메뉴 건너뛰기




Volumn 197, Issue 41-42, 2008, Pages 3225-3248

Generalized Mathematical Homogenization: From theory to practice

Author keywords

Atomistic; Constitutive law free; Continuum; Generalized Mathematical Homogenization; Thermo mechanical

Indexed keywords

CONSTITUTIVE EQUATIONS; ELECTRIC WIRE; FINITE ELEMENT METHOD; MOLECULAR DYNAMICS; MOLECULAR MECHANICS; MOLECULES; NUMERICAL ANALYSIS; QUANTUM CHEMISTRY;

EID: 48149111693     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cma.2007.12.002     Document Type: Article
Times cited : (41)

References (28)
  • 1
    • 48149103567 scopus 로고    scopus 로고
    • National Nanotechnology Initiative, Supplement to the President's FY 2004 Budget, National Science and Technology Council Committee on Technology.
    • National Nanotechnology Initiative, Supplement to the President's FY 2004 Budget, National Science and Technology Council Committee on Technology.
  • 2
    • 0001259264 scopus 로고    scopus 로고
    • Coarse-grained molecular dynamics and the atomic limit of finite elements
    • Rudd R.E., and Broughton J.Q. Coarse-grained molecular dynamics and the atomic limit of finite elements. Phys. Rev. B 58 10 (1998) R5893-R5896
    • (1998) Phys. Rev. B , vol.58 , Issue.10
    • Rudd, R.E.1    Broughton, J.Q.2
  • 3
    • 0038579633 scopus 로고    scopus 로고
    • Atomistic/continuum coupling in computational materials science
    • Curtin W.A., and Miller R.E. Atomistic/continuum coupling in computational materials science. Modeling Simulat. Mater. Sci. Engrg. 11 3 (2003) R33-R68
    • (2003) Modeling Simulat. Mater. Sci. Engrg. , vol.11 , Issue.3
    • Curtin, W.A.1    Miller, R.E.2
  • 4
    • 33750993211 scopus 로고    scopus 로고
    • Bridging the scales in nano engineering and science
    • Fish J. Bridging the scales in nano engineering and science. J. Nanoparticle Res. 8 (2006) 577-594
    • (2006) J. Nanoparticle Res. , vol.8 , pp. 577-594
    • Fish, J.1
  • 6
    • 0041848500 scopus 로고    scopus 로고
    • The emerging role of multiscale modeling in nano- and micro-mechanics of materials
    • Ghoniem N.M., and Cho K. The emerging role of multiscale modeling in nano- and micro-mechanics of materials. Modeling Engrg. Sci. 3 2 (2002) 147-173
    • (2002) Modeling Engrg. Sci. , vol.3 , Issue.2 , pp. 147-173
    • Ghoniem, N.M.1    Cho, K.2
  • 7
    • 1842708892 scopus 로고    scopus 로고
    • An introduction to computational nanomechanics and materials
    • Liu W.K., Karpov E.G., et al. An introduction to computational nanomechanics and materials. Comput. Methods Appl. Mech. Engrg. 193 (2004) 1529-1578
    • (2004) Comput. Methods Appl. Mech. Engrg. , vol.193 , pp. 1529-1578
    • Liu, W.K.1    Karpov, E.G.2
  • 8
    • 33846920064 scopus 로고    scopus 로고
    • Coupled quantum mechanical/molecular mechanical modeling of the fracture of defective carbon nanotubes and graphene sheets
    • (Art. No. 075412)
    • Khare R., Mielke S.L., Paci J.T., Zhang S.L., Ballarini R., Schatz G.C., and Belytschko T. Coupled quantum mechanical/molecular mechanical modeling of the fracture of defective carbon nanotubes and graphene sheets. Phys. Rev. B 75 7 (2007) (Art. No. 075412)
    • (2007) Phys. Rev. B , vol.75 , Issue.7
    • Khare, R.1    Mielke, S.L.2    Paci, J.T.3    Zhang, S.L.4    Ballarini, R.5    Schatz, G.C.6    Belytschko, T.7
  • 10
    • 33745905282 scopus 로고    scopus 로고
    • Generalized mathematical homogenization of atomistic media at finite temperatures
    • Fish J., Chen W., and Tang T. Generalized mathematical homogenization of atomistic media at finite temperatures. Int. J. Multiscale Comput. Engrg. 3 (2005) 393-413
    • (2005) Int. J. Multiscale Comput. Engrg. , vol.3 , pp. 393-413
    • Fish, J.1    Chen, W.2    Tang, T.3
  • 11
    • 33750446704 scopus 로고    scopus 로고
    • Generalized mathematical homogenization of atomistic media at finite temperatures in three dimensions
    • Fish J., Chen W., and Li R. Generalized mathematical homogenization of atomistic media at finite temperatures in three dimensions. Comput. Methods Appl. Mech. Engrg. 196 (2007) 908-922
    • (2007) Comput. Methods Appl. Mech. Engrg. , vol.196 , pp. 908-922
    • Fish, J.1    Chen, W.2    Li, R.3
  • 14
    • 0025505232 scopus 로고
    • Preprocessing and postprocessing for materials based on the homogenization method with adaptive finite element methods
    • Guedes J.M., and Kikuchi N. Preprocessing and postprocessing for materials based on the homogenization method with adaptive finite element methods. Comp. Methods Appl. Mech. Engrg. 83 (1990) 143-198
    • (1990) Comp. Methods Appl. Mech. Engrg. , vol.83 , pp. 143-198
    • Guedes, J.M.1    Kikuchi, N.2
  • 15
    • 85128805678 scopus 로고    scopus 로고
    • The heterogeneous multi-scale methods
    • E W., and Engquist B. The heterogeneous multi-scale methods. Comm. Math. Sci. 1 (2002) 87-132
    • (2002) Comm. Math. Sci. , vol.1 , pp. 87-132
    • Engquist, B.1
  • 16
    • 1542327302 scopus 로고    scopus 로고
    • A new look at the atomic level virial stress: on continuum-molecular system equivalence
    • Zhou M. A new look at the atomic level virial stress: on continuum-molecular system equivalence. Proc. Roy. Soc. Lond. Ser. A - Math. Phys. Engrg. Sci. 459 (2003) 2347-2392
    • (2003) Proc. Roy. Soc. Lond. Ser. A - Math. Phys. Engrg. Sci. , vol.459 , pp. 2347-2392
    • Zhou, M.1
  • 18
    • 0003098637 scopus 로고    scopus 로고
    • Stress calculation in atomistic simulations of perfect and imperfect solids
    • Cormier J., Rickman J.M., and Delph T.J. Stress calculation in atomistic simulations of perfect and imperfect solids. J. Appl. Phys. 89 (2001) 99-104
    • (2001) J. Appl. Phys. , vol.89 , pp. 99-104
    • Cormier, J.1    Rickman, J.M.2    Delph, T.J.3
  • 19
    • 18544383450 scopus 로고    scopus 로고
    • Multiscale modeling of the dynamics of solids at finite temperature
    • Li X., and Weinan E. Multiscale modeling of the dynamics of solids at finite temperature. J. Mech. Phys. Solids 53 (2005) 1650-1685
    • (2005) J. Mech. Phys. Solids , vol.53 , pp. 1650-1685
    • Li, X.1    Weinan, E.2
  • 20
    • 0037438283 scopus 로고    scopus 로고
    • Comparative study of Si(0 0 1) surface structure and interatomic potentials in finite-temperature simulations
    • Nurminen L., Tavazza F., Landau D.P., Kuronen A., and Kaski K. Comparative study of Si(0 0 1) surface structure and interatomic potentials in finite-temperature simulations. Phys. Rev. B 67 (2003) 1-10
    • (2003) Phys. Rev. B , vol.67 , pp. 1-10
    • Nurminen, L.1    Tavazza, F.2    Landau, D.P.3    Kuronen, A.4    Kaski, K.5
  • 21
    • 0001471515 scopus 로고    scopus 로고
    • The Nosé-Poincaré method for constant temperature molecular dynamics
    • Bond S.D., Leimkuhler B.J., and Laird b.B. The Nosé-Poincaré method for constant temperature molecular dynamics. J. Comput. Phys. 151 (1999) 114-134
    • (1999) J. Comput. Phys. , vol.151 , pp. 114-134
    • Bond, S.D.1    Leimkuhler, B.J.2    Laird, b.B.3
  • 22
    • 19744382644 scopus 로고    scopus 로고
    • Chernozatonskii, Nanomechanics of silicon nanowires
    • (Art. No. 125313)
    • Menon M., Srivastava D., Ponomareva I., and Leonid A. Chernozatonskii, Nanomechanics of silicon nanowires. Phys. Rev. B 70 12 (2004) (Art. No. 125313)
    • (2004) Phys. Rev. B , vol.70 , Issue.12
    • Menon, M.1    Srivastava, D.2    Ponomareva, I.3    Leonid, A.4
  • 23
    • 34247223067 scopus 로고    scopus 로고
    • A space-time multiscale method for molecular dynamics simulation of biomolecules
    • Li A., Waisman H., and Fish J. A space-time multiscale method for molecular dynamics simulation of biomolecules. Int. J. Multiscale Computat. Engrg. 4 5-6 (2006) 791-803
    • (2006) Int. J. Multiscale Computat. Engrg. , vol.4 , Issue.5-6 , pp. 791-803
    • Li, A.1    Waisman, H.2    Fish, J.3
  • 24
    • 29744464063 scopus 로고    scopus 로고
    • Coarse-grained molecular dynamics for computer modeling of nanomechanical systems
    • E Rudd R. Coarse-grained molecular dynamics for computer modeling of nanomechanical systems. Int. J. Multiscale Comput. Engrg. 2 2 (2004) 203-220
    • (2004) Int. J. Multiscale Comput. Engrg. , vol.2 , Issue.2 , pp. 203-220
    • E Rudd, R.1
  • 25
    • 34249714264 scopus 로고    scopus 로고
    • A bridging domain and strain computation method for coupled atomistic-continuum modeling of solids
    • Zhang S., Khare R., Lu Q., and Belytschko T. A bridging domain and strain computation method for coupled atomistic-continuum modeling of solids. Int. J. Numer. Methods Engrg. 70 (2007) 913-933
    • (2007) Int. J. Numer. Methods Engrg. , vol.70 , pp. 913-933
    • Zhang, S.1    Khare, R.2    Lu, Q.3    Belytschko, T.4
  • 26
    • 34247116809 scopus 로고    scopus 로고
    • A phonon heat bath approach for the atomistic and multiscale simulation of solids
    • Karpov E.G., Park H.S., and Liu W.K. A phonon heat bath approach for the atomistic and multiscale simulation of solids. Int. J. Numer. Methods Engrg. 70 (2007) 351-378
    • (2007) Int. J. Numer. Methods Engrg. , vol.70 , pp. 351-378
    • Karpov, E.G.1    Park, H.S.2    Liu, W.K.3
  • 27
    • 38349133352 scopus 로고    scopus 로고
    • Towards realization of computational homogenization in practice
    • Yuan Z., and Fish J. Towards realization of computational homogenization in practice. Int. J. Numer. Methods Engrg. 73 3 (2008) 361-380
    • (2008) Int. J. Numer. Methods Engrg. , vol.73 , Issue.3 , pp. 361-380
    • Yuan, Z.1    Fish, J.2
  • 28
    • 41049102740 scopus 로고    scopus 로고
    • The rs-method for material failure simulations
    • Fan R., and Fish J. The rs-method for material failure simulations. Int. J. Numer. Methods Engrg. 73 11 (2008) 1607-1623
    • (2008) Int. J. Numer. Methods Engrg. , vol.73 , Issue.11 , pp. 1607-1623
    • Fan, R.1    Fish, J.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.