메뉴 건너뛰기




Volumn 179, Issue 3-4, 1999, Pages 215-245

Numerical implementation of multiplicative elasto-plasticity into assumed strain elements with application to shells at large strains

Author keywords

Assumed strain method; Finite elasto plasticity; Shells

Indexed keywords

DEFORMATION; EIGENVALUES AND EIGENFUNCTIONS; ELASTOPLASTICITY; FINITE ELEMENT METHOD; MATHEMATICAL MODELS; MATHEMATICAL TRANSFORMATIONS; STRAIN; STRUCTURAL ANALYSIS; TENSORS;

EID: 0033312831     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0045-7825(99)00063-8     Document Type: Article
Times cited : (72)

References (57)
  • 1
    • 0030102317 scopus 로고    scopus 로고
    • A 4 node finite shell element for the implementation of general hyperelastic 3d elasticity at finite strains
    • Betsch P., Gruttmann F., Stein E. A 4 node finite shell element for the implementation of general hyperelastic 3d elasticity at finite strains. Comp. Meth. Appl. Mech. Engrg. 130:1996;57-79.
    • (1996) Comp. Meth. Appl. Mech. Engrg. , vol.130 , pp. 57-79
    • Betsch, P.1    Gruttmann, F.2    Stein, E.3
  • 2
    • 0032024870 scopus 로고    scopus 로고
    • On the parametrization of finite rotations in computational mechanics: A classification of concepts with application to smooth shells
    • Betsch P., Menzel A., Stein E. On the parametrization of finite rotations in computational mechanics: A classification of concepts with application to smooth shells. Comput. Methods Appl. Mech. Engrg. 155:1998;273-305.
    • (1998) Comput. Methods Appl. Mech. Engrg. , vol.155 , pp. 273-305
    • Betsch, P.1    Menzel, A.2    Stein, E.3
  • 3
    • 84989463351 scopus 로고
    • An assumed strain approach avoiding artificial thickness straining for a nonlinear 4 node shell element
    • Betsch P., Stein E. An assumed strain approach avoiding artificial thickness straining for a nonlinear 4 node shell element. Comm. Num. Meth. Engrg. 11:1995;899-909.
    • (1995) Comm. Num. Meth. Engrg. , vol.11 , pp. 899-909
    • Betsch, P.1    Stein, E.2
  • 4
    • 0001317365 scopus 로고    scopus 로고
    • A nonlinear extensible 4 node shell element based on continuum theory and assumed strain interpolations
    • Betsch P., Stein E. A nonlinear extensible 4 node shell element based on continuum theory and assumed strain interpolations. J. Nonlinear Sci. 6:1996;169-199.
    • (1996) J. Nonlinear Sci. , vol.6 , pp. 169-199
    • Betsch, P.1    Stein, E.2
  • 5
    • 0040239160 scopus 로고    scopus 로고
    • Derivation of the fourth-order tangent operator based on a generalized eigenvalue problem
    • to appear
    • P. Betsch, P. Steinmann, Derivation of the fourth-order tangent operator based on a generalized eigenvalue problem. Int. J. Solids Structures, to appear.
    • Int. J. Solids Structures
    • Betsch, P.1    Steinmann, P.2
  • 6
    • 0012122869 scopus 로고
    • Acceleration waves in inhomogeneous isotropic elastic bodies
    • Bowen R.M., Wang C.C. Acceleration waves in inhomogeneous isotropic elastic bodies. Arch. Rational Mech. Anal. 38:1970;13-45.
    • (1970) Arch. Rational Mech. Anal. , vol.38 , pp. 13-45
    • Bowen, R.M.1    Wang, C.C.2
  • 7
    • 0031076038 scopus 로고    scopus 로고
    • On large deformations of thin elasto-plastic shells: Implementation of a finite rotation model for quadrilateral shell element
    • Brank B., Peric D., Damjanic F.B. On large deformations of thin elasto-plastic shells: Implementation of a finite rotation model for quadrilateral shell element. J. Numer. Methods Engrg. 40:1997;689-726.
    • (1997) J. Numer. Methods Engrg. , vol.40 , pp. 689-726
    • Brank, B.1    Peric, D.2    Damjanic, F.B.3
  • 8
    • 0028483483 scopus 로고
    • Three-dimensional extension of non linear shell formulation based on the enhanced assumed strain concept
    • Büchter N., Ramm E., Roehl D. Three-dimensional extension of non linear shell formulation based on the enhanced assumed strain concept. Int. J. Numer. Methods Engrg. 37:1994;2551-2568.
    • (1994) Int. J. Numer. Methods Engrg. , vol.37 , pp. 2551-2568
    • Büchter, N.1    Ramm, E.2    Roehl, D.3
  • 9
    • 0003150111 scopus 로고
    • A theorem of tensor calculus and its application to isotropic elasticity
    • Chadwick P., Ogden R.W. A theorem of tensor calculus and its application to isotropic elasticity. Arch. Rational Mech. Anal. 44:1971;54-68.
    • (1971) Arch. Rational Mech. Anal. , vol.44 , pp. 54-68
    • Chadwick, P.1    Ogden, R.W.2
  • 11
    • 0026904029 scopus 로고
    • A material-independent method for extending stress update algorithms from small-strain plasticity to finite plasticity with multiplicative kinematics
    • Cuitino A., Ortiz M. A material-independent method for extending stress update algorithms from small-strain plasticity to finite plasticity with multiplicative kinematics. Engrg. Comp. 9:1992;437-451.
    • (1992) Engrg. Comp. , vol.9 , pp. 437-451
    • Cuitino, A.1    Ortiz, M.2
  • 12
    • 0021384182 scopus 로고
    • A continuum mechanics based four-node shell element for general nonlinear analysis
    • Dvorkin E.N., Bathe K.J. A continuum mechanics based four-node shell element for general nonlinear analysis. Eng. Comput. 1:1984;77-88.
    • (1984) Eng. Comput. , vol.1 , pp. 77-88
    • Dvorkin, E.N.1    Bathe, K.J.2
  • 13
    • 0029375860 scopus 로고
    • A formulation of the mitc4 shell element for finite strain elasto-plastic analysis
    • Dvorkin E.N., Pantuso D., Repetto E.A. A formulation of the mitc4 shell element for finite strain elasto-plastic analysis. Comp. Meth. Appl. Mech. Engrg. 125:1995;17-40.
    • (1995) Comp. Meth. Appl. Mech. Engrg. , vol.125 , pp. 17-40
    • Dvorkin, E.N.1    Pantuso, D.2    Repetto, E.A.3
  • 14
    • 0002118214 scopus 로고    scopus 로고
    • Finite element formulations of five and six parameter shell theories accounting for finite plastic strains
    • Barcelona, Spain
    • R. Eberlein, P. Wriggers, Finite element formulations of five and six parameter shell theories accounting for finite plastic strains, Conference on Computational Plasticity IV, Barcelona, Spain (1997) 1898-1903.
    • (1997) Conference on Computational Plasticity , vol.4 , pp. 1898-1903
    • Eberlein, R.1    Wriggers, P.2
  • 16
    • 0025497179 scopus 로고
    • A hyperelastic based large strain formulation with combined isotropic kinematic hardening using the logarithmic stress and strain measures
    • Eterovic A.L., Bathe K.J. A hyperelastic based large strain formulation with combined isotropic kinematic hardening using the logarithmic stress and strain measures. Int. J. Numer. Methods Engrg. 30:1990;1099-1114.
    • (1990) Int. J. Numer. Methods Engrg. , vol.30 , pp. 1099-1114
    • Eterovic, A.L.1    Bathe, K.J.2
  • 17
    • 0022239164 scopus 로고
    • On the concept of an intermediate configuration and its application to a representation of viscoelastic plastic material behavior
    • Haupt P. On the concept of an intermediate configuration and its application to a representation of viscoelastic plastic material behavior. Int. J. of Plasticity. 1:1985;303-316.
    • (1985) Int. J. of Plasticity , vol.1 , pp. 303-316
    • Haupt, P.1
  • 18
    • 0014923642 scopus 로고
    • Constitutive inequalities for isotropic elastic solids under finite strain
    • Hill R. Constitutive inequalities for isotropic elastic solids under finite strain. Proc. Roy. Soc. Lond. A 314:1970;457-472.
    • (1970) Proc. Roy. Soc. Lond. , vol.314 , pp. 457-472
    • Hill, R.1
  • 20
    • 0028541834 scopus 로고
    • Equivalent spatial and material descriptions of finite deformation elastoplasticity in principal axes
    • Ibrahimbegović A. Equivalent spatial and material descriptions of finite deformation elastoplasticity in principal axes. Int. J. Solids Structures. 31:1994;3027-3040.
    • (1994) Int. J. Solids Structures , vol.31 , pp. 3027-3040
    • Ibrahimbegović, A.1
  • 21
    • 0028753348 scopus 로고
    • Finite elastoplastic deformations of space-curved membranes
    • Ibrahimbegović A. Finite elastoplastic deformations of space-curved membranes. Comp. Meth. Appl. Mech. Engrg. 119:1994;371-394.
    • (1994) Comp. Meth. Appl. Mech. Engrg. , vol.119 , pp. 371-394
    • Ibrahimbegović, A.1
  • 22
    • 0022674479 scopus 로고
    • Normality rules in large-deformation plasticity
    • Lubliner J. Normality rules in large-deformation plasticity. Mech. Mater. 5:1986;29-34.
    • (1986) Mech. Mater. , vol.5 , pp. 29-34
    • Lubliner, J.1
  • 25
    • 0003232369 scopus 로고
    • plasticité classique et viscoplasticité
    • Springer, Berlin
    • J. Mandel. plasticité classique et viscoplasticité. CISM Courses and Lectures No. 97, Springer, Berlin, 1972.
    • (1972) CISM Courses and Lectures , vol.97
    • Mandel, J.1
  • 27
    • 0002696760 scopus 로고
    • Reduction of the symmetric eigenproblem Ax=λBx and related problems to standard form
    • Martin R.S., Wilkinson J.H. Reduction of the symmetric eigenproblem. Ax=λBx and related problems to standard form Numerische Mathematik. 11:1968;99-110.
    • (1968) Numerische Mathematik , vol.11 , pp. 99-110
    • Martin, R.S.1    Wilkinson, J.H.2
  • 29
    • 0027702707 scopus 로고
    • Computation of isotropic tensor functions
    • Miehe C. Computation of isotropic tensor functions. Comm. Num. Meth. Engrg. 9:1993;889-896.
    • (1993) Comm. Num. Meth. Engrg. , vol.9 , pp. 889-896
    • Miehe, C.1
  • 30
    • 0029488530 scopus 로고
    • A theory of large-strain isotropic thermoplasticity based on metric transformation tensors
    • Miehe C. A theory of large-strain isotropic thermoplasticity based on metric transformation tensors. Archive of Appl. Mech. 66:1995;45-64.
    • (1995) Archive of Appl. Mech. , vol.66 , pp. 45-64
    • Miehe, C.1
  • 31
    • 0032182779 scopus 로고    scopus 로고
    • A constitutive frame of elastoplasticity at large strains based on the notion of plastic metric
    • Miehe C. A constitutive frame of elastoplasticity at large strains based on the notion of plastic metric. Int. J. Solids Struct. 35:1998;3859-3897.
    • (1998) Int. J. Solids Struct. , vol.35 , pp. 3859-3897
    • Miehe, C.1
  • 32
    • 0032496867 scopus 로고    scopus 로고
    • A formulation of finite elastoplasticity based on dual co and contra variant eigenvector triads normalized with respect to a plastic metric
    • Miehe C. A formulation of finite elastoplasticity based on dual co and contra variant eigenvector triads normalized with respect to a plastic metric. Comp. Meth. Appl. Mech. Engrg. 159:1998;223-260.
    • (1998) Comp. Meth. Appl. Mech. Engrg. , vol.159 , pp. 223-260
    • Miehe, C.1
  • 33
    • 0032025970 scopus 로고    scopus 로고
    • A theoretical and computational model for isotropic elastoplastic stress analysis in shells at large strains
    • Miehe C. A theoretical and computational model for isotropic elastoplastic stress analysis in shells at large strains. Comp. Meth. Appl. Mech. Engrg. 155:1998;193-233.
    • (1998) Comp. Meth. Appl. Mech. Engrg. , vol.155 , pp. 193-233
    • Miehe, C.1
  • 34
    • 0003016302 scopus 로고
    • A canonical model of multiplicative elasto-plasticity: Formulation and aspects of the numerical implementation European Journal of Mechanics A, special issue
    • Miehe C., Stein E. A canonical model of multiplicative elasto-plasticity: Formulation and aspects of the numerical implementation European Journal of Mechanics A, special issue. 11. 1992;25-43.
    • (1992) 11 , pp. 25-43
    • Miehe, C.1    Stein, E.2
  • 35
    • 0000838996 scopus 로고
    • The theory of plates and shells
    • Springer, Berlin
    • P.M. Naghdi, The Theory of Plates and Shells, Handbuch der Physik, Band, VIa/2 Springer, Berlin, 1972 pp. 425-640.
    • (1972) Handbuch Der Physik, Band , vol.6 A , Issue.2 , pp. 425-640
    • Naghdi, P.M.1
  • 37
    • 0025838443 scopus 로고
    • An investigation of a finite rotation four node assumed strain shell element
    • Parisch H. An investigation of a finite rotation four node assumed strain shell element. Int. J. Numer. Meth. Engrg. 31:1991;127-150.
    • (1991) Int. J. Numer. Meth. Engrg. , vol.31 , pp. 127-150
    • Parisch, H.1
  • 38
    • 84987045177 scopus 로고
    • A continuum-based shell theory for non-linear applications
    • Parisch H. A continuum-based shell theory for non-linear applications. Int. J. Numer. Meth. Engrg. 38:1995;1855-1883.
    • (1995) Int. J. Numer. Meth. Engrg. , vol.38 , pp. 1855-1883
    • Parisch, H.1
  • 39
    • 0026626280 scopus 로고
    • A model for finite strain elasto plasticity based on logarithmic strains: Computational aspects
    • Peric D., Owen D.R.J., Honnor M.E. A model for finite strain elasto plasticity based on logarithmic strains: Computational aspects. Comp. Meth. Appl. Mech. Engrg. 94:1992;35-61.
    • (1992) Comp. Meth. Appl. Mech. Engrg. , vol.94 , pp. 35-61
    • Peric, D.1    Owen, D.R.J.2    Honnor, M.E.3
  • 40
    • 0029289617 scopus 로고
    • A finite element method for stability problems in finite elasticity
    • Reese S., Wriggers P. A finite element method for stability problems in finite elasticity. Int. J. Num. Meth. Engrg. 38:1995;1171-1200.
    • (1995) Int. J. Num. Meth. Engrg. , vol.38 , pp. 1171-1200
    • Reese, S.1    Wriggers, P.2
  • 41
    • 0030214836 scopus 로고    scopus 로고
    • Large elasto-plastic finite element analysis of solids and shells with the enhanced assumed strain formulation
    • Roehl D., Ramm E. Large elasto-plastic finite element analysis of solids and shells with the enhanced assumed strain formulation. Int. J. Solids Struct. 33:1996;3215-3237.
    • (1996) Int. J. Solids Struct. , vol.33 , pp. 3215-3237
    • Roehl, D.1    Ramm, E.2
  • 42
    • 0029277716 scopus 로고
    • A theory and finite element formulation of shells at finite deformations including thickness change: Circumventing the use of a rotation tensor
    • Sansour C. A theory and finite element formulation of shells at finite deformations including thickness change: Circumventing the use of a rotation tensor. Arch. Appl. Mech. 65:1995;194-216.
    • (1995) Arch. Appl. Mech. , vol.65 , pp. 194-216
    • Sansour, C.1
  • 43
    • 0022915154 scopus 로고    scopus 로고
    • Oberflächenorientierte Schalentheorien endlicher Verschiebungen
    • Schoop H. Oberflächenorientierte Schalentheorien endlicher Verschiebungen. Ingenieur Archiv. 56:1996;427-437.
    • (1996) Ingenieur Archiv , vol.56 , pp. 427-437
    • Schoop, H.1
  • 45
    • 0023964056 scopus 로고
    • A framework for finite strain elastoplasticity based on maximum plastic dissipation and the multiplicative decomposition: Part I. Continuum formulation
    • Simo J.C. A framework for finite strain elastoplasticity based on maximum plastic dissipation and the multiplicative decomposition: Part I. Continuum formulation. Comp. Meth. Appl. Mech. Engrg. 66:1988;199-219.
    • (1988) Comp. Meth. Appl. Mech. Engrg. , vol.66 , pp. 199-219
    • Simo, J.C.1
  • 46
    • 0026910667 scopus 로고
    • Algorithms for static and dynamic multiplicative plasticity that preserve the classical return mapping schemes of the infinitesimal theory
    • Simo J.C. Algorithms for static and dynamic multiplicative plasticity that preserve the classical return mapping schemes of the infinitesimal theory. Comp. Meth. Appl. Mech. Engrg. 99:1992;61-112.
    • (1992) Comp. Meth. Appl. Mech. Engrg. , vol.99 , pp. 61-112
    • Simo, J.C.1
  • 47
    • 0026867998 scopus 로고
    • Geometrically nonlinear enhanced strain mixed methods and the method of incompatible modes
    • Simo J.C., Armero F. Geometrically nonlinear enhanced strain mixed methods and the method of incompatible modes. Int. J. Num. Meth. Engrg. 33:1992;1413-1449.
    • (1992) Int. J. Num. Meth. Engrg. , vol.33 , pp. 1413-1449
    • Simo, J.C.1    Armero, F.2
  • 48
    • 0022676227 scopus 로고
    • On the variational foundations of assumed strain methods
    • Simo J.C., Hughes T.J.R. On the variational foundations of assumed strain methods. J. Appl. Mech. 53:1986;51-54.
    • (1986) J. Appl. Mech. , vol.53 , pp. 51-54
    • Simo, J.C.1    Hughes, T.J.R.2
  • 50
    • 0026852491 scopus 로고
    • On a stress resultant geometrically exact shell model. Part V: Formulation and integration algorithms
    • Simo J.C., Kennedy J.G. On a stress resultant geometrically exact shell model. Part V: Formulation and integration algorithms. Comp. Meth. Appl. Mech. Engrg. 96:1992;133-171.
    • (1992) Comp. Meth. Appl. Mech. Engrg. , vol.96 , pp. 133-171
    • Simo, J.C.1    Kennedy, J.G.2
  • 51
    • 0026898028 scopus 로고
    • Associative coupled thermoplasticity at finite strains: Formulation numerical analysis and implementation
    • Simo J.C., Miehe C. Associative coupled thermoplasticity at finite strains: Formulation numerical analysis and implementation. Comp. Meth. Appl. Mech. Engrg. 98:1992;41-104.
    • (1992) Comp. Meth. Appl. Mech. Engrg. , vol.98 , pp. 41-104
    • Simo, J.C.1    Miehe, C.2
  • 52
    • 0025457448 scopus 로고
    • On a stress resultant geometrically exact shell model. Part IV: Variable thickness shells with through-the-thickness stretching
    • Simo J.C., Rifai M.S., Fox D.D. On a stress resultant geometrically exact shell model. Part IV: Variable thickness shells with through-the-thickness stretching. Comp. Meth. Appl. Mech. Engrg. 81:1990;91-126.
    • (1990) Comp. Meth. Appl. Mech. Engrg. , vol.81 , pp. 91-126
    • Simo, J.C.1    Rifai, M.S.2    Fox, D.D.3
  • 53
    • 0026103678 scopus 로고
    • Quasi-incompressible finite elasticity in principal stretches. Continuum basis and numerical algorithms
    • Simo J.C., Taylor R.L. Quasi-incompressible finite elasticity in principal stretches. Continuum basis and numerical algorithms. Comp. Meth. Appl. Mech. Engrg. 85:1991;273-310.
    • (1991) Comp. Meth. Appl. Mech. Engrg. , vol.85 , pp. 273-310
    • Simo, J.C.1    Taylor, R.L.2
  • 54
    • 0031554852 scopus 로고    scopus 로고
    • An efficient formulation of integration algorithms for elastoplastic shell analysis based on layered finite element approach
    • Soric J., Montag U., Krätzig W.B. An efficient formulation of integration algorithms for elastoplastic shell analysis based on layered finite element approach. Comp. Meth. Appl. Mech. Engrg. 148:1997;315-328.
    • (1997) Comp. Meth. Appl. Mech. Engrg. , vol.148 , pp. 315-328
    • Soric, J.1    Montag, U.2    Krätzig, W.B.3
  • 55
    • 0000521689 scopus 로고
    • General and exact theory of waves in finite elastic strain
    • Truesdell C. General and exact theory of waves in finite elastic strain. Arch. Rational Mech. Anal. 8:1961;263-296.
    • (1961) Arch. Rational Mech. Anal. , vol.8 , pp. 263-296
    • Truesdell, C.1
  • 56
    • 0025401322 scopus 로고
    • Finite deformation constitutive equations and a time integration procedure for isotropic, hyperelastic-viscoplastic solids
    • Weber G., Anand L. Finite deformation constitutive equations and a time integration procedure for isotropic, hyperelastic-viscoplastic solids. Comp. Meth. Appl. Mech. Engrg. 79:1990;173-202.
    • (1990) Comp. Meth. Appl. Mech. Engrg. , vol.79 , pp. 173-202
    • Weber, G.1    Anand, L.2
  • 57
    • 0030215974 scopus 로고    scopus 로고
    • A comparison of three-dimensional continuum and shell elements for finite plasticity
    • Wriggers P., Eberlein R., Reese S. A comparison of three-dimensional continuum and shell elements for finite plasticity. Int. J. Solids Structures. 33:1996;3309-3326.
    • (1996) Int. J. Solids Structures , vol.33 , pp. 3309-3326
    • Wriggers, P.1    Eberlein, R.2    Reese, S.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.