메뉴 건너뛰기




Volumn 15, Issue 2, 2003, Pages 161-195

Finite multiplicative plasticity for small elastic strains with linear balance equations and grain boundary relaxation

Author keywords

Elliptic systems; Grain boundary relaxation; Internal friction; Plasticity; Polar materials; Solid mechanics; Texture; Variational methods; Visco plasticity

Indexed keywords


EID: 0038538235     PISSN: 09351175     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00161-002-0109-x     Document Type: Article
Times cited : (23)

References (100)
  • 2
    • 0002605297 scopus 로고
    • Die theorie der nichtmetrischen spannungen in kristallen
    • Anthony KH (1971) Die Theorie der nichtmetrischen Spannungen in Kristallen. Arch. Rat. Mech. Anal. 40:50-78
    • (1971) Arch. Rat. Mech. Anal. , vol.40 , pp. 50-78
    • Anthony, K.H.1
  • 3
    • 0027073018 scopus 로고
    • Finite elastoplastic transformations of transversely isotropic materials
    • Aravas N (1992) Finite elastoplastic transformations of transversely isotropic materials. Int. J. Solids Structures 29(17):2137-2157
    • (1992) Int. J. Solids Structures , vol.29 , Issue.17 , pp. 2137-2157
    • Aravas, N.1
  • 4
    • 0038272853 scopus 로고
    • Experimentelle prüfung der neueren formeln für die torsion prismatischer körper
    • Bauschinger J (1881) Experimentelle Prüfung der neueren Formeln für die Torsion prismatischer Körper. Civilingenieur 27:115-130
    • (1881) Civilingenieur , vol.27 , pp. 115-130
    • Bauschinger, J.1
  • 5
    • 4243848031 scopus 로고
    • Festkörpermechanik I
    • C. Truesdell, editor, 1 ed. Springer, Berlin
    • Bell JF (1973) Festkörpermechanik I. In C. Truesdell, editor, Handbuch der Physik, volume Via/1, 1. ed. Springer, Berlin
    • (1973) Handbuch der Physik , vol.6 A-1
    • Bell, J.F.1
  • 6
    • 0032650520 scopus 로고    scopus 로고
    • An alternative approach to finite plasticity based on material isomorphisms
    • Bertram A (1998) An alternative approach to finite plasticity based on material isomorphisms. Int. J. Plasticity 52:353-374
    • (1998) Int. J. Plasticity , vol.52 , pp. 353-374
    • Bertram, A.1
  • 12
    • 0035400701 scopus 로고    scopus 로고
    • On the characterization of geometrically necessary dislocations in finite plasticity
    • Cermelli P, Gurtin ME (2001) On the characterization of geometrically necessary dislocations in finite plasticity. J. Mech. Phys. Solids 49:1539-1568
    • (2001) J. Mech. Phys. Solids , vol.49 , pp. 1539-1568
    • Cermelli, P.1    Gurtin, M.E.2
  • 13
    • 0032222133 scopus 로고    scopus 로고
    • On self-controlling models in the theory of inelastic material behaviour of metals
    • Chelminski K (1998) On self-controlling models in the theory of inelastic material behaviour of metals. Cont. Mech. Thermodyn. 10:121-133
    • (1998) Cont. Mech. Thermodyn. , vol.10 , pp. 121-133
    • Chelminski, K.1
  • 14
    • 0000971651 scopus 로고    scopus 로고
    • On monotone plastic constitutive equations with polynomial growth condition
    • Chelminski K (1999) On monotone plastic constitutive equations with polynomial growth condition. Math. Meth. App. Se. 22:547-562
    • (1999) Math. Meth. App. Se. , vol.22 , pp. 547-562
    • Chelminski, K.1
  • 18
    • 0021498156 scopus 로고
    • The plastic spin concept and a simple illustration of its role in finite plastic transformations
    • Dafalias YF (1984) The plastic spin concept and a simple illustration of its role in finite plastic transformations. Mechanics of Materials 3:223-233
    • (1984) Mechanics of Materials , vol.3 , pp. 223-233
    • Dafalias, Y.F.1
  • 19
    • 0023537860 scopus 로고
    • Issues on the constitutive formulation at large elastoplastic deformations, Part I: Kinematics
    • Dafalias YF (1987) Issues on the constitutive formulation at large elastoplastic deformations, Part I: Kinematics. Acta Mechanica 69:119-138
    • (1987) Acta Mechanica , vol.69 , pp. 119-138
    • Dafalias, Y.F.1
  • 20
    • 0032291386 scopus 로고    scopus 로고
    • Plastic spin: Necessity or redundancy?
    • Dafalias YF (1998) Plastic spin: necessity or redundancy? Int. J. Plasticity 14(9):909-931
    • (1998) Int. J. Plasticity , vol.14 , Issue.9 , pp. 909-931
    • Dafalias, Y.F.1
  • 21
    • 0025842044 scopus 로고
    • The Cosserat continuum, a model for grain rotations in metals?
    • Diepholder W, Mannl V, Lippmann H (1991) The Cosserat continuum, a model for grain rotations in metals? Int. J. Plasticity 7:313-328
    • (1991) Int. J. Plasticity , vol.7 , pp. 313-328
    • Diepholder, W.1    Mannl, V.2    Lippmann, H.3
  • 23
    • 0001271626 scopus 로고    scopus 로고
    • A Cosserat theory for elastoviscoplastic single crystals at finite deformation
    • Forest S, Cailletaud G, Sievert R (1997) A Cosserat theory for elastoviscoplastic single crystals at finite deformation. Arch. Mech. 49(4):705-736
    • (1997) Arch. Mech. , vol.49 , Issue.4 , pp. 705-736
    • Forest, S.1    Cailletaud, G.2    Sievert, R.3
  • 25
  • 26
    • 0035599103 scopus 로고    scopus 로고
    • Hardening rules for finite deformation micropolar plasticity: Restrictions imposed by the second law of thermodynamics and the postulate of Iljuschin
    • Grammenoudis P, Tsakmakis C (2001) Hardening rules for finite deformation micropolar plasticity: restrictions imposed by the second law of thermodynamics and the postulate of Iljuschin. Cont. Mech. Thermodyn. 13:325-363
    • (2001) Cont. Mech. Thermodyn. , vol.13 , pp. 325-363
    • Grammenoudis, P.1    Tsakmakis, C.2
  • 29
    • 0343337643 scopus 로고    scopus 로고
    • On the plasticity of single crystals: Free energy, microforces, plastic-strain gradients
    • Gurtin ME (2000) On the plasticity of single crystals: free energy, microforces, plastic-strain gradients. J. Mech. Phys. Solids 48:989-1036
    • (2000) J. Mech. Phys. Solids , vol.48 , pp. 989-1036
    • Gurtin, M.E.1
  • 31
    • 0022239164 scopus 로고
    • On the concept of an intermediate configuration and its application to a representation of viscoelastic-plastic material behaviour
    • Haupt P (1985) On the concept of an intermediate configuration and its application to a representation of viscoelastic-plastic material behaviour. Int. J. Plasticity 1:303-316
    • (1985) Int. J. Plasticity , vol.1 , pp. 303-316
    • Haupt, P.1
  • 33
    • 33748722160 scopus 로고
    • Experimental identification and mathematical modeling of viscoplastic material behavior
    • Haupt P, Lion A (1995) Experimental identification and mathematical modeling of viscoplastic material behavior. Cont. Mech. Thermodyn. 7:73-96
    • (1995) Cont. Mech. Thermodyn. , vol.7 , pp. 73-96
    • Haupt, P.1    Lion, A.2
  • 35
    • 0019229765 scopus 로고
    • Finite rotation effects in numerical integration of rate constitutive equations arising in large deformation analysis
    • Hughes TJR, Winget J (1980) Finite rotation effects in numerical integration of rate constitutive equations arising in large deformation analysis. Num. Methods Engrg. 15:1862-1867
    • (1980) Num. Methods Engrg. , vol.15 , pp. 1862-1867
    • Hughes, T.J.R.1    Winget, J.2
  • 37
    • 0007048913 scopus 로고
    • Anelastic relaxations due to grain boundaries
    • Magalas LB, Gorczyca S (eds). Trans Tech Publications, Switzerland
    • Iwasaki K (1993) Anelastic relaxations due to grain boundaries. In: Magalas LB, Gorczyca S (eds), Material Science Forum: Internal Friction and Ultrasonic Attenuation in Solids., volume 119-121, pages 775-777. Trans Tech Publications, Switzerland
    • (1993) Material Science Forum: Internal Friction and Ultrasonic Attenuation in Solids , vol.119-121 , pp. 775-777
    • Iwasaki, K.1
  • 38
    • 84980088555 scopus 로고
    • Rotation and strain
    • John F (1961) Rotation and strain. Comm. Pure Appl. Math. 19:391-413
    • (1961) Comm. Pure Appl. Math. , vol.19 , pp. 391-413
    • John, F.1
  • 39
    • 84980167888 scopus 로고
    • Uniqueness of non-linear elastic equilibrium for prescribed boundary displacements and sufficiently small strain
    • John F (1972) Uniqueness of non-linear elastic equilibrium for prescribed boundary displacements and sufficiently small strain. Comm. Pure Appl. Math. 25:617-634
    • (1972) Comm. Pure Appl. Math. , vol.25 , pp. 617-634
    • John, F.1
  • 40
    • 19944419409 scopus 로고
    • Experimental evidence of the viscous behaviour of grain boundaries in metals
    • Ke TS (1947) Experimental evidence of the viscous behaviour of grain boundaries in metals. Phys. Rev. 71:533-546
    • (1947) Phys. Rev. , vol.71 , pp. 533-546
    • Ke, T.S.1
  • 41
    • 0003161346 scopus 로고
    • Stress relaxation across grain boundaries in metals
    • Ke TS (1947) Stress relaxation across grain boundaries in metals. Phys. Rev. 72:41-47
    • (1947) Phys. Rev. , vol.72 , pp. 41-47
    • Ke, T.S.1
  • 42
    • 0038611808 scopus 로고
    • Viscous slip along grain boundaries and diffusion of Zinc in alpha-brass
    • Ke TS (1947) Viscous slip along grain boundaries and diffusion of Zinc in alpha-brass. J. Appl. Phys. 19:285-290
    • (1947) J. Appl. Phys. , vol.19 , pp. 285-290
    • Ke, T.S.1
  • 43
    • 0022470232 scopus 로고
    • On rate sensitivity of f.c.c. metals, instantaneous rate sensitivity and rate sensitivity of strain hardening
    • Klepaczko JR, Chiem CY (1986) On rate sensitivity of f.c.c. metals, instantaneous rate sensitivity and rate sensitivity of strain hardening. J. Mech. Phys. Solids 34:29-54
    • (1986) J. Mech. Phys. Solids , vol.34 , pp. 29-54
    • Klepaczko, J.R.1    Chiem, C.Y.2
  • 46
    • 0006677446 scopus 로고
    • Non-Riemannien geometry of imperfect crystals from a macroscopic viewpoint
    • Kondo K (ed), Division D-I. Gakujutsu Bunken Fukyo-Kai
    • Kondo K (1955) Non-Riemannien geometry of imperfect crystals from a macroscopic viewpoint. In: Kondo K (ed), Memoirs of the Unifying Study of the Basic Problems in Engineering Science by Means of Geometry, volume 1, Division D-I, pages 6-17 (458-469). Gakujutsu Bunken Fukyo-Kai
    • (1955) Memoirs of the Unifying Study of the Basic Problems in Engineering Science by Means of Geometry , vol.1 , pp. 6-17
    • Kondo, K.1
  • 47
    • 0016437287 scopus 로고
    • A comprehensive constitutive inequality in finite elastic strain
    • Krawietz A (1975) A comprehensive constitutive inequality in finite elastic strain. Arch. Rat. Mech. Anal. 58:127-149
    • (1975) Arch. Rat. Mech. Anal. , vol.58 , pp. 127-149
    • Krawietz, A.1
  • 49
    • 85171876147 scopus 로고
    • Dislocation: A new concept in the continuum theory of plasticity
    • Kröner E (1963) Dislocation: a new concept in the continuum theory of plasticity. J. Math. Phys. 42:27-37
    • (1963) J. Math. Phys. , vol.42 , pp. 27-37
    • Kröner, E.1
  • 50
    • 0002185713 scopus 로고
    • Nichtlineare Elastizitätstheorie der Versetzungen und Eigenspannungen
    • Kröner E, Seeger A (1959) Nichtlineare Elastizitätstheorie der Versetzungen und Eigenspannungen. Arch. Rat. Mech. Anal. 3:97-119
    • (1959) Arch. Rat. Mech. Anal. , vol.3 , pp. 97-119
    • Kröner, E.1    Seeger, A.2
  • 52
    • 85024545548 scopus 로고
    • Elastic-plastic deformation at finite strain
    • Lee EH (1969) Elastic-plastic deformation at finite strain. J. Appl. Mech. 36:1-6
    • (1969) J. Appl. Mech. , vol.36 , pp. 1-6
    • Lee, E.H.1
  • 54
    • 0031141255 scopus 로고    scopus 로고
    • On the numerical treatment of finite deformations in elastoviscoplasticity
    • Lührs G, Hartmann S, Haupt P (1997) On the numerical treatment of finite deformations in elastoviscoplasticity. Comp. Meth. Appl. Mech. Engrg. 144:1-21
    • (1997) Comp. Meth. Appl. Mech. Engrg. , vol.144 , pp. 1-21
    • Lührs, G.1    Hartmann, S.2    Haupt, P.3
  • 57
    • 0023849185 scopus 로고
    • Materials with elastic range: A theory with a view toward applications. Part I
    • Lucchesi M, Podio-Guidugli P (1988) Materials with elastic range: a theory with a view toward applications. Part I. Arch. Rat. Mech. Anal. 102:23-43
    • (1988) Arch. Rat. Mech. Anal. , vol.102 , pp. 23-43
    • Lucchesi, M.1    Podio-Guidugli, P.2
  • 59
    • 0015639886 scopus 로고
    • Equations constitutives et directeurs dans les milieux plastiques et viscoplastiques
    • Mandel J (1973) Equations constitutives et directeurs dans les milieux plastiques et viscoplastiques. Int. J. Solids Structures 9:725-740
    • (1973) Int. J. Solids Structures , vol.9 , pp. 725-740
    • Mandel, J.1
  • 60
    • 0038611832 scopus 로고    scopus 로고
    • Dynamical methods for polar decomposition and inversion of matrizes
    • Marsden JE, Getz NH (1997) Dynamical methods for polar decomposition and inversion of matrizes. Lin. Alg. Appl 258:311-343
    • (1997) Lin. Alg. Appl , vol.258 , pp. 311-343
    • Marsden, J.E.1    Getz, N.H.2
  • 62
    • 0004281322 scopus 로고
    • Applied Mathematics and Mathematical Computations. Chapman-Hall, London
    • Maugin G (1993) Material Inhomogeneities in Elasticity. Applied Mathematics and Mathematical Computations. Chapman-Hall, London
    • (1993) Material Inhomogeneities in Elasticity
    • Maugin, G.1
  • 65
    • 0029488530 scopus 로고
    • A theory of large-strain isotropic thermoplasticity based on metric transformation tensors
    • Miehe C (1995) A theory of large-strain isotropic thermoplasticity based on metric transformation tensors. Archive Appl. Mech. 66:45-64
    • (1995) Archive Appl. Mech. , vol.66 , pp. 45-64
    • Miehe, C.1
  • 66
    • 0038272873 scopus 로고    scopus 로고
    • Lie groups and geodesics on SL(d). Sonderforschungsbereich 404 Bericht 2000/26, University of Stuttgart
    • Mielke A (2000) Finite elastoplasticity, Lie groups and geodesics on SL(d). Sonderforschungsbereich 404 Bericht 2000/26, University of Stuttgart
    • (2000) Finite Elastoplasticity
    • Mielke, A.1
  • 67
    • 4143067463 scopus 로고
    • On the controversy about grain boundary relaxation
    • Magalas LB, Gorczyca S (eds). Trans Tech Publications, Switzerland
    • Molinas BJ, Pavolo F (1993) On the controversy about grain boundary relaxation. In: Magalas LB, Gorczyca S (eds) Material Science Forum: Internal Friction and Ultrasonic Attenuation in Solids., volume 119-121, pp 39-48. Trans Tech Publications, Switzerland
    • (1993) Material Science Forum: Internal Friction and Ultrasonic Attenuation in Solids , vol.119-121 , pp. 39-48
    • Molinas, B.J.1    Pavolo, F.2
  • 68
  • 69
    • 34249963313 scopus 로고
    • A critical review of the state of finite plasticity
    • Naghdi PM (1990) A critical review of the state of finite plasticity. J. Appl. Math. Phys.(ZAMP) 41:315-394
    • (1990) J. Appl. Math. Phys.(ZAMP) , vol.41 , pp. 315-394
    • Naghdi, P.M.1
  • 72
    • 0038611831 scopus 로고    scopus 로고
    • Local existence and uniqueness for quasistatic finite plasticity with grain boundary relaxation
    • Neff P (2002) Local existence and uniqueness for quasistatic finite plasticity with grain boundary relaxation, submitted to SIAM J. Math. Anal.
    • (2002) SIAM J. Math. Anal.
    • Neff, P.1
  • 73
    • 0036993445 scopus 로고    scopus 로고
    • On Korn's first inequality with nonconstant coefficients
    • Preprint 2080 TU Darmstadt
    • Neff P (2002) On Korn's first inequality with nonconstant coefficients, Preprint 2080 TU Darmstadt. Proc. Roy. Soc. Edinb. 132A:221-243
    • (2002) Proc. Roy. Soc. Edinb. , vol.132 A , pp. 221-243
    • Neff, P.1
  • 76
    • 0033076749 scopus 로고    scopus 로고
    • Nonconvex energy minimization and dislocation structures in ductile single crystals
    • Ortiz M, Repetto EA (1999) Nonconvex energy minimization and dislocation structures in ductile single crystals. J. Mech. Phys. Solids 47:397-462
    • (1999) J. Mech. Phys. Solids , vol.47 , pp. 397-462
    • Ortiz, M.1    Repetto, E.A.2
  • 79
    • 0005607161 scopus 로고
    • Internal dissipation in solids for small cyclic strains
    • Wegel RL, Walter H (1935) Internal dissipation in solids for small cyclic strains. Physics 6:141-157
    • (1935) Physics , vol.6 , pp. 141-157
    • Wegel, R.L.1    Walter, H.2
  • 80
    • 0028516293 scopus 로고
    • Plasticity theory formulated in terms of physically based microstructrural variables - Part I
    • Rubin MB (1994) Plasticity theory formulated in terms of physically based microstructrural variables -Part I. Theory. Int. J. Solids Structures 31(19):2615-2634
    • (1994) Theory. Int. J. Solids Structures , vol.31 , Issue.19 , pp. 2615-2634
    • Rubin, M.B.1
  • 83
    • 0017416767 scopus 로고
    • On transformation laws for plastic deformations of materials with elastic range
    • Silhavy M (1976) On transformation laws for plastic deformations of materials with elastic range. Arch. Rat. Mech. Anal. 63:169-182
    • (1976) Arch. Rat. Mech. Anal. , vol.63 , pp. 169-182
    • Silhavy, M.1
  • 84
    • 70350313479 scopus 로고    scopus 로고
    • Numerical analysis and simulation of plasticity
    • Ciarlet PG, Lions JL (eds). Elsevier, Amsterdam
    • Simo JC (1998) Numerical analysis and simulation of plasticity. In: Ciarlet PG, Lions JL (eds) Handbook of Numerical Analysis, volume VI. Elsevier, Amsterdam
    • (1998) Handbook of Numerical Analysis , vol.6
    • Simo, J.C.1
  • 87
    • 0022076781 scopus 로고
    • A unified approach to finite deformation elastoplastic analysis based on the use of hyperelastic constitutive equations
    • Simo JC, Ortiz M (1985) A unified approach to finite deformation elastoplastic analysis based on the use of hyperelastic constitutive equations. Comp. Meth. Appl. Mech. Engrg. 49:221-245
    • (1985) Comp. Meth. Appl. Mech. Engrg. , vol.49 , pp. 221-245
    • Simo, J.C.1    Ortiz, M.2
  • 88
    • 0002640490 scopus 로고
    • A micropolar theory of finite deformation and finite rotation multiplicative elastoplasticity
    • Steinmann P (1993) A micropolar theory of finite deformation and finite rotation multiplicative elastoplasticity. Int. J. Solids Structures 31(8):1063-1084
    • (1993) Int. J. Solids Structures , vol.31 , Issue.8 , pp. 1063-1084
    • Steinmann, P.1
  • 89
    • 0030676139 scopus 로고    scopus 로고
    • A unifying treatise of variational principles for two types of micropolar continus
    • P Steinmann (1997) A unifying treatise of variational principles for two types of micropolar continus. Acta Mech. 121:215-232
    • (1997) Acta Mech. , vol.121 , pp. 215-232
    • Steinmann, P.1
  • 90
    • 0000522553 scopus 로고    scopus 로고
    • Views on multiplicative elastoplasticity and the continuum theory of dislocations
    • Steinmann P, (1996) Views on multiplicative elastoplasticity and the continuum theory of dislocations. Int. J. Engrg. Sci. 34:1717-1735
    • (1996) Int. J. Engrg. Sci. , vol.34 , pp. 1717-1735
    • Steinmann, P.1
  • 91
    • 0002565890 scopus 로고
    • The non-linear field theories of mechanics
    • Flügge S (ed). Springer, Heidelberg
    • Truesdell C, Noll W (1965) The non-linear field theories of mechanics. In: Flügge S (ed) Handbuch der Physik, volume III/3. Springer, Heidelberg
    • (1965) Handbuch der Physik , vol.3 , Issue.3
    • Truesdell, C.1    Noll, W.2
  • 95
    • 0347136738 scopus 로고
    • The behaviour of the lattice of polycrystalline iron in tension
    • Wood WA (1948) The behaviour of the lattice of polycrystalline iron in tension. Proc. Roy. Soc. London,A 192:218-231
    • (1948) Proc. Roy. Soc. London, A , vol.192 , pp. 218-231
    • Wood, W.A.1
  • 97
    • 0038272893 scopus 로고
    • Anelasticity of metals
    • Zener C (1946) Anelasticity of metals. Trans. A.I.M.E 167:155-191
    • (1946) Trans. A.I.M.E , vol.167 , pp. 155-191
    • Zener, C.1
  • 99
    • 0038272892 scopus 로고
    • Relaxation phenomena in metals
    • Zener C (1949) Relaxation phenomena in metals. Physica 15:111-118
    • (1949) Physica , vol.15 , pp. 111-118
    • Zener, C.1
  • 100
    • 0008872224 scopus 로고
    • Effect of cold work and annealing upon internal friction of alpha-brass
    • Zener C, Clarke H, Smith CS (1942) Effect of cold work and annealing upon internal friction of alpha-brass. Trans. A.I.M.E 147:90-103
    • (1942) Trans. A.I.M.E , vol.147 , pp. 90-103
    • Zener, C.1    Clarke, H.2    Smith, C.S.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.