메뉴 건너뛰기




Volumn 196, Issue 37-40 SPEC. ISS., 2007, Pages 3881-3897

A discontinuous Galerkin formulation for classical and gradient plasticity - Part 1: Formulation and analysis

Author keywords

Convergence; Discontinuous Galerkin; Elastoplasticity; Gradient plasticity; Variational inequality

Indexed keywords

ELASTOPLASTICITY; ERROR ANALYSIS; GALERKIN METHODS; LAPLACE EQUATION;

EID: 34447103174     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cma.2006.10.045     Document Type: Article
Times cited : (73)

References (28)
  • 3
    • 0021502102 scopus 로고
    • On the microstructural origin of certain inelastic models
    • Aifantis E.C. On the microstructural origin of certain inelastic models. J. Engrg. Mater. Technol. 106 (1984) 326-330
    • (1984) J. Engrg. Mater. Technol. , vol.106 , pp. 326-330
    • Aifantis, E.C.1
  • 4
    • 0023174893 scopus 로고
    • The physics of plastic deformation
    • Aifantis E.C. The physics of plastic deformation. Int. J. Plasticity 3 (1987) 211-247
    • (1987) Int. J. Plasticity , vol.3 , pp. 211-247
    • Aifantis, E.C.1
  • 5
    • 44949281328 scopus 로고
    • A variational principle for gradient plasticity
    • Mühlhaus H.-B., and Aifantis E. A variational principle for gradient plasticity. Int. J. Solids Struct. 28 7 (1991) 845-857
    • (1991) Int. J. Solids Struct. , vol.28 , Issue.7 , pp. 845-857
    • Mühlhaus, H.-B.1    Aifantis, E.2
  • 6
    • 0026908533 scopus 로고
    • Gradient-dependent plasticity: formulation and algorithmic aspects
    • de Borst R., and Mühlhaus H.-B. Gradient-dependent plasticity: formulation and algorithmic aspects. Int. J. Numer. Methods Engrg. 35 (1992) 521-539
    • (1992) Int. J. Numer. Methods Engrg. , vol.35 , pp. 521-539
    • de Borst, R.1    Mühlhaus, H.-B.2
  • 8
    • 0033888582 scopus 로고    scopus 로고
    • Computational mechanics at the mesoscale
    • Needleman A. Computational mechanics at the mesoscale. Acta Mater. 48 (2000) 105-124
    • (2000) Acta Mater. , vol.48 , pp. 105-124
    • Needleman, A.1
  • 9
    • 4544279140 scopus 로고    scopus 로고
    • A gradient theory of small-deformation isotropic plasticity that accounts for the burgers vector and for dissipation due to plastic spin
    • Gurtin M.E. A gradient theory of small-deformation isotropic plasticity that accounts for the burgers vector and for dissipation due to plastic spin. J. Mech. Phys. Solids 52 (2004) 2545-2568
    • (2004) J. Mech. Phys. Solids , vol.52 , pp. 2545-2568
    • Gurtin, M.E.1
  • 10
    • 1642633214 scopus 로고    scopus 로고
    • A unified treatment of strain gradient plasticity
    • Gudmundson P. A unified treatment of strain gradient plasticity. J. Mech. Phys. Solids 52 (2004) 1379-1406
    • (2004) J. Mech. Phys. Solids , vol.52 , pp. 1379-1406
    • Gudmundson, P.1
  • 11
    • 0032479690 scopus 로고    scopus 로고
    • An algorithm for gradient-regularized plasticity coupled to damage based on a dual mixed fe-formulation
    • Svedberg T., and Runesson K. An algorithm for gradient-regularized plasticity coupled to damage based on a dual mixed fe-formulation. Comput. Methods Appl. Mech. Engrg. 161 (1998) 49-65
    • (1998) Comput. Methods Appl. Mech. Engrg. , vol.161 , pp. 49-65
    • Svedberg, T.1    Runesson, K.2
  • 12
    • 0035975245 scopus 로고    scopus 로고
    • Theory and numerics of a thermodynamically consistent framework for geometrically linear gradient plasticity
    • Liebe T., and Steinmann P. Theory and numerics of a thermodynamically consistent framework for geometrically linear gradient plasticity. Int. J. Numer. Methods Eng. 51 (2001) 1437-1467
    • (2001) Int. J. Numer. Methods Eng. , vol.51 , pp. 1437-1467
    • Liebe, T.1    Steinmann, P.2
  • 13
    • 0038018660 scopus 로고    scopus 로고
    • Theory and numerics of geometrically non-linear gradient plasticity
    • Liebe T., Menzel A., and Steinmann P. Theory and numerics of geometrically non-linear gradient plasticity. Int. J. Engrg. Sci. 41 (2003) 1603-1629
    • (2003) Int. J. Engrg. Sci. , vol.41 , pp. 1603-1629
    • Liebe, T.1    Menzel, A.2    Steinmann, P.3
  • 14
    • 84951671794 scopus 로고
    • Über ein Variationspringzip zur Lösung von Dirichlet-problemen bei Verwendung von Teilräumen, die keinen Randbedingungen unterworfen sind
    • Nitsche J.A. Über ein Variationspringzip zur Lösung von Dirichlet-problemen bei Verwendung von Teilräumen, die keinen Randbedingungen unterworfen sind. Abhandlungen der mathematischer Seminar der Universität Hamburg 36 (1971) 9-15
    • (1971) Abhandlungen der mathematischer Seminar der Universität Hamburg , vol.36 , pp. 9-15
    • Nitsche, J.A.1
  • 15
    • 0001163226 scopus 로고
    • An interior penalty finite element method with discontinuous elements
    • Arnold D.N. An interior penalty finite element method with discontinuous elements. SIAM J. Numer. Anal. 19 (1982) 742-760
    • (1982) SIAM J. Numer. Anal. , vol.19 , pp. 742-760
    • Arnold, D.N.1
  • 17
    • 34447098958 scopus 로고    scopus 로고
    • B. Rivière, M.F. Wheeler, Optimal error estimates for discontinuous Galerkin methods applied to linear elasticity problems, Technical Report 00-30, Texas Institute for Computational and Applied Mathematics.
  • 18
    • 0000802762 scopus 로고
    • An elliptic collocation-finite element method with interior penalty
    • Wheeler M.F. An elliptic collocation-finite element method with interior penalty. SIAM J. Numer. Anal. 15 (1978) 152-161
    • (1978) SIAM J. Numer. Anal. , vol.15 , pp. 152-161
    • Wheeler, M.F.1
  • 19
    • 3142713775 scopus 로고    scopus 로고
    • A discontinuous Galerkin formulation for a strain gradient-dependent damage model
    • Wells G.N., Garikipati K., and Molari L. A discontinuous Galerkin formulation for a strain gradient-dependent damage model. Comput. Methods Appl. Mech. Engrg. 193 (2004) 3633-3645
    • (2004) Comput. Methods Appl. Mech. Engrg. , vol.193 , pp. 3633-3645
    • Wells, G.N.1    Garikipati, K.2    Molari, L.3
  • 20
    • 30944446864 scopus 로고    scopus 로고
    • A discontinuous Galerkin method for strain gradient-dependent damage: study of interpolations and convergence
    • Molari L., Wells G.N., Garikipati K., and Ubertini F. A discontinuous Galerkin method for strain gradient-dependent damage: study of interpolations and convergence. Comput. Methods Appl. Mech. Engrg. 195 (2006) 1480-1498
    • (2006) Comput. Methods Appl. Mech. Engrg. , vol.195 , pp. 1480-1498
    • Molari, L.1    Wells, G.N.2    Garikipati, K.3    Ubertini, F.4
  • 21
    • 0037025251 scopus 로고    scopus 로고
    • Continuous/discontinuous finite element approximations of fourth-order elliptic problems in structural and continuum mechanics with applications to thin beams and plates, and strain gradient elasticity
    • Engel G., Garikipati K., Hughes T.J.R., Larson M.G., Mazzei L., and Taylor R.L. Continuous/discontinuous finite element approximations of fourth-order elliptic problems in structural and continuum mechanics with applications to thin beams and plates, and strain gradient elasticity. Comput. Methods Appl. Mech. Engrg. 191 (2002) 3669-3750
    • (2002) Comput. Methods Appl. Mech. Engrg. , vol.191 , pp. 3669-3750
    • Engel, G.1    Garikipati, K.2    Hughes, T.J.R.3    Larson, M.G.4    Mazzei, L.5    Taylor, R.L.6
  • 22
    • 34447108132 scopus 로고    scopus 로고
    • J.K. Djoko, F. Ebobisse, A.T. McBride, B.D. Reddy, A discontinuous Galerkin formulation for classical and gradient plasticity. Part 2: Solution algorithms and numerical examples, submitted for publication.
  • 23
    • 0343337643 scopus 로고    scopus 로고
    • On the plasticity of single crystals: free energy, microforces, plastic strain gradients
    • Gurtin M.E. On the plasticity of single crystals: free energy, microforces, plastic strain gradients. J. Mech. Phys. Solids 48 (2000) 989-1036
    • (2000) J. Mech. Phys. Solids , vol.48 , pp. 989-1036
    • Gurtin, M.E.1
  • 24
    • 0036131798 scopus 로고    scopus 로고
    • A gradient theory of single-crystal viscoplasticty that accounts for geometrically necessary dislocations
    • Gurtin M.E. A gradient theory of single-crystal viscoplasticty that accounts for geometrically necessary dislocations. J. Mech. Phys. Solids 50 (2002) 5-32
    • (2002) J. Mech. Phys. Solids , vol.50 , pp. 5-32
    • Gurtin, M.E.1
  • 25
    • 0030494614 scopus 로고    scopus 로고
    • Errors of finite element method for perfectly elastoplastic problems
    • Repin S. Errors of finite element method for perfectly elastoplastic problems. Math. Mod. Meth. Appl. Sci. 6 (1996) 587-604
    • (1996) Math. Mod. Meth. Appl. Sci. , vol.6 , pp. 587-604
    • Repin, S.1
  • 26
    • 0036410391 scopus 로고    scopus 로고
    • Unified analysis of discontinuous Galerkin methods for elliptic problems
    • Arnold D.N., Brezzi F., Cockburn B., and Marini L.D. Unified analysis of discontinuous Galerkin methods for elliptic problems. SIAM J. Numer. Anal. 39 (2002) 1749-1779
    • (2002) SIAM J. Numer. Anal. , vol.39 , pp. 1749-1779
    • Arnold, D.N.1    Brezzi, F.2    Cockburn, B.3    Marini, L.D.4


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.