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Volumn 454, Issue 1974, 1998, Pages 1573-1613

A 'non-local' variational approach to the elastic energy minimization of martensitic polycrystals

Author keywords

Energy minimization; Martensitic phase transformations; Non local variational principles; Polycrystals; Relaxation problems; Statistical averaging

Indexed keywords


EID: 0342840044     PISSN: 13645021     EISSN: None     Source Type: Journal    
DOI: 10.1098/rspa.1998.0222     Document Type: Article
Times cited : (28)

References (32)
  • 1
    • 34250138457 scopus 로고
    • Semicontinuity problems in the calculus of variations
    • Acerbi, E. & Fusco, N. 1984 Semicontinuity problems in the calculus of variations. Arch. Ration. Mech. Analysis 86, 125-145.
    • (1984) Arch. Ration. Mech. Analysis , vol.86 , pp. 125-145
    • Acerbi, E.1    Fusco, N.2
  • 2
    • 0023592964 scopus 로고
    • Optimal bounds and microgeometries for elastic two-phase composites
    • Avellaneda, M. 1987 Optimal bounds and microgeometries for elastic two-phase composites. SIAM J. Appl. Math. 47, 1216-1228.
    • (1987) SIAM J. Appl. Math. , vol.47 , pp. 1216-1228
    • Avellaneda, M.1
  • 3
    • 33750297145 scopus 로고
    • Fine phase mixtures as minimizers of energy
    • Ball, J. M. & James, R. D. 1987 Fine phase mixtures as minimizers of energy. Arch. Ration. Mech. Analysis 100, 13-52.
    • (1987) Arch. Ration. Mech. Analysis , vol.100 , pp. 13-52
    • Ball, J.M.1    James, R.D.2
  • 4
    • 0002854369 scopus 로고
    • Proposed experimental tests of a theory of fine microstructure and the two-well problem
    • Ball, J. M. & James, R. D. 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
  • 5
    • 0031240687 scopus 로고    scopus 로고
    • Elastic energy minimization and the recoverable strains of polycrystalline shape-memory materials
    • Bhattacharya, K. & Kohn, R. V. 1997 Elastic energy minimization and the recoverable strains of polycrystalline shape-memory materials. Arch. Ration. Mech. Analysis 139, 99-180.
    • (1997) Arch. Ration. Mech. Analysis , vol.139 , pp. 99-180
    • Bhattacharya, K.1    Kohn, R.V.2
  • 7
    • 0030189380 scopus 로고    scopus 로고
    • The overall elastic energy of polycrystalline martensitic solids
    • Bruno, O. P., Reitich, F. & Leo, P. H. 1996 The overall elastic energy of polycrystalline martensitic solids. J. Mech. Phys. Solids 44, 1051-1101.
    • (1996) J. Mech. Phys. Solids , vol.44 , pp. 1051-1101
    • Bruno, O.P.1    Reitich, F.2    Leo, P.H.3
  • 8
    • 0001822618 scopus 로고
    • Quasiconvexity and relaxation of nonconvex variational problems
    • Dacorogna, B. 1982 Quasiconvexity and relaxation of nonconvex variational problems. J. Funct. Analysis 46, 102-118.
    • (1982) J. Funct. Analysis , vol.46 , pp. 102-118
    • Dacorogna, B.1
  • 11
    • 0000929676 scopus 로고
    • The determination of the elastic field of an ellipsoidal inclusion, and related problems
    • Eshelby, J. D. 1957 The determination of the elastic field of an ellipsoidal inclusion, and related problems. Proc. R. Soc. Lond. A 241, 376-396.
    • (1957) Proc. R. Soc. Lond. A , vol.241 , pp. 376-396
    • Eshelby, J.D.1
  • 12
    • 9444258726 scopus 로고
    • Geometric parameters and the relaxation of multiwell energies
    • ed. D. Kinderlehrer, R. James, M. Lusk & J. L. Ericksen, New York: Springer
    • Firoozye, N. B. & Kohn, R. V. 1993 Geometric parameters and the relaxation of multiwell energies. In Microstructure and phase transition (ed. D. Kinderlehrer, R. James, M. Lusk & J. L. Ericksen), pp. 85-109. New York: Springer.
    • (1993) Microstructure and Phase Transition , pp. 85-109
    • Firoozye, N.B.1    Kohn, R.V.2
  • 13
    • 0022862030 scopus 로고
    • Homogenization and optimal bounds in linear elasticity
    • Francfort, G. A. & Murat, F. 1986 Homogenization and optimal bounds in linear elasticity. Arch. Ration. Mech. Analysis 94, 307-334.
    • (1986) Arch. Ration. Mech. Analysis , vol.94 , pp. 307-334
    • Francfort, G.A.1    Murat, F.2
  • 15
    • 0001342333 scopus 로고
    • Microlocal defect measures
    • Gerard, P. 1991 Microlocal defect measures. Commun. Partial Diff. Equat. 16, 1761-1794.
    • (1991) Commun. Partial Diff. Equat. , vol.16 , pp. 1761-1794
    • Gerard, P.1
  • 17
    • 27744489677 scopus 로고
    • On some variational principles in anisotropic and inhomogeneous elasticity
    • Hashin, Z. & Shtrikman, S. 1962 On some variational principles in anisotropic and inhomogeneous elasticity. J. Mech. Phys. Solids 10, 335-342.
    • (1962) J. Mech. Phys. Solids , vol.10 , pp. 335-342
    • Hashin, Z.1    Shtrikman, S.2
  • 18
    • 49749215641 scopus 로고
    • Continuum micromechanics of elasto-plastic polycrystals
    • Hill, R. 1965 Continuum micromechanics of elasto-plastic polycrystals. J. Mech. Phys. Solids 13, 89-101.
    • (1965) J. Mech. Phys. Solids , vol.13 , pp. 89-101
    • Hill, R.1
  • 19
    • 0000581335 scopus 로고
    • Some questions concerning the theory of phase transformations in solids
    • Khachaturyan, A. G. 1967 Some questions concerning the theory of phase transformations in solids. Sov. Phys. Solid State 8, 2163-2168.
    • (1967) Sov. Phys. Solid State , vol.8 , pp. 2163-2168
    • Khachaturyan, A.G.1
  • 20
    • 0001000267 scopus 로고
    • The relaxation of a double-well energy
    • Kohn, R. V. 1991 The relaxation of a double-well energy. Continuum Mech. Thermodyn. 3, 193-236.
    • (1991) Continuum Mech. Thermodyn. , vol.3 , pp. 193-236
    • Kohn, R.V.1
  • 21
    • 84990623154 scopus 로고
    • Optimal design and relaxation of variational problems. I-III
    • Kohn, R. V. & Strang, G. 1986 Optimal design and relaxation of variational problems. I-III. Commun. Pure Appl. Math. 39, 113-137, 139-182 and 353-377.
    • (1986) Commun. Pure Appl. Math. , vol.39 , pp. 113-137
    • Kohn, R.V.1    Strang, G.2
  • 22
    • 0025505596 scopus 로고
    • Pseudoelastic behavior in a polycrystalline CuAlNi shape memory alloy in comparison with the modified Taylor model
    • Ono, N. 1990 Pseudoelastic behavior in a polycrystalline CuAlNi shape memory alloy in comparison with the modified Taylor model. Mat. Trans. Jap. Inst. Metals 31, 855-860.
    • (1990) Mat. Trans. Jap. Inst. Metals , vol.31 , pp. 855-860
    • Ono, N.1
  • 23
    • 0023994708 scopus 로고
    • Plastic deformation governed by the stress induces martensitic transformation in polycrystals
    • Ono, N. & Sato, A. 1988 Plastic deformation governed by the stress induces martensitic transformation in polycrystals. Trans. Jap. Inst. Metals 29, 267-273.
    • (1988) Trans. Jap. Inst. Metals , vol.29 , pp. 267-273
    • Ono, N.1    Sato, A.2
  • 24
    • 0026103883 scopus 로고
    • Elastic materials with two preferred states
    • Pipkin, A. C. 1991 Elastic materials with two preferred states. Q. J. Mech. Appl. Math. 44, 1-15.
    • (1991) Q. J. Mech. Appl. Math. , vol.44 , pp. 1-15
    • Pipkin, A.C.1
  • 25
    • 0015600971 scopus 로고
    • Domain structure caused by internal stresses in heterophase solids
    • Roitburd, A. L. 1973 Domain structure caused by internal stresses in heterophase solids. Phys. Status Solidi A16, 329-339.
    • (1973) Phys. Status Solidi A , vol.16 , pp. 329-339
    • Roitburd, A.L.1
  • 28
    • 84974050752 scopus 로고
    • H-measures, a new approach for studying homogenization, oscillation and concentration effects in partial differential equations
    • Tartar, L. 1990 H-measures, a new approach for studying homogenization, oscillation and concentration effects in partial differential equations. Proc. R. Soc. Edinb. A115, 193-230.
    • (1990) Proc. R. Soc. Edinb. A , vol.115 , pp. 193-230
    • Tartar, L.1
  • 29
    • 0000649503 scopus 로고
    • Plastic strain in metals
    • Taylor, G. I. 1938 Plastic strain in metals. J. Inst. Metals 62, 307-324.
    • (1938) J. Inst. Metals , vol.62 , pp. 307-324
    • Taylor, G.I.1
  • 30
    • 0017502751 scopus 로고
    • Bounds and self-consistent estimates for the overall moduli of anisotropic composites
    • Willis, J. R. 1977 Bounds and self-consistent estimates for the overall moduli of anisotropic composites. J. Mech. Phys. Solids 25, 185-202.
    • (1977) J. Mech. Phys. Solids , vol.25 , pp. 185-202
    • Willis, J.R.1
  • 31
    • 0019265450 scopus 로고
    • A polarization approach to the scattering of elastic waves. I. Scattering by a single inclusion
    • Willis, J. R. 1980 A polarization approach to the scattering of elastic waves. I. Scattering by a single inclusion. J. Mech. Phys. Solids 28, 287-305.
    • (1980) J. Mech. Phys. Solids , vol.28 , pp. 287-305
    • Willis, J.R.1
  • 32
    • 0019697033 scopus 로고
    • Variational and related methods for the overall properties of composites
    • ed. C.-S. Yih, New York: Academic
    • Willis, J. R. 1981 Variational and related methods for the overall properties of composites. In Advances in applied mechanics (ed. C.-S. Yih), vol. 21, pp. 1-78. New York: Academic.
    • (1981) Advances in Applied Mechanics , vol.21 , pp. 1-78
    • Willis, J.R.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.