메뉴 건너뛰기




Volumn 8, Issue 3, 2006, Pages 515-530

Sufficient conditions for the validity of the Cauchy-Born rule close to SO(n)

Author keywords

Atomistic models; Cauchy Born rule; Null Lagrangian

Indexed keywords


EID: 33746481805     PISSN: 14359855     EISSN: None     Source Type: Journal    
DOI: 10.4171/jems/65     Document Type: Article
Times cited : (47)

References (28)
  • 1
    • 0017417265 scopus 로고
    • Convexity conditions and existence theorems in nonlinear elasticity
    • [Ba77] Zbl 0368.73040 MR 0475169
    • [Ba77] Ball, J. M.: Convexity conditions and existence theorems in nonlinear elasticity. Arch. Rat. Mech. Anal. 63, 337-403 (1977) Zbl 0368.73040 MR 0475169
    • (1977) Arch. Rat. Mech. Anal. , vol.63 , pp. 337-403
    • Ball, J.M.1
  • 2
    • 0000966233 scopus 로고
    • Null Lagrangians, weak continuity and variational problems of arbitrary order
    • [BCO81] Zbl 0459.35020 MR 0615159
    • [BCO81] Ball, J. M., Currie, J. C., Olver, P. C.: Null Lagrangians, weak continuity and variational problems of arbitrary order. J. Funct. Anal. 41, 135-174 (1981) Zbl 0459.35020 MR 0615159
    • (1981) J. Funct. Anal. , vol.41 , pp. 135-174
    • Ball, J.M.1    Currie, J.C.2    Olver, P.C.3
  • 4
    • 33750297145 scopus 로고
    • Fine phase mixtures as minimizers of energy
    • [BJ87] Zbl 0629.49020 MR 0906132
    • [BJ87] Ball, J. M., James, R. D.: Fine phase mixtures as minimizers of energy. Arch. Rat. Mech. Anal. 100, 13-52 (1987) Zbl 0629.49020 MR 0906132
    • (1987) Arch. Rat. Mech. Anal. , vol.100 , pp. 13-52
    • Ball, J.M.1    James, R.D.2
  • 6
    • 1542619690 scopus 로고    scopus 로고
    • Crystal symmetry and the reversibility of phase transformations
    • [BCZZ04]
    • [BCZZ04] Bhattacharya, K., Conti, S., Zanzotto, G., Zimmer, J.: Crystal symmetry and the reversibility of phase transformations. Nature 428, 55-59 (2004)
    • (2004) Nature , vol.428 , pp. 55-59
    • Bhattacharya, K.1    Conti, S.2    Zanzotto, G.3    Zimmer, J.4
  • 7
    • 0001246325 scopus 로고
    • Equilibrium configurations of crystals
    • [CK88] Zbl 0673.73012 MR 0955934
    • [CK88] Chipot, M., Kinderlehrer, D.: Equilibrium configurations of crystals. Arch. Rat. Mech. Anal. 103, 237-277 (1988) Zbl 0673.73012 MR 0955934
    • (1988) Arch. Rat. Mech. Anal. , vol.103 , pp. 237-277
    • Chipot, M.1    Kinderlehrer, D.2
  • 8
    • 3142717294 scopus 로고    scopus 로고
    • A variational model for reconstructive phase transformations in crystals, and their relation to dislocations and plasticity
    • [CZ04] Zbl pre02113861 MR 2073505
    • [CZ04] Conti, S., Zanzotto, G.: A variational model for reconstructive phase transformations in crystals, and their relation to dislocations and plasticity. Arch. Rat. Mech. Anal. 173, 69-88(2004) Zbl pre02113861 MR 2073505
    • (2004) Arch. Rat. Mech. Anal. , vol.173 , pp. 69-88
    • Conti, S.1    Zanzotto, G.2
  • 10
    • 33746562458 scopus 로고
    • La più generale funzione d'invarianza per criteri sufficienti di minimo con condizioni di Dirichlet per integrali pluridimensionali del primo ordine dipendenti da un vettore a più componenti
    • [DF64] Zbl 0128.10004 MR 0176366
    • [DF64] De Franchis, M.: La più generale funzione d'invarianza per criteri sufficienti di minimo con condizioni di Dirichlet per integrali pluridimensionali del primo ordine dipendenti da un vettore a più componenti. Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. 37, no. 8, 129-140 (1964) Zbl 0128.10004 MR 0176366
    • (1964) Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. , vol.37 , Issue.8 , pp. 129-140
    • De Franchis, M.1
  • 12
    • 33746558175 scopus 로고    scopus 로고
    • [EM05] E, W., Ming, P. B.: in preparation
    • [EM05] E, W., Ming, P. B.: in preparation.
  • 13
    • 0000493460 scopus 로고
    • The null set of the Euler-Lagrange operator
    • [Ed62] Zbl 0125.33002 MR 0150623
    • [Ed62] Edelen, D. G. B.: The null set of the Euler-Lagrange operator. Arch. Rat. Mech. Anal. 11, 117-121(1962) Zbl 0125.33002 MR 0150623
    • (1962) Arch. Rat. Mech. Anal. , vol.11 , pp. 117-121
    • Edelen, D.G.B.1
  • 14
    • 0000115840 scopus 로고
    • Nilpotent energies in liquid crystal theory
    • [Er62] Zbl 0109.23002 MR 0169513
    • [Er62] Ericksen, J. L.: Nilpotent energies in liquid crystal theory. Arch. Rat. Mech. Anal. 10, 189-196(1962) Zbl 0109.23002 MR 0169513
    • (1962) Arch. Rat. Mech. Anal. , vol.10 , pp. 189-196
    • Ericksen, J.L.1
  • 15
    • 0002162989 scopus 로고
    • The Cauchy and Born hypotheses for crystals
    • [Er82], M. Gurtin (ed.), Academic Press Zbl 0567.73112 MR 0802219
    • [Er82] Ericksen, J.: The Cauchy and Born hypotheses for crystals. In: Phase Transitions and Material Instabilities in Solids, M. Gurtin (ed.), Academic Press, 61-77 (1984) Zbl 0567.73112 MR 0802219
    • (1984) Phase Transitions and Material Instabilities in Solids , pp. 61-77
    • Ericksen, J.1
  • 16
    • 0031240691 scopus 로고    scopus 로고
    • Equilibrium theory for X-ray observations of crystals
    • [Er97] Zbl 0910.73056 MR 1478777
    • [Er97] Ericksen, J.: Equilibrium theory for X-ray observations of crystals. Arch. Rat. Mech. Anal. 139, 181-200 (1997) Zbl 0910.73056 MR 1478777
    • (1997) Arch. Rat. Mech. Anal. , vol.139 , pp. 181-200
    • Ericksen, J.1
  • 17
    • 0023142918 scopus 로고
    • Variational methods for elastic crystals
    • [Fo87] Zbl 0611.73023 MR 0862547
    • [Fo87] Fonseca, I.: Variational methods for elastic crystals. Arch. Rat. Mech. Anal. 97, 189-220 (1987) Zbl 0611.73023 MR 0862547
    • (1987) Arch. Rat. Mech. Anal. , vol.97 , pp. 189-220
    • Fonseca, I.1
  • 18
    • 0000937706 scopus 로고
    • The lower quasiconvex envelope of the stored energy function for an elastic crystal
    • [Fo88] Zbl 0718.73075 MR 0949107
    • [Fo88] Fonseca, I.: The lower quasiconvex envelope of the stored energy function for an elastic crystal. J. Math. Pures Appl. 67, 175-195 (1988) Zbl 0718.73075 MR 0949107
    • (1988) J. Math. Pures Appl. , vol.67 , pp. 175-195
    • Fonseca, I.1
  • 19
    • 0042964912 scopus 로고    scopus 로고
    • Validity and failure of the Cauchy-Born rule in a two-dimensional mass-spring lattice
    • [FT02] Zbl pre01903651 MR 1923388
    • [FT02] Friesecke, G., Theil, F.: Validity and failure of the Cauchy-Born rule in a two-dimensional mass-spring lattice. J. Nonlinear Sci. 12, 445-478 (2002) Zbl pre01903651 MR 1923388
    • (2002) J. Nonlinear Sci. , vol.12 , pp. 445-478
    • Friesecke, G.1    Theil, F.2
  • 20
    • 0033892030 scopus 로고    scopus 로고
    • Martensitic transformations and shape-memory materials
    • [JH00]
    • [JH00] James, R. D., Hane, K. F.: Martensitic transformations and shape-memory materials. Acta Materialia 48, 197-222 (2000)
    • (2000) Acta Materialia , vol.48 , pp. 197-222
    • James, R.D.1    Hane, K.F.2
  • 21
    • 70350422475 scopus 로고
    • Invariant multiple integrals in the calculus of variations
    • [La42], Univ. Chicago Press Zbl 0063.03441 MR 0006821
    • [La42] Landers, A. W.: Invariant multiple integrals in the calculus of variations. In: Contributions to the Calculus of Variations, 1938-1941, Univ. Chicago Press, 184-189 (1942) Zbl 0063.03441 MR 0006821
    • (1942) Contributions to the Calculus of Variations, 1938-1941 , pp. 184-189
    • Landers, A.W.1
  • 22
    • 84972497511 scopus 로고
    • Quasi-convexity and the lower semicontinuity of multiple integrals
    • [Mo52] Zbl 0046.10803 MR 0054865
    • [Mo52] Morrey, C. B.: Quasi-convexity and the lower semicontinuity of multiple integrals. Pacific J. Math. 2, 25-53 (1952) Zbl 0046.10803 MR 0054865
    • (1952) Pacific J. Math. , vol.2 , pp. 25-53
    • Morrey, C.B.1
  • 23
    • 0002142597 scopus 로고    scopus 로고
    • Variational methods for microstructure and phase transitions
    • [Mü99]. Proc. CIME Summer School on Calculus of Variations and Geometric Evolution Problems, F. Bethuel et al. (eds.). Springer, Zbl 0968.74050 MR 1731640
    • [Mü99] Müller, S.: Variational methods for microstructure and phase transitions. In: Proc. CIME Summer School on Calculus of Variations and Geometric Evolution Problems, F. Bethuel et al. (eds.). Lecture Notes in Math. 1713, Springer, 85-210 (1999) Zbl 0968.74050 MR 1731640
    • (1999) Lecture Notes in Math. , vol.1713 , pp. 85-210
    • Müller, S.1
  • 24
    • 0019476939 scopus 로고
    • On phase transitions involving internal strain
    • [Pa80] Zbl 0464.73004 MR 0611096
    • [Pa80] Parry, G. P.: On phase transitions involving internal strain. Int. J. Solids Structures 17, 361-378 (1980) Zbl 0464.73004 MR 0611096
    • (1980) Int. J. Solids Structures , vol.17 , pp. 361-378
    • Parry, G.P.1
  • 27
    • 0001188273 scopus 로고
    • Integral formulae associated with the Euler-Lagrange operator of multiple integrals
    • [Ru74] Zbl 0293.49001 MR 0361971
    • [Ru74] Rund, H.: Integral formulae associated with the Euler-Lagrange operator of multiple integrals, Aequationes Math. 11, 212-229 (1974) Zbl 0293.49001 MR 0361971
    • (1974) Aequationes Math. , vol.11 , pp. 212-229
    • Rund, H.1
  • 28
    • 21144474420 scopus 로고
    • On the material symmetry group of elastic crystals and the Born rule
    • [Za92] Zbl 0781.73005 MR 1185569
    • [Za92] Zanzotto, G.: On the material symmetry group of elastic crystals and the Born rule. Arch. Rat. Mech. Anal. 121, 1-36 (1992) Zbl 0781.73005 MR 1185569
    • (1992) Arch. Rat. Mech. Anal. , vol.121 , pp. 1-36
    • Zanzotto, G.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.