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Multi-scale boundary element modelling of material degradation and fracture. (English) Zbl 1173.74459
Summary: A multi-scale boundary element method for modelling damage is proposed. The constitutive behaviour of a polycrystalline macro-continuum is described by micromechanics simulations using averaging theorems. An integral non-local approach is employed to avoid the pathological localization of micro-damage at the macro-scale. At the micro-scale, multiple intergranular crack initiation and propagation under mixed mode failure conditions is considered. Moreover, a non-linear frictional contact analysis is employed for modelling the cohesive-frictional grain boundary interfaces. Both micro- and macro-scales are being modelled with the boundary element method. Additionally, a scheme for coupling the micro-BEM with a macro-FEM is also proposed. To demonstrate the accuracy of the proposed method, the mesh independency is investigated and comparisons with two macro-FEM models are made to validate the different modelling approaches. Finally, microstructural variability of the macro-continuum is considered to investigate possible applications to heterogeneous materials.

74S15 Boundary element methods applied to problems in solid mechanics
74R99 Fracture and damage
74S05 Finite element methods applied to problems in solid mechanics
Full Text: DOI
[1] Gagg, C.R., Failure of components and products by ‘engineered-in’ defects: case studies, Engrg. fail. anal., 12, 1000-1026, (2005)
[2] Scutti, J.J.; McBrine, W.J., Failure analysis and prevention, ()
[3] Kachanov, L.M., On the time to failure under creep conditions, Izv. akad. nauk. SSSR, otd. tekhn. nauk., 8, 26-31, (1958)
[4] Lemaitre, J.; Chaboche, J.-L., Mechanics of solid materials, (1990), Cambridge University Press Cambridge
[5] Lemaitre, J., A course on damage mechanics, (1996), Springer Berlin · Zbl 0852.73003
[6] Ghosh, S.; Lee, K.; Moorthy, S., Two scale analysis of heterogeneous elastic – plastic materials with asymptotic homogenisation and Voronoi cell finite element model, Comput. methods appl. mech. engrg., 132, 63-116, (1996) · Zbl 0892.73061
[7] Terada, K.; Hori, M.; Kyoya, T.; Kikuchi, N., Simulation of the multi-scale convergence in computational homogenization approaches, Int. J. solids struct., 37, 2285-2311, (2000) · Zbl 0991.74056
[8] Kouznetsova, V.; 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 engrg., 54, 1235-1260, (2002) · Zbl 1058.74070
[9] Kouznetsova, V.; 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. engrg., 193, 5525-5550, (2004) · Zbl 1112.74469
[10] Flewitt, P.E.J.; Moskovic, R., Contribution of multiscale materials modelling for underwriting nuclear pressure vessel integrity, Mater. sci. technol., 20, 553-566, (2004)
[11] Clayton, J.D.; McDowell, D.L., Finite polycrystalline elastoplasticity and damage: multiscale kinematics, Int. J. solids struct., 40, 5669-5688, (2003) · Zbl 1059.74017
[12] Ladevèze, P., Multiscale modelling and computational strategies for composites, Int. J. numer. methods engrg., 60, 233-253, (2004) · Zbl 1060.74526
[13] Ghosh, S.; Kyunghoon, L.; Raghavan, P., A multi-level computational model for multi-scale damage analysis in composite and porous materials, Int. J. solids struct., 38, 2335-2385, (2001) · Zbl 1015.74058
[14] Raghavan, P.; Ghosh, S., A continuum damage mechanics model for unidirectional composites undergoing interfacial debonding, Mech. mater., 37, 955-979, (2005)
[15] Aliabadi, M.H., The boundary element method, Appl. solids struct., 2, (2002), Wiley London · Zbl 0994.74003
[16] Aliabadi, M.H., A new generation of boundary element methods in fracture mechanics, Int. J. fracture, 86, 91-125, (1997)
[17] Crocker, A.G.; J Flewitt, P.E.; Smith, G.E., Computational modelling of fracture in polycrystalline materials, Int. mater. rev., 50, 99-124, (2005)
[18] Rice, R.W., Mechanical properties of ceramics and composites: grain and particle effects, (2000), Marcel Dekker New York
[19] McMahon, C.J., Hydrogen-induced intergranular fracture of steels, Engrg. fract. mech., 68, 773-788, (2001)
[20] George, E.P.; Liu, C.T.; Lin, H.; Pope, D.P., Environmental embrittlement and other causes of brittle grain boundary fracture in ni_3al, Mater. sci. engrg. A, 92/93, 277-288, (1995)
[21] Ortiz, M.; Pandolfi, A., Finite-deformation irreversible cohesive elements for three-dimensional crack-propagation analysis, Int. J. numer. methods engrg., 44, 1267-1282, (1999) · Zbl 0932.74067
[22] Tvergaard, V., Effect of fibre debonding in a whisker-reinforced metal, Mater. sci. engrg. A: struct. mater. properties, microstruct. process. A, 125, 203-213, (1990)
[23] Xu, X.-P.; Needleman, A., Numerical simulations of dynamic crack growth along an interface, Int. J. fracture, 74, 289-324, (1995-1996)
[24] Sfantos, G.K.; Aliabadi, M.H., A boundary cohesive grain element formulation for modelling intergranular microfracture in polycrystalline brittle materials, Int. J. numer. methods engrg., (2006) · Zbl 1194.74503
[25] Bažant, Z.P.; Belytschko, T.; Chang, T.P., Continuum theory for strain-softening, J. engrg. mech., 110, 1666-1692, (1984)
[26] de Borst, R.; Sluys, L.J.; Mühlhaus, H.-B.; Pamin, J., Fundamental issues in finite element analysis of localization of deformation, Engrg. comput., 10, 99-121, (1993)
[27] de Vree, J.H.P.; Brekelmans, W.A.M.; van Gils, M.A.J., Comparison of nonlocal approaches in continuum damage mechanics, Comput. struct., 55, 581-588, (1995) · Zbl 0919.73187
[28] Needleman, A.; Tvergaard, V., Mesh effects in the analysis of dynamic ductile crack growth, Engrg. fract. mech., 47, 75-91, (1994)
[29] Jirásek, M., Nonlocal models for damage and fracture: comparison of approaches, Int. J. solids struct., 35, 4133-4145, (1998) · Zbl 0930.74054
[30] Bažant, Z.P.; Jirásek, M., Nonlocal integral formulations of plasticity and damage:survey of progress, J. engrg. mech., 128, 1119-1149, (2002)
[31] Mühlhaus, H.-B.; Aifantis, E.C., A variational principle for gradient plasticity, Int. J. solids struct., 28, 845-857, (1991) · Zbl 0749.73029
[32] de Borst, R.; Pamin, J.; Peerlings, R.H.J.; Sluys, L.J., On gradient-enhanced damage and plasticity models for failure in quasi-brittle and frictional materials, Comput. mech., 17, 130-141, (1995) · Zbl 0840.73047
[33] Peerlings, R.H.J.; Brekelmans, W.A.M.; de Borst, R.; Geers, M.G.D., Gradient-enhanced damage modelling of high-cycle fatigue, Int. J. numer. methods engrg., 49, 1547-1569, (2000) · Zbl 0995.74056
[34] Sládek, J.; Sládek, V.; Bažant, Z.P., Non-local boundary integral formulation for softening damage, Int. J. numer. methods engrg., 57, 103-116, (2003) · Zbl 1062.74644
[35] Lin, F.-B.; Yan, G.; Bažant, Z.P.; Ding, F., Nonlocal strain-softening model of quasi-brittle materials using the boundary element method, Engrg. anal. bound. elem., 26, 417-424, (2002) · Zbl 1024.74048
[36] Nemat-Nasser, S.; Hori, M., Micromechanics: overall properties of heterogeneous materials, (1999), Elsevier Science Amsterdam · Zbl 0924.73006
[37] Nemat-Nasser, S., Averaging theorems in finite deformation plasticity, Mech. mater., 31, 493-523, (1999)
[38] Press, W.H.; Teukolsky, S.A.; Vetterling, W.T.; Flannery, B.P., Numerical recipes in Fortran, the art of scientific computing, (1994), Cambridge University Press Cambridge
[39] Okabe, A.; Boots, B.; Sugihara, K.; Chiu, S.N., Spatial tessellations: concepts and applications of Voronoi diagrams, (2000), Wiley Chichester · Zbl 0946.68144
[40] Espinosa, H.D.; Zavattieri, P.D., A grain level model for the study of failure initiation and evolution in polycrystalline brittle materials. part I: theory and numerical implementation, Mech. mater., 35, 333-364, (2003)
[41] Lissenden, C.J.; Herakovich, C.T., Numerical modeling of damage development and viscoplasticity in metal matrix composites, Comput. methods appl. mech. engrg., 126, 289-303, (1995)
[42] Tomar, V.; Jun, Z.; Min, Z., Bounds for element size in a variable stiffness cohesive finite element model, Int. J. numer. methods engrg., 61, 1894-1920, (2004) · Zbl 1075.74683
[43] Hazanov, S., Hill condition and overall properties of composites, Arch. appl. mech., 68, 385-394, (1998) · Zbl 0912.73031
[44] V. Kouznetsova, Computational homogenization for the multi-scale analysis of multi-phase materials, Ph.D. dissertation, University of Technology, Eindhoven, The Netherlands, 2002.
[45] 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., 32, 449-462, (2000)
[46] Patzák, B.; Jirásek, M., Adaptive resolution of localized damage in quasi-brittle materials, J. engrg. mech., 130, 720-732, (2004)
[47] Wachtman, J.B.; Tefft, W.E.; Lam, D.G.; Stinchfield, R.P., Elastic constants of synthetic single crystal corundum at room temperature, J. res. natl. bureau stand., 64, 213-228, (1960)
[48] ASTM E112-96 (Reapproved 2004): Standard Test Methods for Determining Average Grain Size. ASTM International.
[49] Hertzberg, R.W., Deformation and fracture mechanics of engineering materials, (1996), Wiley Chichester
[50] ABAQUS 6.5 Documentation. ABAQUS Inc: USA, 2004.
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