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Volumn 23, Issue 4, 2007, Pages 529-550

Cauchy-Born rule and the stability of crystalline solids: Dynamic problems

Author keywords

Cauchy Born rule; Crystal elasticity; Stability of crystals

Indexed keywords


EID: 34547805499     PISSN: 01689673     EISSN: 16183932     Source Type: Journal    
DOI: 10.1007/s10255-007-0393     Document Type: Article
Times cited : (39)

References (35)
  • 3
    • 0035981342 scopus 로고    scopus 로고
    • From molecular models to continuum mechanics
    • Blanc, X., Le Bris, C., Lions, P.L. From molecular models to continuum mechanics. Arch. Ration. Mech. Anal., 164(4): 341-381 (2002)
    • (2002) Arch. Ration. Mech. Anal , vol.164 , Issue.4 , pp. 341-381
    • Blanc, X.1    Le Bris, C.2    Lions, P.L.3
  • 6
    • 0033411059 scopus 로고    scopus 로고
    • Variational formulation of softening phenomena in fracture mechanics: The one-dimensional case
    • Braides, A., Dal Maso, G., Garroni, A. Variational formulation of softening phenomena in fracture mechanics: the one-dimensional case. Arch. Ration. Mech. Anal., 146(1): 23-58 (1999)
    • (1999) Arch. Ration. Mech. Anal , vol.146 , Issue.1 , pp. 23-58
    • Braides, A.1    Dal Maso, G.2    Garroni, A.3
  • 7
    • 0000890461 scopus 로고
    • d'un système de points materiels sollicités par forces d'attraction ou de répulsion mutuelle
    • Cauchy, A.L. Sur l'equilibre et le mouvement d'un système de points materiels sollicités par forces d'attraction ou de répulsion mutuelle. Ex. de Math., 3: 187-213 (1828)
    • (1828) Ex. de Math , vol.3 , pp. 187-213
    • Cauchy1    Sur l'equilibre, A.L.2    le mouvement3
  • 8
    • 33746481805 scopus 로고    scopus 로고
    • Sufficient conditions for the validity of the cauchy-born rule close to SO(n)
    • Conti, S., Dolzmann, G., Kirchheim, B., Müller, S. Sufficient conditions for the validity of the cauchy-born rule close to SO(n). J. Eur. Math. Soc., 8(3): 515-530 (2006)
    • (2006) J. Eur. Math. Soc , vol.8 , Issue.3 , pp. 515-530
    • Conti, S.1    Dolzmann, G.2    Kirchheim, B.3    Müller, S.4
  • 9
    • 0021818126 scopus 로고
    • Energy methods for quasilinear hyperbolic initial-boundary value problems. applications to elastodynamics
    • Dafermos, C.M., Hrusa, W.J. Energy methods for quasilinear hyperbolic initial-boundary value problems. applications to elastodynamics. Arch. Ration. Mech. Anal., 87(3): 267-292 (1985)
    • (1985) Arch. Ration. Mech. Anal , vol.87 , Issue.3 , pp. 267-292
    • Dafermos, C.M.1    Hrusa, W.J.2
  • 10
    • 34547796244 scopus 로고    scopus 로고
    • E, W., Liu, J.G. Projection method. I. Convergence and numerical boundary layers. SIAM J. Numer. Anal., 32(4): 1017-1057 (1995)
    • E, W., Liu, J.G. Projection method. I. Convergence and numerical boundary layers. SIAM J. Numer. Anal., 32(4): 1017-1057 (1995)
  • 11
    • 33846861564 scopus 로고    scopus 로고
    • E, W., Ming, P.B. Cauchy-born rule and the stability of crystalline solids: static problems. Arch. Ration. Mech. Anal., 183(2): 241-297 (2007)
    • E, W., Ming, P.B. Cauchy-born rule and the stability of crystalline solids: static problems. Arch. Ration. Mech. Anal., 183(2): 241-297 (2007)
  • 12
    • 34547803548 scopus 로고    scopus 로고
    • Ericksen, J.L. The Cauchy and born hypotheses for crystals. in: phase transformations and material instabilities in solids. ed. by M.E. Gurtin, Academic Press, 1984, 61-77
    • Ericksen, J.L. The Cauchy and born hypotheses for crystals. in: phase transformations and material instabilities in solids. ed. by M.E. Gurtin, Academic Press, 1984, 61-77
  • 13
    • 0042964912 scopus 로고    scopus 로고
    • Validity and failure of the cauchy-born hypothesis in a two dimensional mass-spring lattice
    • Friesecke, G., Theil, F. Validity and failure of the cauchy-born hypothesis in a two dimensional mass-spring lattice. J. Nonlinear Sci., 12(5): 445-478 (2002)
    • (2002) J. Nonlinear Sci , vol.12 , Issue.5 , pp. 445-478
    • Friesecke, G.1    Theil, F.2
  • 14
    • 0017428498 scopus 로고
    • Well-posed quasi-linear second-order hyperbolic systems with applications to nonlinear elastodynamics and general relativity
    • Hughes, T.J.R., Kato, T., Marsden, J. Well-posed quasi-linear second-order hyperbolic systems with applications to nonlinear elastodynamics and general relativity. Arch. Ration. Mech. Anal., 63(3): 273-294 (1977)
    • (1977) Arch. Ration. Mech. Anal , vol.63 , Issue.3 , pp. 273-294
    • Hughes, T.J.R.1    Kato, T.2    Marsden, J.3
  • 15
    • 29144453140 scopus 로고
    • Effect of invariance requirements on the elastic strain energy of crystals with application to the diamond structure
    • Keating, P.N. Effect of invariance requirements on the elastic strain energy of crystals with application to the diamond structure. Phys. Rev., 145(2): 637-645 (1965)
    • (1965) Phys. Rev , vol.145 , Issue.2 , pp. 637-645
    • Keating, P.N.1
  • 16
    • 0001215347 scopus 로고
    • Critical and cooperative phenomena. III. a theory of melting and the structure of liquids
    • Lennard-Jones, J.E., Devonshire, A.F. Critical and cooperative phenomena. III. a theory of melting and the structure of liquids. Proc. Roy. Soc. Lond., A169(938): 317-338 (1939)
    • (1939) Proc. Roy. Soc. Lond , vol.A169 , Issue.938 , pp. 317-338
    • Lennard-Jones, J.E.1    Devonshire, A.F.2
  • 17
    • 33846893335 scopus 로고    scopus 로고
    • Crystal stability and instability
    • In preparation
    • Liu, F., Ming, P.B. Crystal stability and instability. In preparation
    • Liu, F.1    Ming, P.B.2
  • 20
    • 0002142552 scopus 로고
    • Symmetry properties of the normal vibrations of a crystal
    • Maradudin, A.A., Vosko, S.H. Symmetry properties of the normal vibrations of a crystal. Rev. Mod. Phy., 40(1): 1-37 (1968)
    • (1968) Rev. Mod. Phy , vol.40 , Issue.1 , pp. 1-37
    • Maradudin, A.A.1    Vosko, S.H.2
  • 23
    • 0019476939 scopus 로고
    • On Phase transitions involving internal strain
    • Parry, G.P. On Phase transitions involving internal strain. Int. J. Solids Structures, 17(4): 361-378 (1981)
    • (1981) Int. J. Solids Structures , vol.17 , Issue.4 , pp. 361-378
    • Parry, G.P.1
  • 24
    • 0002331359 scopus 로고
    • On v + 1-Lattices
    • Pitteri, M. On v + 1-Lattices. J. of Elasticity, 15(1): 3-25 (1985)
    • (1985) J. of Elasticity , vol.15 , Issue.1 , pp. 3-25
    • Pitteri, M.1
  • 27
    • 0040027791 scopus 로고
    • The incompressible limit in nonlinear elasticity
    • Schochet, S. The incompressible limit in nonlinear elasticity. Comm. Math. Phys., 102(2): 207-215 (1985)
    • (1985) Comm. Math. Phys , vol.102 , Issue.2 , pp. 207-215
    • Schochet, S.1
  • 29
    • 0001473461 scopus 로고
    • The Cauchy relations in a molecular theory of elasticity
    • Stakgold, I. The Cauchy relations in a molecular theory of elasticity. Quart. Appl. Math., 8(2): 169-186 (1950)
    • (1950) Quart. Appl. Math , vol.8 , Issue.2 , pp. 169-186
    • Stakgold, I.1
  • 30
    • 33748538768 scopus 로고
    • Accurate partial difference methods, ii: Non-linear problems
    • Strang, G. Accurate partial difference methods, ii: non-linear problems. Numer. Math., 6(1): 37-46 (1964)
    • (1964) Numer. Math , vol.6 , Issue.1 , pp. 37-46
    • Strang, G.1
  • 32
    • 34547814954 scopus 로고    scopus 로고
    • Weiner, J.H. Statistical mechanics of elasticity. A Wiley-Interscience Publication, 1983
    • Weiner, J.H. Statistical mechanics of elasticity. A Wiley-Interscience Publication, 1983
  • 33
    • 34547787002 scopus 로고    scopus 로고
    • E, W. Instability of crystalline solids under stress
    • In preparation
    • Xuan, Y., E, W. Instability of crystalline solids under stress. In preparation.
    • Xuan, Y.1
  • 34
    • 21144474420 scopus 로고
    • On the material symmetry group of elastic crystals and the born rule
    • Zanzotto, G. On the material symmetry group of elastic crystals and the born rule. Arch. Ration. Mech. Anal., 121(1): 1-36 (1992)
    • (1992) Arch. Ration. Mech. Anal , vol.121 , Issue.1 , pp. 1-36
    • Zanzotto, G.1
  • 35
    • 0000369691 scopus 로고    scopus 로고
    • The cauchy and born hypothesis, nonlinear elasticity and mechanical twinning in crystals
    • Zanzotto, G. The cauchy and born hypothesis, nonlinear elasticity and mechanical twinning in crystals. Acta Cryst., A52(6): 839-849 (1996)
    • (1996) Acta Cryst , vol.A52 , Issue.6 , pp. 839-849
    • Zanzotto, G.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.