메뉴 건너뛰기




Volumn 193, Issue 48-51, 2004, Pages 5525-5550

Multi-scale second-order computational homogenization of multi-phase materials: A nested finite element solution strategy

Author keywords

Coarse graining; Computational homogenization; Heterogeneous materials; Higher order constitutive modelling; Multi scale modelling; Second gradient continuum; Size effects

Indexed keywords

COMPUTATIONAL COMPLEXITY; COMPUTATIONAL METHODS; FINITE ELEMENT METHOD; MATRIX ALGEBRA; MICROSTRUCTURE; SHEAR STRESS; TENSORS;

EID: 8644290775     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cma.2003.12.073     Document Type: Article
Times cited : (591)

References (55)
  • 2
    • 0031211346 scopus 로고    scopus 로고
    • Computational plasticity for composite structures based on mathematical homogenization: Theory and practice
    • J. Fish K. Shek M. Pandheeradi M.S. Shephard Computational plasticity for composite structures based on mathematical homogenization: Theory and practice Comput. Methods Appl. Mech. Engrg. 148 1997 53-73
    • (1997) Comput. Methods Appl. Mech. Engrg. , vol.148 , pp. 53-73
    • Fish, J.1    Shek, K.2    Pandheeradi, M.3    Shephard, M.S.4
  • 3
    • 0022199855 scopus 로고
    • Local and global aspects in the mathematical theory of plasticity
    • A. Sawczuk G. Bianchi eds. Elsevier Applied Science Publishers London
    • P.M. Suquet Local and global aspects in the mathematical theory of plasticity in: A. Sawczuk G. Bianchi eds. Plasticity Today: Modelling, Methods and Applications 1985 Elsevier Applied Science Publishers London 279-310
    • (1985) Plasticity Today: Modelling, Methods and Applications , pp. 279-310
    • Suquet, P.M.1
  • 4
    • 0025505232 scopus 로고
    • Preprocessing and postprocessing for materials based on the homogenization method with adaptive finite element methods
    • J.M. Guedes N. Kikuchi Preprocessing and postprocessing for materials based on the homogenization method with adaptive finite element methods Comput. Methods Appl. Mech. Engrg. 83 1990 143-198
    • (1990) Comput. Methods Appl. Mech. Engrg. , vol.83 , pp. 143-198
    • Guedes, J.M.1    Kikuchi, N.2
  • 5
    • 0029423823 scopus 로고
    • Nonlinear homogenization method for practical applications
    • S. Ghosh, M. Ostoja-Starzewski (Eds.) vol. AMD-212/MD-62, ASME
    • K. Terada, N. Kikuchi, Nonlinear homogenization method for practical applications, in: S. Ghosh, M. Ostoja-Starzewski (Eds.), Computational Methods in Micromechanics, vol. AMD-212/MD-62, ASME, 1995, pp. 1-16
    • (1995) Computational Methods in Micromechanics , pp. 1-16
    • Terada, K.1    Kikuchi, N.2
  • 6
    • 0030143667 scopus 로고    scopus 로고
    • Two scale analysis of heterogeneous elastic-plastic materials with asymptotic homogenisation and Voronoi cell finite element model
    • S. Ghosh K. Lee S. Moorthy Two scale analysis of heterogeneous elastic-plastic materials with asymptotic homogenisation and Voronoi cell finite element model Comput. Methods Appl. Mech. Engrg. 132 1996 63-116
    • (1996) Comput. Methods Appl. Mech. Engrg. , vol.132 , pp. 63-116
    • Ghosh, S.1    Lee, K.2    Moorthy, S.3
  • 7
    • 0032026085 scopus 로고    scopus 로고
    • Prediction of the mechanical behaviour of non-linear heterogeneous systems by multi-level finite element modeling
    • R.J.M. Smit W.A.M. Brekelmans H.E.H. Meijer Prediction of the mechanical behaviour of non-linear heterogeneous systems by multi-level finite element modeling Comput. Methods Appl. Mech. Engrg. 155 1998 181-192
    • (1998) Comput. Methods Appl. Mech. Engrg. , vol.155 , pp. 181-192
    • Smit, R.J.M.1    Brekelmans, W.A.M.2    Meijer, H.E.H.3
  • 8
    • 0033116492 scopus 로고    scopus 로고
    • Computational homogenization analysis in finite plasticity. Simulation of texture development in polycrystalline materials
    • C. Miehe J. Schröder J. Schotte Computational homogenization analysis in finite plasticity. Simulation of texture development in polycrystalline materials Comput. Methods Appl. Mech. Engrg. 171 1999 387-418
    • (1999) Comput. Methods Appl. Mech. Engrg. , vol.171 , pp. 387-418
    • Miehe, C.1    Schröder, J.2    Schotte, J.3
  • 9
    • 0036631366 scopus 로고    scopus 로고
    • Computational micro-to-macro transition of discretized microstructures undergoing small strain
    • C. Miehe A. Koch Computational micro-to-macro transition of discretized microstructures undergoing small strain Arch. Appl. Mech. 72 2002 300-317
    • (2002) Arch. Appl. Mech. , vol.72 , pp. 300-317
    • Miehe, C.1    Koch, A.2
  • 10
    • 0032686773 scopus 로고    scopus 로고
    • Effective properties of composite materials with periodic microstructure: A computational approach
    • J.C. Michel H. Moulinec P. Suquet Effective properties of composite materials with periodic microstructure: A computational approach Comput. Methods Appl. Mech. Engrg. 172 1999 109-143
    • (1999) Comput. Methods Appl. Mech. Engrg. , vol.172 , pp. 109-143
    • Michel, J.C.1    Moulinec, H.2    Suquet, P.3
  • 11
    • 0034677856 scopus 로고    scopus 로고
    • 2 multiscale approach for modelling the elastoviscoplastic behaviour of long fiber SiC/Ti composite materials
    • 2 multiscale approach for modelling the elastoviscoplastic behaviour of long fiber SiC/Ti composite materials Comput. Methods Appl. Mech. Engrg. 183 2000 309-330
    • (2000) Comput. Methods Appl. Mech. Engrg. , vol.183 , pp. 309-330
    • Feyel, F.1    Chaboche, J.-L.2
  • 12
    • 0035919604 scopus 로고    scopus 로고
    • A class of general algorithms for multi-scale analysis of heterogeneous media
    • K. Terada N. Kikuchi A class of general algorithms for multi-scale analysis of heterogeneous media Comput. Methods Appl. Mech. Engrg. 190 2001 5427-5464
    • (2001) Comput. Methods Appl. Mech. Engrg. , vol.190 , pp. 5427-5464
    • Terada, K.1    Kikuchi, N.2
  • 13
    • 0035061914 scopus 로고    scopus 로고
    • A multi-level computational model for multi-scale damage analysis in composite and porous materials
    • S. Ghosh K. Lee P. Raghavan A multi-level computational model for multi-scale damage analysis in composite and porous materials Int. J. Solids Struct. 38 2001 2335-2385
    • (2001) Int. J. Solids Struct. , vol.38 , pp. 2335-2385
    • Ghosh, S.1    Lee, K.2    Raghavan, P.3
  • 16
    • 0021502102 scopus 로고
    • On the microstructural origin of certain inelastic models
    • E.C. Aifantis On the microstructural origin of certain inelastic models Trans. ASME J. Engrg. Mater. Tech. 106 1984 326-330
    • (1984) Trans. ASME J. Engrg. Mater. Tech. , vol.106 , pp. 326-330
    • Aifantis, E.C.1
  • 17
    • 0026908533 scopus 로고
    • Gradient-dependent plasticity: Formulation and algorithmic aspects
    • R. de Borst H.-B. Mühlhaus Gradient-dependent plasticity: formulation and algorithmic aspects Int. J. Numer. Meth. Engrg. 35 1992 521-539
    • (1992) Int. J. Numer. Meth. Engrg. , vol.35 , pp. 521-539
    • de Borst, R.1    Mühlhaus, H.-B.2
  • 18
    • 0035479791 scopus 로고    scopus 로고
    • A reformulation of strain gradient plasticity
    • N.A. Fleck J.W. Hutchinson A reformulation of strain gradient plasticity J. Mech. Phys. Solids 49 2001 2245-2271
    • (2001) J. Mech. Phys. Solids , vol.49 , pp. 2245-2271
    • Fleck, N.A.1    Hutchinson, J.W.2
  • 21
    • 0036555599 scopus 로고    scopus 로고
    • Nonlocal implicit gradient-enhanced elasto-plasticity for the modelling of softening behaviour
    • R.A.B. Engelen M.G.D. Geers F.P.T. Baaijens Nonlocal implicit gradient-enhanced elasto-plasticity for the modelling of softening behaviour Int. J. Plasticity 19 2003 403-433
    • (2003) Int. J. Plasticity , vol.19 , pp. 403-433
    • Engelen, R.A.B.1    Geers, M.G.D.2    Baaijens, F.P.T.3
  • 23
    • 0001530684 scopus 로고
    • Bounds and estimates for linear composites with strain gradient effects
    • V.P. Smyshlyaev N.A. Fleck Bounds and estimates for linear composites with strain gradient effects J. Mech. Phys. Solids 42 12 1994 1851-1882
    • (1994) J. Mech. Phys. Solids , vol.42 , Issue.12 , pp. 1851-1882
    • Smyshlyaev, V.P.1    Fleck, N.A.2
  • 24
    • 0030128871 scopus 로고    scopus 로고
    • A micromechanics-based nonlocal constitutive equation and estimates of representative volume element size for elastic composites
    • W.J. Drugan J.R. Willis A micromechanics-based nonlocal constitutive equation and estimates of representative volume element size for elastic composites J. Mech. Phys. Solids 44 4 1996 497-524
    • (1996) J. Mech. Phys. Solids , vol.44 , Issue.4 , pp. 497-524
    • Drugan, W.J.1    Willis, J.R.2
  • 25
    • 0030290932 scopus 로고    scopus 로고
    • The influence of scale size on the stability of periodic solids and the role of associated higher order gradient continuum models
    • N. Triantafyllidis S. Bardenhagen The influence of scale size on the stability of periodic solids and the role of associated higher order gradient continuum models J. Mech. Phys. Solids 44 11 1996 1891-1928
    • (1996) J. Mech. Phys. Solids , vol.44 , Issue.11 , pp. 1891-1928
    • Triantafyllidis, N.1    Bardenhagen, S.2
  • 26
    • 0030645297 scopus 로고    scopus 로고
    • Strain gradients and continuum modeling of size effect in metal matrix composites
    • H.T. Zhu H.M. Zbib E.C. Aifantis Strain gradients and continuum modeling of size effect in metal matrix composites Acta Mech. 121 1997 165-176
    • (1997) Acta Mech. , vol.121 , pp. 165-176
    • Zhu, H.T.1    Zbib, H.M.2    Aifantis, E.C.3
  • 28
    • 0009689153 scopus 로고    scopus 로고
    • Couple-stress moduli and characteristic length of a two-phase composite
    • M. Ostoja-Starzewski S.D. Boccara I. Jasiuk Couple-stress moduli and characteristic length of a two-phase composite Mech. Res. Comm. 26 4 1999 387-396
    • (1999) Mech. Res. Comm. , vol.26 , Issue.4 , pp. 387-396
    • Ostoja-Starzewski, M.1    Boccara, S.D.2    Jasiuk, I.3
  • 29
    • 0033902368 scopus 로고    scopus 로고
    • On rigorous derivation of strain gradient effects in the overall behaviour of periodic heterogeneous media
    • V.P. Smyshlyaev K.D. Cherednichenko On rigorous derivation of strain gradient effects in the overall behaviour of periodic heterogeneous media J. Mech. Phys. Solids 48 2000 1325-1357
    • (2000) J. Mech. Phys. Solids , vol.48 , pp. 1325-1357
    • Smyshlyaev, V.P.1    Cherednichenko, K.D.2
  • 30
    • 0035465814 scopus 로고    scopus 로고
    • Numerical analysis of strain gradient effects in periodic media
    • R.H.J. Peerlings N.A. Fleck Numerical analysis of strain gradient effects in periodic media J. Phys. IV 11 2001 153-160
    • (2001) J. Phys. IV , vol.11 , pp. 153-160
    • Peerlings, R.H.J.1    Fleck, N.A.2
  • 31
    • 0035872670 scopus 로고    scopus 로고
    • Asymptotic analysis of heterogeneous Cosserat media
    • S. Forest F. Pradel K. Sab Asymptotic analysis of heterogeneous Cosserat media Int. J. Solids Struct. 38 2001 4585-4608
    • (2001) Int. J. Solids Struct. , vol.38 , pp. 4585-4608
    • Forest, S.1    Pradel, F.2    Sab, K.3
  • 32
    • 0035465988 scopus 로고    scopus 로고
    • Gradient-enhanced computational homogenization for the micro-macro scale transition
    • M.G.D. Geers V. Kouznetsova W.A.M. Brekelmans Gradient-enhanced computational homogenization for the micro-macro scale transition J. Phys. IV 11 2001 145-152
    • (2001) J. Phys. IV , vol.11 , pp. 145-152
    • Geers, M.G.D.1    Kouznetsova, V.2    Brekelmans, W.A.M.3
  • 33
    • 0037143110 scopus 로고    scopus 로고
    • Multi-scale constitutive modelling of heterogeneous materials with a gradient-enhanced computational homogenization scheme
    • V. Kouznetsova M.G.D. Geers W.A.M. Brekelmans Multi-scale constitutive modelling of heterogeneous materials with a gradient-enhanced computational homogenization scheme Int. J. Numer. Meth. Engrg. 54 2002 1235-1260
    • (2002) Int. J. Numer. Meth. Engrg. , vol.54 , pp. 1235-1260
    • Kouznetsova, V.1    Geers, M.G.D.2    Brekelmans, W.A.M.3
  • 34
    • 8644272007 scopus 로고    scopus 로고
    • Computational homogenization for the multi-scale analysis of multi-phase materials
    • Ph.D. thesis, Eindhoven University of Technology, Eindhoven, The Netherlands
    • V. Kouznetsova, Computational homogenization for the multi-scale analysis of multi-phase materials, Ph.D. thesis, Eindhoven University of Technology, Eindhoven, The Netherlands, 2002
    • (2002)
    • Kouznetsova, V.1
  • 35
    • 6544226089 scopus 로고
    • Elastic properties of reinforced solids: Some theoretical principles
    • R. Hill Elastic properties of reinforced solids: Some theoretical principles J. Mech. Phys. Solids 11 1963 357-372
    • (1963) J. Mech. Phys. Solids , vol.11 , pp. 357-372
    • Hill, R.1
  • 36
    • 0033169420 scopus 로고    scopus 로고
    • Averaging theorems in finite deformation plasticity
    • S. Nemat-Nasser Averaging theorems in finite deformation plasticity Mech. Mater. 31 1999 493-523
    • (1999) Mech. Mater. , vol.31 , pp. 493-523
    • Nemat-Nasser, S.1
  • 38
    • 0030218264 scopus 로고    scopus 로고
    • Numerical computation of algorithmic (consistent) tangent moduli in large-strain computational inelasticity
    • C. Miehe Numerical computation of algorithmic (consistent) tangent moduli in large-strain computational inelasticity Comput. Methods Appl. Mech. Engrg. 134 1996 223-240
    • (1996) Comput. Methods Appl. Mech. Engrg. , vol.134 , pp. 223-240
    • Miehe, C.1
  • 39
    • 0037474370 scopus 로고    scopus 로고
    • Computational micro-to-macro transitions for discretized micro-structures of heterogeneous materials at finite strains based on the minimization of averaged incremental energy
    • C. Miehe Computational micro-to-macro transitions for discretized micro-structures of heterogeneous materials at finite strains based on the minimization of averaged incremental energy Comput. Methods Appl. Mech. Engrg. 192 2003 559-591
    • (2003) Comput. Methods Appl. Mech. Engrg. , vol.192 , pp. 559-591
    • Miehe, C.1
  • 40
    • 33947180779 scopus 로고
    • Elastic materials with couple-stress
    • R.A. Toupin Elastic materials with couple-stress Arch. Ration. Mech. Anal. 11 1962 385-414
    • (1962) Arch. Ration. Mech. Anal. , vol.11 , pp. 385-414
    • Toupin, R.A.1
  • 41
    • 34250940617 scopus 로고
    • Theories of elasticity with couple-stress
    • R.A. Toupin Theories of elasticity with couple-stress Arch. Ration. Mech. Anal. 17 1964 85-112
    • (1964) Arch. Ration. Mech. Anal. , vol.17 , pp. 85-112
    • Toupin, R.A.1
  • 42
    • 0040366845 scopus 로고
    • Micro-structure in linear elasticity
    • R.D. Mindlin Micro-structure in linear elasticity Arch. Ration. Mech. Anal. 16 1964 51-78
    • (1964) Arch. Ration. Mech. Anal. , vol.16 , pp. 51-78
    • Mindlin, R.D.1
  • 43
    • 0001357580 scopus 로고
    • On first strain-gradient theories in linear elasticity
    • R.D. Mindlin N.N. Eshel On first strain-gradient theories in linear elasticity Int. J. Solids Struct. 4 1968 109-124
    • (1968) Int. J. Solids Struct. , vol.4 , pp. 109-124
    • Mindlin, R.D.1    Eshel, N.N.2
  • 45
    • 0030269548 scopus 로고    scopus 로고
    • Crack tip fields in strain gradient plasticity
    • Z.C. Xia J.W. Hutchinson Crack tip fields in strain gradient plasticity J. Mech. Phys. Solids 44 10 1996 1621-1648
    • (1996) J. Mech. Phys. Solids , vol.44 , Issue.10 , pp. 1621-1648
    • Xia, Z.C.1    Hutchinson, J.W.2
  • 46
    • 0032180495 scopus 로고    scopus 로고
    • The mechanics of size-dependent indentation
    • M.R. Begley J.W. Hutchinson The mechanics of size-dependent indentation J. Mech. Phys. Solids 46 10 1998 2049-2068
    • (1998) J. Mech. Phys. Solids , vol.46 , Issue.10 , pp. 2049-2068
    • Begley, M.R.1    Hutchinson, J.W.2
  • 47
  • 48
    • 0008514342 scopus 로고
    • Mixed finite elements for couple-stress analysis
    • S.N. Atluri R.H. Gallagher O.C. Zienkiewicz eds. John Wiley & Sons Ltd
    • L.R. Herrmann Mixed finite elements for couple-stress analysis in: S.N. Atluri R.H. Gallagher O.C. Zienkiewicz eds. Hybrid and Mixed Finite Element Methods 1983 John Wiley & Sons Ltd. 1-17
    • (1983) Hybrid and Mixed Finite Element Methods , pp. 1-17
    • Herrmann, L.R.1
  • 49
    • 0032710222 scopus 로고    scopus 로고
    • Finite elements for materials with strain gradient effects
    • J.Y. Shu W.E. King N.A. Fleck Finite elements for materials with strain gradient effects Int. J. Numer. Meth. Engrg. 44 1999 373-391
    • (1999) Int. J. Numer. Meth. Engrg. , vol.44 , pp. 373-391
    • Shu, J.Y.1    King, W.E.2    Fleck, N.A.3
  • 50
    • 0036471631 scopus 로고    scopus 로고
    • Mixed finite element formulations of strain-gradient elasticity problems
    • E. Amanatidou A. Aravas Mixed finite element formulations of strain-gradient elasticity problems Comput. Methods Appl. Mech. Engrg. 191 2002 1723-1751
    • (2002) Comput. Methods Appl. Mech. Engrg. , vol.191 , pp. 1723-1751
    • Amanatidou, E.1    Aravas, A.2
  • 51
    • 0037053923 scopus 로고    scopus 로고
    • Large strain finite element analysis of a local second gradient model: Application to localization
    • T. Matsushima R. Chambon D. Caillerie Large strain finite element analysis of a local second gradient model: Application to localization Int. J. Numer. Meth. Engrg. 54 2002 499-521
    • (2002) Int. J. Numer. Meth. Engrg. , vol.54 , pp. 499-521
    • Matsushima, T.1    Chambon, R.2    Caillerie, D.3
  • 52
    • 0033886012 scopus 로고    scopus 로고
    • Strain gradient effects on microscopic strain field in a metal matrix composite
    • J.Y. Shu C.Y. Barlow Strain gradient effects on microscopic strain field in a metal matrix composite Int. J. Plasticity 16 2000 563-591
    • (2000) Int. J. Plasticity , vol.16 , pp. 563-591
    • Shu, J.Y.1    Barlow, C.Y.2
  • 53
    • 0035371582 scopus 로고    scopus 로고
    • Boundary layers in constrained plastic flow: Comparison of nonlocal and discrete dislocation plasticity
    • J.Y. Shu N.A. Fleck E. van der Giessen N. Needleman Boundary layers in constrained plastic flow: Comparison of nonlocal and discrete dislocation plasticity J. Mech. Phys. Solids 49 2001 1361-1395
    • (2001) J. Mech. Phys. Solids , vol.49 , pp. 1361-1395
    • Shu, J.Y.1    Fleck, N.A.2    van der Giessen, E.3    Needleman, N.4
  • 55
    • 34250168866 scopus 로고    scopus 로고
    • Multi-scale first-order and second-order computational homogenization of microstructures towards continua
    • in press
    • M.G.D. Geers, V.G. Kouznetsova, W.A.M. Brekelmans, Multi-scale first-order and second-order computational homogenization of microstructures towards continua, Int. J. Multiscale Comput. Engrg. in press
    • Int. J. Multiscale Comput. Engrg.
    • Geers, M.G.D.1    Kouznetsova, V.G.2    Brekelmans, W.A.M.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.