Preview
Unable to display preview. Download preview PDF.
References
Ball, J. M. 1976 Constitutive equations and existence theorems in nonlinear elastostatics, Heriot-Watt Symp., I, (R. Knops,ed.) Pitman, 187–241
Ball, J. M. 1980 Strict convexity, strong ellipticity, and regularity in the calculus of variations, Math Proc Camb Phil Soc, 87, 501–513
Ball, J. M. 1984 Singular minimizers and their significance in elasticity, Phase Transformations and Material Instabilities in Solids, (Gurtin, M., ed) Academic Press, 1–20
Ball, J. M. 1989 Sets of gradients with no rank-one connections (to appear)
Ball, J. M. 1989 A version of the fundamental theorem for Young measures, these proceedings
Ball, J. M. and James, R. 1987 Fine phase mixtures as minimizers of energy, Arch. Rat. Mech. Anal.,100, 15–52
Ball, J. M. and James, R. 1989 Proposed experimental tests of a theory of fine microstructure and the two well problem (to appear)
Ball, J. M. and Murat, F. 1984 W1,p — quasiconvexity and variational problems for multiple integrals, J. Fnal Anal, 58,225–253
Ball, J. M., and Knowles, G. 1986 Liapunov functions for thermomechanics with spatially varying boundary temperatures, Arch. Rat. mech. Anal., 92, 193–204
Basinski, Z. S. and Christian, J. W. 1954 Experiments on the martensitic transformations in single crystals of indium-thallium alloys, Acta Met. 2, 149–166
Battacharya, K 1989 Thesis, University of Minnesota
Burkart, M. W. and Read, T. A. 1953 Diffusionless phase change in the indium-thallium system, J. of Metals, 5, 1516–1524
Chipot, M. and Evans, L. C. 1986 Linearisation at infinity and Lipschitz estimates for certain problems in the calculus of variations, Proc. R. Soc. Edin., 102A, 291–303
Chipot, M. and Kinderlehrer, D. 1988 Equilibrium configurations of crystals, Arch. Rat. Mech. Anal. 103,237–277
Chipot, M., Kinderlehrer, D., and Vergara-Caffarelli, G. 1986 Smoothness of linear laminates, Arch. Rat. Mech. and Anal. 96, 81–96
Christian, J. W. 1975 The theory of transformations in metals and alloys, Pergamon
Collins, C. and Luskin, M. 1989 The computation of the austenitic-martensitic phase transition (these proceedings)
Dacorogna, B. 1982 Weak continuity and weak lower semicontinuity of nonlinear functionals, Springer Lecture Notes 922 (1982)
Dacorogna, B. and Fusco, N. 1985 Semi-continuité des fonctionnelles avec contraintes du type “det grad u > 0”, Boll. U M I, 6, 179–189
Eftis, J., MacDonald, D. E., and Arkilic, G. M. 1971 Theoretical calculation of the pressure variation of second-order elastic coefficients for alkali metals, Mater. Sci. Eng. 7, 141–150
Ericksen, J. L. 1973 Loading devices and stability of equilibrium, in Nonlinear Elasticity, Academic Press, 161–173
Ericksen, J. L. 1977 Special topics in elastostatics, Adv. in appl. mechanics, (C.-S. Yih, ed.) Academic Press 7, 189–243
Ericksen, J. L. 1979 On the symmetry of deformable crystals, Arch. Rat. Mech. Anal. 72, 1–13
Ericksen, J. L. 1980 Some phase transitions in crystals, Arch. Rat. Mech. Anal. 73, 99–124
Ericksen, J. L. 1981 Some simpler cases of the Gibbs phenomenon for thermoelastic solids, J.of thermal stresses, 4, 13–30
Ericksen, J. L. 1983 Ill posed problems in thermoelasticity theory, Systems of Nonlinear Partial Differential Equations, (Ball, J., ed) D. Reidel, 71–95
Ericksen, J. L. 1984 The Cauchy and Born hypotheses for crystals, Phase Transformations and Material Instabilities in Solids, (Gurtin, M., ed) Academic Press, 61–78
Ericksen, J. L. 1986 Stable equilibrium configurations of elastic crystals, Arch. Rat. Mech. Anal. 94, 1–14
Ericksen, J. L. 1987 Twinning of crystals I, Metastability and Incompletely Posed Problems, IMA Vol. Math. Appl. 3,(Antman, S., Ericksen, J.L., Kinderlehrer, D., Müller, I.,eds) Springer, 77–96
Ericksen, J. L. 1988 Some constrained elastic crystals, Proc. Symp. Material instabilities in continuum mechanics, Heriot-Watt (Ball, J. M. ed.) Oxford, 119–136
Fonseca, I. 1985 Variational methods for elastic crystals, Arch. Rat. Mech. Anal., 97, 189–220
Fonseca, I. 1988 The lower quasiconvex envelope of the stored energy function for an elastic crystal, J. Math. pures et appl, 67, 175–195
Fonseca, I. 1989 Interfacial energy and the Maxwell rule, Arch. Rat. Mech. Anal.
Gibbs, J. W. 1961 On the equilibrium of heterogeneous substances, The Scientific Papers of J. Willard Gibbs, Vol 1., Dover
Gurtin, M. E. 1983 Two phase deformations of elastic solids, Arch. Rat. Mech. Anal., 84, 1–29
IGurtin, M. E. 1986 On phase transitions with bulk, interfacial, and boundary energy, Arch. Rat. Mech. Anal., 96, 243–264
Herring, C. 1951 Some theorems on the free energy of crystal surfaces, Phys. Rev. 82, 87–93
James, R. D. 1986 Displacive phase transformations in solids, J. Mech. Phys. Solids, 34, 359–394
James, R. D. 1986 Phase transformations and non-elliptic free energy, New Perspectives in Thermodynamics (Serrin, J., ed) Springer, 223–239
James, R. D. 1987 The stability and metastability of quartz, Metastability and Incompletely Posed Problems, IMA Vol. Math. Appl. 3,(Antman, S., Ericksen, J.L., Kinderlehrer, D., Müller, I.,eds) Springer, 147–176
James, R. D. 1988 Microstructure and weak convergence, Proc. Symp. Material instabilities in continuum mechanics, Heriot-Watt (Ball, J. M. ed.) Oxford, 175–196
Kinderlehrer, D. 1987 Twinning in crystals II, Metastability and Incompletely Posed Problems, IMA Vol. Math. Appl. 3,(Antman, S., Ericksen, J.L., Kinderlehrer, D., Müller, I.,eds) Springer, 185–211
Kinderlehrer, D. 1988 Remarks about the equilibrium configurations of crystals, Proc. Symp. Material instabilities in continuum mechanics, Heriot-Watt (Ball, J. M. ed.) Oxford, 217–242
Kinderlehrer, D. and Vergara-Caffarelli, G. The relaxation of functionals with surface energies, to appear
Kohn, R. V. and Strang, G. 1987 Optimal design and relaxation of variational problems, I, CPAM 34, 113–137
Kohn, R. V. and Strang, G. 1987 Optimal design and relaxation of variational problems, II,CPAM 34, 139–182
Kohn, R. V. and Strang,G. 1987 Optimal design and relaxation of variational problems, III,CPAM 34, 353–377
Marcellini, P. 1986 On the definition and the lower semicontinuity of certain quasiconvex integrals, Ann. Inst. H. Poincaré; Analyse non linéaire, 3, 391–409
Mascolo, E. and Schianchi, R. 1983 Existence theorems for non convex problems, J. Math pures et appl, 62,(1983), 349–359
Matos, J. 1989 Thesis, University of Minnesota
Morrey, C. B., Jr. 1966 Multiple Integrals in the Calculus of Variations, Springer
Müller, I. 1979 A model for a body with shape memory, Arch. Rat. Mech. Anal., 70, 61–77
Müller, I. and Wilmanski, K. 1980 A model for phase transition in pseudoelastic bodies, Il Nuovo Cim., 57B, 283–318
Parry, G. 1981 On phase transitions involving internal strain, Int. J. Solids Structures, 17, 361–378
Parry, G. On shear bands in unloaded crystals, to appear
Pedregal, P. Thesis, University of Minnesota
Pego, R. 1985 Phase transitions in one dimensional nonlinear viscoelasticity: admissibility and stability, Arch. Rat. Meth. Anal. 97, 353–394
Pego, R. 1987 Phase transitions in one dimensional nonlinear viscoelasticity: admissibility and stability, Dynamical Problems in Continuum Physics, I M A Vol. Math. Appl. 4 (Bona, J., Dafermos, C., Ericksen, J. L., and Kinderlehrer,., eds)277–288
Pipkin, A. C. 1986 The relaxed energy density for isotropic elastic membranes, IMA J Appl Math, 36, 85–99
Pippard, A. B. 1957 The elements of classical thermodynamics, Cambridge
Pitteri, M. 1985 On v + 1 lattices, J. Elasticity, 15, 3–25
Pitteri, M. 1986 On type-2 twins in crystals, Int. J. Plasticity, 2, 99–106
Pitteri, M. 1987 A contribution to the description of natural states for elastic crystalline solids, Metastability and Incompletely Posed Problems, IMA Vol. Math. Appl. 3,(Antman, S., Ericksen, J.L., Kinderlehrer, D., Müller, L,eds) Springer, 295–310
Reshetnyak, Yu. G. 1967 Liouville's theorem on conformal mappings under minimal regularity assumptions, Siberian Math J., 8, 631–653
Reshetnyak, Yu. G. 1967 On the stability of conformal mappings in multidimensional spaces, Siberian Math J., 8, 69–85
Simpson, H. C. and Spector, S. J. 1987 On the sign of the second variation in finite elasticity, Arch. Rat. Meth. Anal. 98, 1–30
Slemrod, M. 1986 Interrelationships among mechanics, numerical analysis, compensated compactness, and oscillation theory, Oscillation Theory, Computation, and Methods of Compensated Compactness, I M A Vol. Math. Appl. 2, (Dafermos, C., Ericksen, J. L, 309–336., Kinderlehrer, D., and Slemrod, M. eds)
Tartar, L. 1979 Compensated compactness and applications to partial differential equations, Nonlinear analysis and mechanics: Heriot-Watt symp. IV, (Knops, R. J. ed) Pitman, (1979), 136–212
Tartar, L. 1983 The compensated compactness method applied to systems of conservation laws, Systems of nonlinear partial differential equations (Ball, J. M., ed) Riedel, 263–285
Tartar, L. 1984 Étude des oscillations dans les équations aux dérivées partielles nonlinéaires, Springer Lect. Notes Physics, 195, 384–412
Tisza, L. 1951 On the general theory of phase transformations in solids, (Smoluchowski, R., Mayer, J. E., and Weyl, W. A., eds) Wiley, 1–35
van Tendeloo, G., van Landuyt, J., and Amelinckx, S. 1976 The α-β phase transition in quartz and AlPo4 as studied by electron microscopy and diffraction, Phys. Stat. Sol., a33, 723–735
Wechsler, M. S., Lieberman, D. S., and Read, T. A. 1953 On the theory of the formation of martensite, Trans. AIME J. Metals, 197, 1503–1515
Young, L. C. 1969 Lectures on calculus of variations and optimal control theory, W.B. Saunders
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1989 Springer-Verlag
About this paper
Cite this paper
James, R., Kinderlehrer, D. (1989). Theory of diffusionless phase transitions. In: Rascle, M., Serre, D., Slemrod, M. (eds) PDEs and Continuum Models of Phase Transitions. Lecture Notes in Physics, vol 344. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0024935
Download citation
DOI: https://doi.org/10.1007/BFb0024935
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-51617-0
Online ISBN: 978-3-540-46717-5
eBook Packages: Springer Book Archive