메뉴 건너뛰기




Volumn 18, Issue 1-2, 2006, Pages 1-21

Quasicontinuum models of dynamic phase transitions

Author keywords

Configurational forces; Gradient models; Kinetic relations; Lattice models; Martensitic phase transitions; Microkinetics; Nonlocal interactions; Quasicontinuum approximations

Indexed keywords

APPROXIMATION THEORY; CONTINUUM MECHANICS; CRYSTAL LATTICES; KINETIC ENERGY; MATHEMATICAL MODELS; ONE DIMENSIONAL; PHASE TRANSITIONS; POTENTIAL ENERGY;

EID: 33746064533     PISSN: 09351175     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00161-006-0018-5     Document Type: Article
Times cited : (35)

References (37)
  • 1
    • 0027553650 scopus 로고
    • A continuum model of a thermoelastic solid capable of undergoing phase transitions
    • Abeyaratne, R., Knowles, J.: A continuum model of a thermoelastic solid capable of undergoing phase transitions. J. Mech. Phys. Solids 41, 541-571 (1993)
    • (1993) J. Mech. Phys. Solids , vol.41 , pp. 541-571
    • Abeyaratne, R.1    Knowles, J.2
  • 2
    • 0042265172 scopus 로고    scopus 로고
    • A lattice-based model of the kinetics of twin boundary motion
    • Abeyaratne, R., Vedantam, S.: A lattice-based model of the kinetics of twin boundary motion. J. Mech. Phys. Solids 51, 1675-1700 (2003)
    • (2003) J. Mech. Phys. Solids , vol.51 , pp. 1675-1700
    • Abeyaratne, R.1    Vedantam, S.2
  • 3
    • 0001865962 scopus 로고
    • Model equations for long waves in nonlinear dispersive systems
    • Benjamin, T.B., Bona, J.L., Mahony, J.J.: Model equations for long waves in nonlinear dispersive systems. Phil. Trans. R. Soc. Lond. 272, 47-78 (1972)
    • (1972) Phil. Trans. R. Soc. Lond. , vol.272 , pp. 47-78
    • Benjamin, T.B.1    Bona, J.L.2    Mahony, J.J.3
  • 5
    • 0002436381 scopus 로고
    • A quasicontinuum approximation for solitons in an atomic chain
    • Collins, M.A.: A quasicontinuum approximation for solitons in an atomic chain. Chem. Phys. Lett. 77, 342-347 (1981)
    • (1981) Chem. Phys. Lett. , vol.77 , pp. 342-347
    • Collins, M.A.1
  • 6
    • 0036153904 scopus 로고    scopus 로고
    • Mathematical andnumerical modeling of two-phase compressible flows with micro-inertia
    • Gavrilyuk,S.,Saurel,R.: Mathematical andnumerical modeling of two-phase compressible flows with micro-inertia. J.Comp. Phys. 175. 326-360 (2002)
    • (2002) J.Comp. Phys. , vol.175 , pp. 326-360
    • Gavrilyuk, S.1    Saurel, R.2
  • 8
    • 0001039692 scopus 로고
    • An iterative method for the calculation of narrow solitary excitations on atomic chains
    • Hochstrasser, D., Mertens, P.O., Büttner, H.: An iterative method for the calculation of narrow solitary excitations on atomic chains. Phys. D 35, 259-266 (1989)
    • (1989) Phys. D , vol.35 , pp. 259-266
    • Hochstrasser, D.1    Mertens, P.O.2    Büttner, H.3
  • 10
    • 0347109789 scopus 로고    scopus 로고
    • Dynamics of lattice kinks
    • Kevrekidis, P.G., Weinstein, M.I.: Dynamics of lattice kinks. Phys. D 142, 113-152 (2000)
    • (2000) Phys. D , vol.142 , pp. 113-152
    • Kevrekidis, P.G.1    Weinstein, M.I.2
  • 12
    • 0037847474 scopus 로고    scopus 로고
    • Mobility of lattice defects: Discrete and continuum approaches
    • Kresse, O., Truskinovsky, L.: Mobility of lattice defects: discrete and continuum approaches. J. Mech. Phys. Solids 51, 1305-1332(2003)
    • (2003) J. Mech. Phys. Solids , vol.51 , pp. 1305-1332
    • Kresse, O.1    Truskinovsky, L.2
  • 13
    • 2442600284 scopus 로고    scopus 로고
    • Lattice friction for crystalline defects: From dislocations to cracks
    • Kresse, O., Truskinovsky, L.: Lattice friction for crystalline defects: from dislocations to cracks. J. Mech. Phys. Solids 52, 2521-2543(2004)
    • (2004) J. Mech. Phys. Solids , vol.52 , pp. 2521-2543
    • Kresse, O.1    Truskinovsky, L.2
  • 14
    • 31444441426 scopus 로고
    • Elastic media with microstructure I: One-dimensional models
    • Springer, Berlin Heidelberg New York
    • Kunin, I.: Elastic Media with Microstructure I: One-dimensional Models, Solid-State Sciences, vol. 26. Springer, Berlin Heidelberg New York (1982)
    • (1982) Solid-state Sciences , vol.26
    • Kunin, I.1
  • 15
    • 0012009827 scopus 로고
    • The generation and propagation of oscillations in dispersive initial value problems and their limiting behavior
    • Fokas, A.S., Zakharov, V.E. (eds.), Springer, Berlin Heidelberg New York
    • Lax, P.D., Levermore, C.D., Venakides, S.: The generation and propagation of oscillations in dispersive initial value problems and their limiting behavior. In: Fokas, A.S., Zakharov, V.E. (eds.) Important Developments in Soliton Theory, Springer Ser. Nonlin Dynam, pp. 205-241, Springer, Berlin Heidelberg New York (1994)
    • (1994) Important Developments in Soliton Theory, Springer Ser. Nonlin Dynam , pp. 205-241
    • Lax, P.D.1    Levermore, C.D.2    Venakides, S.3
  • 16
    • 34548145439 scopus 로고
    • Origin of crack tip instabilities
    • Marder, M., Gross, S.: Origin of crack tip instabilities. J. Mech. Phys. Solids 43, 1-48 (1995)
    • (1995) J. Mech. Phys. Solids , vol.43 , pp. 1-48
    • Marder, M.1    Gross, S.2
  • 17
    • 0000095439 scopus 로고
    • Second gradient of strain and surface tension in linear elasticity
    • Mindlin, R.D.: Second gradient of strain and surface tension in linear elasticity. Int. J. Solids Struct. 1, 417-438 (1965)
    • (1965) Int. J. Solids Struct , vol.1 , pp. 417-438
    • Mindlin, R.D.1
  • 18
  • 20
    • 0001398295 scopus 로고
    • Dynamics of nonlinear mass-spring chains near the continuum limit
    • Rosenau, P.: Dynamics of nonlinear mass-spring chains near the continuum limit. Phys. Lett. A 118(5), 222-227 (1986)
    • (1986) Phys. Lett. A , vol.118 , Issue.5 , pp. 222-227
    • Rosenau, P.1
  • 21
    • 0000427638 scopus 로고
    • Dynamics of dense discrete systems
    • Rosenau, P.: Dynamics of dense discrete systems. Prog. Theor. Phys. 79, 1028-1042 (1988)
    • (1988) Prog. Theor. Phys. , vol.79 , pp. 1028-1042
    • Rosenau, P.1
  • 22
    • 0037420850 scopus 로고    scopus 로고
    • Hamiltonian dynamics of dense chains and lattices: Or how to correct the continuum
    • Rosenau, P.: Hamiltonian dynamics of dense chains and lattices: or how to correct the continuum. Phys. Lett. A 311(1), 39-52 (2003)
    • (2003) Phys. Lett. A , vol.311 , Issue.1 , pp. 39-52
    • Rosenau, P.1
  • 25
    • 10844253863 scopus 로고    scopus 로고
    • Transition waves in bistable structures. II. Analytical solution: Wave speed and energy dissipation
    • Slepyan, L.I., Cherkaev, A., Cherkaev, E.: Transition waves in bistable structures. II. Analytical solution: wave speed and energy dissipation. J. Mech. Phys. Solids 53, 407-436 (2005)
    • (2005) J. Mech. Phys. Solids , vol.53 , pp. 407-436
    • Slepyan, L.I.1    Cherkaev, A.2    Cherkaev, E.3
  • 26
    • 0034262015 scopus 로고    scopus 로고
    • A study of a hamiltonian model for martensitic phase transformations including microkinetic energy
    • Theil, F., Levitas, V.: A study of a hamiltonian model for martensitic phase transformations including microkinetic energy. Math. Mech. Solids 5(3), 337-368 (2000)
    • (2000) Math. Mech. Solids , vol.5 , Issue.3 , pp. 337-368
    • Theil, F.1    Levitas, V.2
  • 27
    • 34250940617 scopus 로고
    • Theories of elasticity with couple-stresses
    • Toupin, R.A.: Theories of elasticity with couple-stresses. Arch. Ration Appl. Mech. Anal. 17, 85-112 (1964)
    • (1964) Arch. Ration Appl. Mech. Anal. , vol.17 , pp. 85-112
    • Toupin, R.A.1
  • 28
    • 0027813754 scopus 로고
    • On higher order gradient continuum theories in 1-D nonlinear elasticity. Derivation from and comparison to the corresponding discrete models
    • Triantafyllidis, N., Bardenhagen, S.: On higher order gradient continuum theories in 1-D nonlinear elasticity. Derivation from and comparison to the corresponding discrete models. J. Elast. 33(3), 259-293 (1993)
    • (1993) J. Elast. , vol.33 , Issue.3 , pp. 259-293
    • Triantafyllidis, N.1    Bardenhagen, S.2
  • 29
    • 2442677705 scopus 로고
    • Dynamics of nonequilibrium phase boundaries in a heat conducting elastic medium
    • Truskinovsky, L.: Dynamics of nonequilibrium phase boundaries in a heat conducting elastic medium. J. Appl. Math. Mech. 51,777-784(1987)
    • (1987) J. Appl. Math. Mech. , vol.51 , pp. 777-784
    • Truskinovsky, L.1
  • 30
    • 0038237007 scopus 로고    scopus 로고
    • Peierls-Nabarro landscape for martensitic phase transitions
    • Truskinovsky, L., Vainchtein, A.: Peierls-Nabarro landscape for martensitic phase transitions. Phys. Rev. B. 67, 172,103 (2003)
    • (2003) Phys. Rev. B. , vol.67 , Issue.172 , pp. 103
    • Truskinovsky, L.1    Vainchtein, A.2
  • 31
    • 1642617747 scopus 로고    scopus 로고
    • The origin of nucleation peak in transformational plasticity
    • Truskinovsky, L., Vainchtein, A.: The origin of nucleation peak in transformational plasticity. J. Mech. Phys. Solids 52, 1421-1446(2004)
    • (2004) J. Mech. Phys. Solids , vol.52 , pp. 1421-1446
    • Truskinovsky, L.1    Vainchtein, A.2
  • 32
    • 33746050197 scopus 로고    scopus 로고
    • Explicit kinetic relation from "first principles"
    • Steinmann, P. Maugin G. (eds.), Springer, Berlin Heidelberg New York
    • Truskinovsky, L., Vainchtein, A.: Explicit kinetic relation from "first principles". In: Steinmann, P. Maugin G. (eds.) Mech Material Forces, pp. 43-50, Springer, Berlin Heidelberg New York (2005)
    • (2005) Mech Material Forces , pp. 43-50
    • Truskinovsky, L.1    Vainchtein, A.2
  • 33
    • 33645776187 scopus 로고    scopus 로고
    • Kinetics of martensitic phase transitions: Lattice model
    • Truskinovsky, L., Vainchtein. A.: Kinetics of martensitic phase transitions: lattice model. SIAM J. Appl. Math. 66, 533-553 (2005)
    • (2005) SIAM J. Appl. Math. , vol.66 , pp. 533-553
    • Truskinovsky, L.1    Vainchtein, A.2
  • 34
    • 31444437724 scopus 로고    scopus 로고
    • Quasicontinuum modeling of short-wave instabilities in crystal lattices
    • Truskinovsky, L., Vainchtein, A.: Quasicontinuum modeling of short-wave instabilities in crystal lattices. Philos. Mag. 85, 4055-4065 (2005)
    • (2005) Philos. Mag. , vol.85 , pp. 4055-4065
    • Truskinovsky, L.1    Vainchtein, A.2
  • 35
    • 21144479491 scopus 로고
    • Approximations to solitary waves on lattices, II: Quasicontinuum methods for fast and slow waves
    • Wattis, J.A.D.: Approximations to solitary waves on lattices, II: quasicontinuum methods for fast and slow waves. J. Phys. A 26, 1193-1209 (1993)
    • (1993) J. Phys. A , vol.26 , pp. 1193-1209
    • Wattis, J.A.D.1
  • 36
    • 0030597484 scopus 로고    scopus 로고
    • Approximations to solitary waves on lattices, III: The monatomic lattice with second-neighbour interactions
    • Wattis, J.A.D.: Approximations to solitary waves on lattices, III: the monatomic lattice with second-neighbour interactions. J. Phys. A 29, 8139-8157 (1996)
    • (1996) J. Phys. A , vol.29 , pp. 8139-8157
    • Wattis, J.A.D.1
  • 37
    • 0032502555 scopus 로고    scopus 로고
    • Stationary breather modes of generalized nonlinear klein-gordon lattices
    • Wattis, J.A.D.: Stationary breather modes of generalized nonlinear Klein-Gordon lattices. J. Phys. A 31, 3301-3323 (1998)
    • (1998) J. Phys. A , vol.31 , pp. 3301-3323
    • Wattis, J.A.D.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.