure in composites by X-FEM and level sets within a multiscale framework. Comput Methods Appl Mech Engng 2008, 197(5):414-424.
4. Eckardt S., Könke C. Adaptive damage simulation of concrete using heterogeneous multiscale models. J Algorithms Comput Technol 2008, 2:275-297.
5. Lloberas-Valls O, Rixen DJ, Simone A, Sluys LJ. Multiscale domain decomposition analysis of quasi-brittle heterogeneous materials. Int J Numer Methods Engng, accepted for publication.
6. Suquet P.M. Local and global aspects in the mathematical theory of plasticity. Plasticity today: modeling, methods and applications 1985, 279-310. Elsevier, London. A. Sawczuk, G. Bianchi (Eds.).
7. 2 elastoviscoplastic analysis of composite structures. Comput Mater Sci 1999, 16(1-4):344-354.
8. Kanit T., Forest S., Galliet I., Mounoury V., Jeulin D. Determination of the size of the representative volume element for random composites: statistical and numerical approach. Int J Solids Struct 2003, 40(13-14):3647-3679.
9. Gitman I.M., Askes H., Sluys L.J. Representative volume: existence and size determination. Engng Fract Mech 2007, 74(16):2518-2534.
10. Smit R.J.M., Brekelmans W.A.M., Meijer H.E.H. Prediction of the mechanical behavior of nonlinear heterogeneous systems by multi-level finite element modeling. Comput Methods Appl Mech Engng 1998, 55:181-192.
11. Ghosh S., Lee K., Moorthy S. Two scale analysis of heterogeneous elastic-plastic materials with asymptotic homogenization and Voronoi cell finite element model. Comput Methods Appl Mech Engng 1996, 132:63-116.
12. Kouznetsova V.G., Brekelmans W.A.M., Baaijens F.P.T. An approach to micro-macro modeling of heterogeneous materials. Comput Mech 2001, 27(1):37-48.
13. Shek K., Fish J. Multiscale analysis of composite materials and structures. Compos Sci Technol 2000, 60:2547-2556.
14. Monteiro E., Yvonnet J., He Q.C. Computational homogenization for nonlinear conduction in heterogeneous materials using model reduction. Comput Mater Sci 2008, 42(4):704-712.
15. Coenen E.W.C., Kouznetsova V.G., Geers M.G.D. Computational homogenization for heterogeneous thin sheets. Int J Numer Methods Engng 2010, 83(8-9):1180-1205.
16. Gitman I.M., Askes H., Sluys L.J. Coupled-volume multi-scale modelling of quasi-brittle material. Eur J Mech - A/Solids 2007, 27(3):302-327.
17. Kouznetsova V.G., Geers M.G.D., Brekelmans W.A.M. Multi-scale constitutive modelling of heterogeneous materials with a gradient-enhanced computational homogenization scheme. Int J Numer Methods Engng 2002, 54(8):1235-1260.
18. Kouznetsova V.G., Geers M.G.D., Brekelmans W.A.M. Multi-scale second-order computational homogenization of multi-phase materials: a nested finite element solution strategy. Comput Methods Appl Mech Engng 2004, 193(48-51):5525-5550.
19. Kaczmarczyk L., Pearce C.J., Bicanic N. Scale transition and enforcement of RVE boundary conditions in second-order computational homogenization. Int J Numer Methods Engng 2008, 74(3):506-522.
20. Geers M.G.D., Kouznetsova V.G., Brekelmans W.A.M. Multi-scale computational homogenization: trends and challenges. J Comput Appl Math 2010, 234(7):2175-2182.
21. Massart T.J., Peerlings R.H.J., Geers M.G.D. An enhanced multi-scale approach for masonry wall computations with localization of damage. Int J Numer Methods Engng 2007, 69(5):1022-1059.
22. Massart T.J., Peerlings R.H.J., Geers M.G.D. Structural damage analysis of masonry walls using computational homogenization. Int J Damage Mech 2007, 16(2):199-226.
23. Massart T.J., Mercatoris B.C.N. Assessment of periodic homogenisation-based multiscale computational schemes for quasi-brittle structural failure. Int J Multiscale Comput Engng 2009, 7(2):153-170.
24. Mercatoris B.C.N., Massart T.J. A coupled two-scale computational scheme for the failure of periodic quasi-brittle thin planar shells and its application to masonry. Int J Numer Methods Engng 2011, 85(9):1177-1206.
25. Belytschko T., Loehnert S., Song J.H. Multiscale aggregating discontinuities: a method for circumventing loss of material stability. Int J Numer Methods Engng 2008, 73(6):869-894.
26. Verhoosel C.V., Remmers J.J.C., Gutiérrez M.A., de Borst R. Computational homogenisation for adhesive and cohesive failure in quasi-brittle solids. Int J Numer Methods Engng 2010, 83(8-9):1155-1179.
27. Hirschberger C.B., Ricker S., Steinmann P., Sukumar N. Computational multiscale modelling of heterogeneous material layers. Engng Fract Mech 2009, 76(6):793-812.
28. Kulkarni M.G., Matouš K., Geubelle P.H. Coupled multi-scale cohesive modeling of failure in heterogeneous adhesives. Int J Numer Methods Engng 2010, 84(8):916-946.
29. Yuan Z., Fish J. Toward realization of computational homogenization in practice. Int J Numer Methods Engng 2008, 73(3):361-380.
30. Wiechert L., Wall W.A. A nested dynamic multi-scale approach for 3D problems accounting for micro-scale multi-physics. Comput Methods Appl Mech Engng 2010, 199(21-22):1342-1351.
31. Souza F.V., Allen D.H. Multiscale modeling of impact on heterogeneous viscoelastic solids containing evolving microcracks. Int J Numer Methods Engng 2010, 82(4):464-504.
32. Nguyen V.P., Lloberas Valls O., Stroeven M., Sluys L.J. On the existence of representative volumes for softening quasi-brittle materials - a failure zone averaging scheme. Comput Methods Appl Mech Engng 2010, 199(45-48):3028-3038.
33. Nguyen V.P., Lloberas-Valls O., Stroeven M., Sluys L.J. Homogenization-based multiscale crack modelling: from micro-diffusive damage to macro-cracks. Comput Methods Appl Mech Engng 2011, 200(9-12):1220-1236.
34. Nguyen V.P., Lloberas-Valls O., Stroeven M., Sluys L.J. Computational homogenization for multiscale crack modelling. Implementational and computational aspects. Int J Numer Methods Engng 2011, 87. 10.1002/nme.3237.
35. Ghosh S., Lee K., Raghavan P. A multi-level computational model for multi-scale damage analysis in composite and porous materials. Int J Solids Struct 2001, 38:2335-2385.
36. Moës N., Dolbow J., Belytschko T. A finite element method for crack growth without remeshing. Int J Numer Methods Engng 1999, 46(1):131-150.
37. Wells G.N., Sluys L.J. A new method for modelling cohesive cracks using finite elements. Int J Numer Methods Engng 2001, 50(12):2667-2682.
38. Mergheim J., Kuhl E., Steinmann P. A finite element method for cohesive crack modelling. PAMM 2004, 4(1):350-351.
39. Song J.H., Areias P.M.A., Belytschko T. A method for dynamic crack and shear band propagation with phantom nodes. Int J Numer Methods Engng 2006, 67(6):868-893.
40. Peerlings R.H.J., de Borst R., Brekelmans W.A.M., de Vree J.H.P. Gradient-enhanced damage for quasi-brittle materials. Int J Numer Methods Engng 1996, 39:3391-3403.
41. Mazars J., Pijaudier-Cabot G. Continuum damage theory - application to concrete. J Engng Mech Div ASCE 1989, 115:345-365.
42. Geers M.G.D., de Borst R., Brekelmans W.A.M., Peerlings R.H.J. Strain-based transient-gradient damage model for failure analyses. Comput Methods Appl Mech Engng 1998, 160:133-153.
43. Krayani A., Pijaudier-Cabot G., Dufour F. Boundary effect on weight function in nonlocal damage model. Engng Fract Mech 2009, 76(14):2217-2231.
44. Pijaudier-Cabot G., Bažant Z.P. Nonlocal damage theory. ASME J Appl Mech 1987, 113:1512-1533.
45. Lemaitre J. A course on damage mechanics 1996, Springer-Verlag.
46. Terada K., Hori M., Kyoya T., Kikuchi N. Simulation of the multi-scale convergence in computational homogenization approaches. Int J Solids Struct 2000, 37(16):2285-2311.
47. van der Sluis O., Schreurs P.J.G., Brekelmans W.A.M., Meijer H.E.H. Overall behaviour of heterogeneous elastoviscoplastic materials: effect of microstructural modelling. Mech Mater 2000, 32(8):449-462.
48. Bažant Z.P., Belytschko T., Chang T.P. Continuum theory for strain-softening. J Engng Mech 1984, 110:1666-1692.
49. Belytschko T., Bachrach W.E. Efficient implementation of quadrilaterals with high coarse-mesh accuracy. Comput Methods Appl Mech Engng 1986, 54:279-301.
50. Willam K., Kang H., Shing B., Spacone E. Analysis of shear failure in concrete materials. Materials instabilities in solids 1998, 27-39. Wiley, Chichester. R. de Borst, E. van der Giessen (Eds.).
51. Larsson F., Runesson K. On two-scale adaptive FE analysis of micro-heterogeneous media with seamless scale-bridging. Comput Methods Appl Mech Engng 2011, 200(37-40):2662-2674.
52. Temizer I., Wriggers P. An adaptive multiscale resolution strategy for the finite deformation analysis of microheterogeneous structures. Comput Methods Appl Mech Engng 2011, 200(37-40):2639-2661.
53. Geuzaine C., Remacle J.-F. Gmsh, a three-dimensional mesh generator with built-in pre- and post-processing facilities. Int J Numer Methods Engng 2009, 79(11):1309-1331.
54. Stroeven M., Stroeven P. SPACE system for simulation of aggregated matter application to cement hydration. Cem Concr Res 1999, 29(8):1299-1304.
55. Wriggers P., Moftah S.O. Mesoscale models for concrete: homogenisation and damage behaviour. Fin Elem Anal Des 2006, 42(7):623-636.
56. Lemaitre J. Handbook of materials behavior models: failures of materials 2001, vol. 2. Academic Press, San Diego.
57. Papoulia K.D., Sam C.H., Vavasis S.A. Time continuity in cohesive finite element modeling. Int J Numer Methods Engng 2003, 58(5):679-701.
58. Somer D.D., de Souza Neto E.A., Dettmer W.G., Perić D. A sub-stepping scheme for multi-scale analysis of solids. Comput Methods Appl Mech Engng 2009, 198(9-12):1006-1016.
59. Rabczuk T., Zi G., Gerstenberger A., Wall W.A. A new crack tip element for the phantomnode method with arbitrary cohesive cracks. Int J Numer Methods Engng 2008, 75(5):577-599.