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Volumn 22, Issue 3, 1998, Pages 239-254

The computational modeling of nonequilibrium thermodynamics of the martensitic transformations

Author keywords

[No Author keywords available]

Indexed keywords

DEFORMATION; MARTENSITE; MATHEMATICAL MODELS; NUMERICAL ANALYSIS; THERMODYNAMIC PROPERTIES;

EID: 0032162625     PISSN: 01787675     EISSN: None     Source Type: Journal    
DOI: 10.1007/s004660050357     Document Type: Article
Times cited : (7)

References (57)
  • 2
    • 0008894832 scopus 로고
    • Kinetic Relations and the Propagation of Phase Boundaries in Solids
    • Abeyaratne R, Knowles JK (1991) Kinetic Relations and the Propagation of Phase Boundaries in Solids. Arch. Rational Mech. Anal. 114:119-154
    • (1991) Arch. Rational Mech. Anal. , vol.114 , pp. 119-154
    • Abeyaratne, R.1    Knowles, J.K.2
  • 5
    • 0000095072 scopus 로고
    • Experiments on the Martensitic transformation in single crystals of indiumthallium alloys
    • Basinski ZS, Christian JW (1954) Experiments on the Martensitic transformation in single crystals of indiumthallium alloys. Acta Met 2:148-166
    • (1954) Acta Met , vol.2 , pp. 148-166
    • Basinski, Z.S.1    Christian, J.W.2
  • 7
    • 33750297145 scopus 로고
    • Fine phase mixtures as minimizers of energy
    • Ball JM, James RD (1987) Fine phase mixtures as minimizers of energy. Arch. Rational Mech. Anal. 100:13-52
    • (1987) Arch. Rational Mech. Anal. , vol.100 , pp. 13-52
    • Ball, J.M.1    James, R.D.2
  • 8
    • 0002854369 scopus 로고
    • Proposed experimental tests of a theory of fine microstructure and the two-well problem
    • Ball JM, James RD (1992) Proposed experimental tests of a theory of fine microstructure and the two-well problem. Phil. Trans. R. Soc. Lond. A 338:389-450
    • (1992) Phil. Trans. R. Soc. Lond. A , vol.338 , pp. 389-450
    • Ball, J.M.1    James, R.D.2
  • 9
    • 0000093666 scopus 로고
    • A version of the fundamental theorem for Young measures
    • M. Rascle, D. Serre and M. Slemrods, eds., Lecture Notes in Physics, Springer-Verlag, New-York
    • Ball JM (1989) A version of the fundamental theorem for Young measures, in Partial Differential Equations and Continuum Models of Phase Transitions (M. Rascle, D. Serre and M. Slemrods, eds.), Lecture Notes in Physics, Springer-Verlag, New-York 344
    • (1989) Partial Differential Equations and Continuum Models of Phase Transitions , pp. 344
    • Ball, J.M.1
  • 10
    • 48549111166 scopus 로고
    • 1,p-Quasiconvexity and Variational Problems for Multiple Integrals
    • 1,p-Quasiconvexity and Variational Problems for Multiple Integrals. J. Funct. Anal. 58
    • (1984) J. Funct. Anal. , vol.58
    • Ball, J.M.1    Murat, F.2
  • 11
    • 0030262462 scopus 로고    scopus 로고
    • Microscopic theory and nonlinear finite element analysis of micromechanics of single crystals at finite strain
    • Brunig M (1996) Microscopic theory and nonlinear finite element analysis of micromechanics of single crystals at finite strain. Comput. Mech. 18:471-484
    • (1996) Comput. Mech. , vol.18 , pp. 471-484
    • Brunig, M.1
  • 12
    • 0006495880 scopus 로고
    • Diffusionless phase change in the Indium-Thallium system
    • Burkart MW, Read TA (1953) Diffusionless phase change in the Indium-Thallium system. Trans. AIME J. Metals 197:1516-1524
    • (1953) Trans. AIME J. Metals , vol.197 , pp. 1516-1524
    • Burkart, M.W.1    Read, T.A.2
  • 13
    • 0001265570 scopus 로고
    • Linear Thermoelasticity
    • C. Trusdel (ed) Springer-Verlag, Berlin
    • Carlson DE (1984) Linear Thermoelasticity. In: Mechanics of Solids, Vol. II, C. Trusdel (ed) Springer-Verlag, Berlin
    • (1984) Mechanics of Solids , vol.2
    • Carlson, D.E.1
  • 14
    • 34250970762 scopus 로고
    • Thermodynamics and Departures from Fouries's Law of Heat Conduction
    • Coleman BD, Mizel VJ (1963) Thermodynamics and Departures from Fouries's Law of Heat Conduction. Arch Rat. Mech. 13:245-260
    • (1963) Arch Rat. Mech. , vol.13 , pp. 245-260
    • Coleman, B.D.1    Mizel, V.J.2
  • 15
    • 0015976463 scopus 로고
    • A Mathematical Foundation for Thermodynamics
    • Coleman BD, Owen DR (1973) A Mathematical Foundation for Thermodynamics. Arch Rat. Mech. Anal. 54:1-102
    • (1973) Arch Rat. Mech. Anal. , vol.54 , pp. 1-102
    • Coleman, B.D.1    Owen, D.R.2
  • 16
    • 0039079087 scopus 로고
    • Numerical approximations in variational problems with potential wells
    • Chipot M, Collins C, Kinderlehrer D (1995) Numerical approximations in variational problems with potential wells. SIAM J. Num. Anal. 70
    • (1995) SIAM J. Num. Anal. , vol.70
    • Chipot, M.1    Collins, C.2    Kinderlehrer, D.3
  • 17
    • 0001800199 scopus 로고
    • Computation of twinning
    • Microstructure and Phase Transitions (James, Kinderlehrer and, Luskin, eds.) Springer-Verlag, New York
    • Collins C (1993) Computation of twinning. In Microstructure and Phase Transitions (James, Kinderlehrer and, Luskin, eds.) IMA Volumes in Mathematics and Its Applications, Springer-Verlag, New York 54
    • (1993) IMA Volumes in Mathematics and Its Applications , pp. 54
    • Collins, C.1
  • 18
    • 0026136907 scopus 로고
    • Numerical approximation of the solution of a variational problem with a double well potential
    • Collins C, Luskin M (1991) Numerical approximation of the solution of a variational problem with a double well potential. SIAM J. Num. Anal. 28
    • (1991) SIAM J. Num. Anal. , vol.28
    • Collins, C.1    Luskin, M.2
  • 19
    • 0026136907 scopus 로고
    • Numerical approximation of the solution of a variational problem with a double well potential
    • Collins C, Luskin M (1991) Numerical approximation of the solution of a variational problem with a double well potential. SIAM J. Num. Anal. 28
    • (1991) SIAM J. Num. Anal. , vol.28
    • Collins, C.1    Luskin, M.2
  • 20
    • 0002058256 scopus 로고
    • The computation of the austenitic-martensitic phase transition
    • M. Rascle, D. Serre and M. Slemrod, eds Lecture Notes in Physics, Springer-Verlag, New York
    • Collins C, Luskin M (1989) The computation of the austenitic-martensitic phase transition, in Partial Differential Equations and Continuum Models of Phase Transitions (M. Rascle, D. Serre and M. Slemrod, eds) Lecture Notes in Physics, Springer-Verlag, New York 34-50
    • (1989) Partial Differential Equations and Continuum Models of Phase Transitions , pp. 34-50
    • Collins, C.1    Luskin, M.2
  • 21
    • 84966255684 scopus 로고
    • Optimal order estimates for the finite element approximation of the solution of a non-convex variational problem
    • Collins G, Luskin M (1991) Optimal order estimates for the finite element approximation of the solution of a non-convex variational problem. Math. Comp 621-637
    • (1991) Math. Comp , pp. 621-637
    • Collins, G.1    Luskin, M.2
  • 22
    • 0026136907 scopus 로고
    • Numerical approximation of the solution of a variational problem with a double well potential
    • Collins C, Luskin M, Kinderlehrer D (1991) Numerical approximation of the solution of a variational problem with a double well potential. SIAM J. Num. Anal. 28
    • (1991) SIAM J. Num. Anal. , vol.28
    • Collins, C.1    Luskin, M.2    Kinderlehrer, D.3
  • 23
    • 0011566457 scopus 로고
    • Convergence and stability in the numerical integration of ordinary differential equations
    • Dahlquist G (1956) Convergence and stability in the numerical integration of ordinary differential equations. Math. Scand. 4:33-53
    • (1956) Math. Scand. , vol.4 , pp. 33-53
    • Dahlquist, G.1
  • 25
    • 0022906928 scopus 로고
    • Constitutive theory for some constrained elastic crystals
    • Ericksen JL (1986) Constitutive theory for some constrained elastic crystals. Int. J. Solids and Structures 22:951-964.
    • (1986) Int. J. Solids and Structures , vol.22 , pp. 951-964
    • Ericksen, J.L.1
  • 26
    • 0019284770 scopus 로고
    • Model Free Energy, Mechanics, and Thermodynamics of Shape Memory Alloys
    • Falk F (1980) Model Free Energy, Mechanics, and Thermodynamics of Shape Memory Alloys. Acta Metallurgica 28:1773-1780
    • (1980) Acta Metallurgica , vol.28 , pp. 1773-1780
    • Falk, F.1
  • 27
    • 0242420138 scopus 로고
    • Long-time behavior of arbitrary order continuous time Galerkin schemes for some one-dimensional phase transtion problems
    • French DA, Jensen S (1994) Long-time behavior of arbitrary order continuous time Galerkin schemes for some one-dimensional phase transtion problems. IMA J. Num. Anal. 14:421-442
    • (1994) IMA J. Num. Anal. , vol.14 , pp. 421-442
    • French, D.A.1    Jensen, S.2
  • 28
    • 0026117358 scopus 로고
    • Behavior in the large of numerical solutions to one-dimensional nonlinear viscoelasticity by continuous time Galerkin method
    • French DA, Jensen S (1991) Behavior in the large of numerical solutions to one-dimensional nonlinear viscoelasticity by continuous time Galerkin method. Comp. Methods Appl. Mech. and Eng. 86:105-124
    • (1991) Comp. Methods Appl. Mech. and Eng. , vol.86 , pp. 105-124
    • French, D.A.1    Jensen, S.2
  • 29
    • 0027640742 scopus 로고
    • On the numerical approximation of an evolution problem in non-linear viscoelasticity
    • French DA, Wahlbin LB (1993) On the numerical approximation of an evolution problem in non-linear viscoelasticity. Comp. Meth. Appl. Mech. Eng. 107:101-116
    • (1993) Comp. Meth. Appl. Mech. Eng. , vol.107 , pp. 101-116
    • French, D.A.1    Wahlbin, L.B.2
  • 30
    • 0030552415 scopus 로고    scopus 로고
    • Dynamics as a mechanism preventing the formation of finer and finer microstructure
    • In the press
    • Friesecke G, McLeod JB (1996) Dynamics as a mechanism preventing the formation of finer and finer microstructure. Arch. Rat. Mech. Analysis (In the press)
    • (1996) Arch. Rat. Mech. Analysis
    • Friesecke, G.1    McLeod, J.B.2
  • 31
    • 0009323248 scopus 로고
    • Crystal Structures and Transformations in Indium-Thallium Solid Solutions
    • Guttman L (1950) Crystal Structures and Transformations in Indium-Thallium Solid Solutions. J. of Metals, Transactions AIME 188
    • (1950) J. of Metals, Transactions AIME , vol.188
    • Guttman, L.1
  • 34
    • 0039079084 scopus 로고
    • Computational modeling of the Martensitic transformation with surface energy
    • Klouček P, Luskin M (1994) Computational modeling of the Martensitic transformation with surface energy. Mathematical and Computer Modelling 20(10/11)
    • (1994) Mathematical and Computer Modelling , vol.20 , Issue.10-11
    • Klouček, P.1    Luskin, M.2
  • 35
    • 0030353045 scopus 로고    scopus 로고
    • Nonconforming finite element approximation of the microstructure
    • Klouček P, Bo Li, Luskin M (1996) Nonconforming finite element approximation of the microstructure. Math. Comp. (65) 215:1111-1135
    • (1996) Math. Comp. (65) , vol.215 , pp. 1111-1135
    • Klouček, P.1    Bo, L.2    Luskin, M.3
  • 36
    • 11344261825 scopus 로고    scopus 로고
    • On the existence of the global strong solutions of the visco-elastic systems associated with the phase transitions
    • Manuscript
    • Klouček P (1996) On the existence of the global strong solutions of the visco-elastic systems associated with the phase transitions. Manuscript (Submitted to J. Diff. Eq.)
    • (1996) J. Diff. Eq.
    • Klouček, P.1
  • 37
    • 11344270205 scopus 로고    scopus 로고
    • Toward the computational modeling of nonequilibrium thermodynamics of the Martensitic transformations
    • Klouček P (1996) Toward the computational modeling of nonequilibrium thermodynamics of the Martensitic transformations. IMA Technical report 1418
    • (1996) IMA Technical Report 1418
    • Klouček, P.1
  • 39
    • 11344281805 scopus 로고    scopus 로고
    • The Relaxation of Non-Quasiconvex Variational Integrals
    • to appear
    • Klouček P (1998) The Relaxation of Non-Quasiconvex Variational Integrals (to appear in Num. Math.)
    • (1998) Num. Math.
    • Klouček, P.1
  • 41
    • 84953602308 scopus 로고
    • Branching of twins near an austenite/twinned-martensite interface
    • Kohn R, Müller S (1992) Branching of twins near an austenite/twinned-martensite interface. Philosophical Magazine 66A:697-715
    • (1992) Philosophical Magazine , vol.66 A , pp. 697-715
    • Kohn, R.1    Müller, S.2
  • 42
    • 0002862304 scopus 로고
    • Relaxation and regularization of nonconvex variational problems
    • Kohn R, Müller S (1992) Relaxation and regularization of nonconvex variational problems. Rend. Sem. Mat. Fis. Univ. Milano 62:89-113
    • (1992) Rend. Sem. Mat. Fis. Univ. Milano , vol.62 , pp. 89-113
    • Kohn, R.1    Müller, S.2
  • 43
    • 84990706266 scopus 로고
    • Surface energy and microstructure in coherent phase transformations
    • Kohn R, Müller S (1994) Surface energy and microstructure in coherent phase transformations. Comm. Pure Appl. Math. 47:405-435
    • (1994) Comm. Pure Appl. Math. , vol.47 , pp. 405-435
    • Kohn, R.1    Müller, S.2
  • 44
    • 0004097995 scopus 로고
    • 3rd Edition by E. M. Lifschitz, A. M. Kosevich and L. P. Pitaevskii Pergamon Press, New York
    • Landau LD, Lifschitz EM (1986) Theory of Elasticity. (3rd Edition by E. M. Lifschitz, A. M. Kosevich and L. P. Pitaevskii) Pergamon Press, New York
    • (1986) Theory of Elasticity
    • Landau, L.D.1    Lifschitz, E.M.2
  • 45
    • 0001425873 scopus 로고
    • Second-Order Phase Transitions
    • Landau LD (1937) Second-Order Phase Transitions. Phys. Z. Sowjet 11:545-563
    • (1937) Phys. Z. Sowjet , vol.11 , pp. 545-563
    • Landau, L.D.1
  • 46
    • 0030353296 scopus 로고    scopus 로고
    • Approximation of a laminated microstructure for a rotationally invariant, double well energy density
    • Luskin M (1996) Approximation of a laminated microstructure for a rotationally invariant, double well energy density. Num. Math.
    • (1996) Num. Math.
    • Luskin, M.1
  • 47
    • 0347284844 scopus 로고    scopus 로고
    • On the computation of Crystalline Mi-crostructure
    • Luskin M (1996) On the computation of Crystalline Mi-crostructure. Acta Numerica
    • (1996) Acta Numerica
    • Luskin, M.1
  • 48
    • 84972553547 scopus 로고
    • Systems of non-linear wave equations with nonlinear viscosity
    • Nečas J, Friedman A (1988) Systems of non-linear wave equations with nonlinear viscosity. Pac. J. Math. 135:31-55
    • (1988) Pac. J. Math. , vol.135 , pp. 31-55
    • Nečas, J.1    Friedman, A.2
  • 49
    • 0010853288 scopus 로고
    • Introduction to the Theory of Nonlinear Elliptic equations
    • Nečas J (1983) Introduction to the Theory of Nonlinear Elliptic equations. Teubner-Texte zur Mathematik 52
    • (1983) Teubner-Texte Zur Mathematik , vol.52
    • Nečas, J.1
  • 50
    • 0030231769 scopus 로고    scopus 로고
    • Computational micromechanics
    • Ortiz M (1996) Computational micromechanics. Comput. Mech. 18:321-338
    • (1996) Comput. Mech. , vol.18 , pp. 321-338
    • Ortiz, M.1
  • 51
    • 0023170272 scopus 로고
    • Phase transitions in one-dimensional nonlinear viscoelasticity: Admissibility and Stability
    • Pego RL (1987) Phase transitions in one-dimensional nonlinear viscoelasticity: Admissibility and Stability. Arch. Rat. Mech. Anal. 97:197-223
    • (1987) Arch. Rat. Mech. Anal. , vol.97 , pp. 197-223
    • Pego, R.L.1
  • 52
    • 0026837268 scopus 로고
    • Simple nonconforming quadrilateral Stokes element
    • Rannacher R, Turek S (1992) Simple nonconforming quadrilateral Stokes element. Numer. Meth. for PDEs 8:97-111
    • (1992) Numer. Meth. for PDEs , vol.8 , pp. 97-111
    • Rannacher, R.1    Turek, S.2
  • 53
    • 84974082050 scopus 로고
    • Dynamics modeling of phase transitions by means of viscoelasticity in many dimensions
    • Rybka P (1992) Dynamics modeling of phase transitions by means of viscoelasticity in many dimensions. Proc. R. Soc. Edinburgh 121A:101-138
    • (1992) Proc. R. Soc. Edinburgh , vol.121 A , pp. 101-138
    • Rybka, P.1
  • 54
    • 0018685219 scopus 로고
    • Conceptual Analysis of the Classical Second Laws of Thermodynamics
    • Serrin J (1979) Conceptual Analysis of the Classical Second Laws of Thermodynamics. Arch. Rat. Mech. Anal. 70:355-371
    • (1979) Arch. Rat. Mech. Anal. , vol.70 , pp. 355-371
    • Serrin, J.1
  • 55
    • 0000137102 scopus 로고
    • Asymptotics for a class of non-linear evolution equations, with applications to geometric problems
    • Simon L (1983) Asymptotics for a class of non-linear evolution equations, with applications to geometric problems. Annals of Math. 118:525-571
    • (1983) Annals of Math. , vol.118 , pp. 525-571
    • Simon, L.1
  • 56
    • 21144484260 scopus 로고
    • Energy minimization and the formation of microstructure in Dynamic anti-plane shear
    • Swart PJ, Holmes PJ (1992) Energy minimization and the formation of microstructure in Dynamic anti-plane shear. Arch. Rat. Mech. Anal 121:37-85
    • (1992) Arch. Rat. Mech. Anal , vol.121 , pp. 37-85
    • Swart, P.J.1    Holmes, P.J.2


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