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Volumn 67, Issue 3, 2006, Pages 400-416

Implicit gradient elasticity

Author keywords

0 continuity; Gradient elasticity; Higher order continuum; Mixed formulation; Singularity

Indexed keywords

APPROXIMATION THEORY; FINITE ELEMENT METHOD; INTERPOLATION; MATHEMATICAL MODELS;

EID: 33746171292     PISSN: 00295981     EISSN: 10970207     Source Type: Journal    
DOI: 10.1002/nme.1640     Document Type: Article
Times cited : (62)

References (48)
  • 6
    • 0022891455 scopus 로고
    • A gradient approach to localization of deformation. I. Hyperelastic materials
    • Triantafyllidis N, Aifantis EC. A gradient approach to localization of deformation. I. Hyperelastic materials. Journal of Elasticity 1986; 16:225-237.
    • (1986) Journal of Elasticity , vol.16 , pp. 225-237
    • Triantafyllidis, N.1    Aifantis, E.C.2
  • 8
    • 0002471276 scopus 로고
    • A simple approach to solve boundary-value problems in gradient elasticity
    • Ru CQ, Aifantis EC. A simple approach to solve boundary-value problems in gradient elasticity. Acta Mechanica 1993; 101:59-68.
    • (1993) Acta Mechanica , vol.101 , pp. 59-68
    • Ru, C.Q.1    Aifantis, E.C.2
  • 11
    • 0002611817 scopus 로고    scopus 로고
    • On gradient regularization for numerical analysis in the presence of damage
    • de Borst R, van der Giessen E (eds), Chapter 26. Wiley: New York
    • Comi C, Driemeier L. On gradient regularization for numerical analysis in the presence of damage. In Material Instabilities in Solids, de Borst R, van der Giessen E (eds), Chapter 26. Wiley: New York, 1998; 425-440.
    • (1998) Material Instabilities in Solids , pp. 425-440
    • Comi, C.1    Driemeier, L.2
  • 12
    • 0342921375 scopus 로고
    • Continuum model of dispersion caused by an inherent material characteristic length
    • Rubin MB, Rosenau P, Gottlieb O. Continuum model of dispersion caused by an inherent material characteristic length. Journal of Applied Physics 1995; 77:4054-4063.
    • (1995) Journal of Applied Physics , vol.77 , pp. 4054-4063
    • Rubin, M.B.1    Rosenau, P.2    Gottlieb, O.3
  • 13
    • 0000258643 scopus 로고    scopus 로고
    • A dispersive model for wave propagation in periodic heterogeneous media based on homogenization with multiple spatial and temporal scales
    • Chen W, Fish J. A dispersive model for wave propagation in periodic heterogeneous media based on homogenization with multiple spatial and temporal scales. Journal of Applied Mechanics (ASME) 2001; 68:153-161.
    • (2001) Journal of Applied Mechanics (ASME) , vol.68 , pp. 153-161
    • Chen, W.1    Fish, J.2
  • 14
    • 0012686118 scopus 로고    scopus 로고
    • One-dimensional dynamically consistent gradient elasticity models derived from a discrete microstructure. Part 1: Generic formulation
    • Metrikine A, Askes H. One-dimensional dynamically consistent gradient elasticity models derived from a discrete microstructure. Part 1: generic formulation. European Journal of Mechanics A/Solids 2002; 21:555-572.
    • (2002) European Journal of Mechanics A/Solids , vol.21 , pp. 555-572
    • Metrikine, A.1    Askes, H.2
  • 15
    • 0012716579 scopus 로고    scopus 로고
    • One-dimensional dynamically consistent gradient elasticity models derived from a discrete microstructure. Part 2: Static and dynamic response
    • Askes H, Metrikine A. One-dimensional dynamically consistent gradient elasticity models derived from a discrete microstructure. Part 2: static and dynamic response. European Journal of Mechanics A/Solids 2002; 21:573-588.
    • (2002) European Journal of Mechanics A/Solids , vol.21 , pp. 573-588
    • Askes, H.1    Metrikine, A.2
  • 16
    • 0032155920 scopus 로고    scopus 로고
    • Finite element implementation of gradient plasticity models. Part I: Gradient-dependent yield functions
    • Ramaswamy S, Aravas N. Finite element implementation of gradient plasticity models. Part I: gradient-dependent yield functions. Computer Methods in Applied Mechanics and Engineering 1998; 163:11-32.
    • (1998) Computer Methods in Applied Mechanics and Engineering , vol.163 , pp. 11-32
    • Ramaswamy, S.1    Aravas, N.2
  • 17
    • 0032154076 scopus 로고    scopus 로고
    • Finite element implementation of gradient plasticity models. Part II: Gradient-dependent evolution equations
    • Ramaswamy S, Aravas N. Finite element implementation of gradient plasticity models. Part II: gradient-dependent evolution equations. Computer Methods in Applied Mechanics and Engineering 1998; 163:33-53.
    • (1998) Computer Methods in Applied Mechanics and Engineering , vol.163 , pp. 33-53
    • Ramaswamy, S.1    Aravas, N.2
  • 18
    • 0035975245 scopus 로고    scopus 로고
    • Theory and numerics of a thermodynamically consistent framework for geometrically linear gradient plasticity
    • Liebe T, Steinmann P. Theory and numerics of a thermodynamically consistent framework for geometrically linear gradient plasticity. International Journal for Numerical Methods in Engineering 2001; 51:1437-1467.
    • (2001) International Journal for Numerical Methods in Engineering , vol.51 , pp. 1437-1467
    • Liebe, T.1    Steinmann, P.2
  • 19
    • 0035850693 scopus 로고    scopus 로고
    • Theoretical and computational aspects of a thermodynamically consistent framework for geometrically linear gradient damage
    • Liebe T, Steinmann P, Benallal A. Theoretical and computational aspects of a thermodynamically consistent framework for geometrically linear gradient damage. Computer Methods in Applied Mechanics and Engineering 2001; 190:6555-6576.
    • (2001) Computer Methods in Applied Mechanics and Engineering , vol.190 , pp. 6555-6576
    • Liebe, T.1    Steinmann, P.2    Benallal, A.3
  • 20
    • 0034298706 scopus 로고    scopus 로고
    • Dispersion analysis and element-free Galerkin solutions of second and fourth-order gradient-enhanced damage models
    • Askes H, Pamin J, de Borst R. Dispersion analysis and element-free Galerkin solutions of second and fourth-order gradient-enhanced damage models. International Journal for Numerical Methods in Engineering 2000; 49:811-832.
    • (2000) International Journal for Numerical Methods in Engineering , vol.49 , pp. 811-832
    • Askes, H.1    Pamin, J.2    de Borst, R.3
  • 21
    • 0036822265 scopus 로고    scopus 로고
    • Numerical modeling of size effects with gradient elasticity - Formulation, meshless discretization and examples
    • Askes H, Aifantis EC. Numerical modeling of size effects with gradient elasticity - formulation, meshless discretization and examples. International Journal of Fracture 2002; 117:347-358.
    • (2002) International Journal of Fracture , vol.117 , pp. 347-358
    • Askes, H.1    Aifantis, E.C.2
  • 23
    • 0242285511 scopus 로고    scopus 로고
    • Analysis of materials with strain-gradient effects: A Meshless Local Petrov Galerkin (MLPG) approach, with nodel displacements only
    • Tang Z, Shen S, Atluri SN. Analysis of materials with strain-gradient effects: a Meshless Local Petrov Galerkin (MLPG) approach, with nodel displacements only. Computer Models in Engineering Science 2003; 4:177-196.
    • (2003) Computer Models in Engineering Science , vol.4 , pp. 177-196
    • Tang, Z.1    Shen, S.2    Atluri, S.N.3
  • 31
    • 8644290775 scopus 로고    scopus 로고
    • Multi-scale second-order computational homogenization of multi-phase materials: A nested finite element solution strategy
    • Kouznetsova VG, Geers MGD, Brekelmans WAM. Multi-scale second-order computational homogenization of multi-phase materials: a nested finite element solution strategy. Computer Methods in Applied Mechanics and Engineering 2004; 193:5525-5550.
    • (2004) Computer Methods in Applied Mechanics and Engineering , vol.193 , pp. 5525-5550
    • Kouznetsova, V.G.1    Geers, M.G.D.2    Brekelmans, W.A.M.3
  • 32
    • 0038746383 scopus 로고    scopus 로고
    • A two-dimensional finite element implementation of a special form of gradient elasticity
    • Tenek LT, Aifantis EC. A two-dimensional finite element implementation of a special form of gradient elasticity. Computer Models in Engineering Science 2002; 3:731-741.
    • (2002) Computer Models in Engineering Science , vol.3 , pp. 731-741
    • Tenek, L.T.1    Aifantis, E.C.2
  • 36
    • 0029357270 scopus 로고
    • Second-gradient constitutive theory for granular material with random packing structure
    • Chang CS, Gao J. Second-gradient constitutive theory for granular material with random packing structure. International Journal of Solids and Structures 1995; 32:2279-2293.
    • (1995) International Journal of Solids and Structures , vol.32 , pp. 2279-2293
    • Chang, C.S.1    Gao, J.2
  • 37
    • 0030208823 scopus 로고    scopus 로고
    • Dispersion and wave propagation in discrete and continuous models for granular materials
    • Mühlhaus H-B, Oka F. Dispersion and wave propagation in discrete and continuous models for granular materials. International Journal of Solids and Structures 1996; 33:271-283.
    • (1996) International Journal of Solids and Structures , vol.33 , pp. 271-283
    • Mühlhaus, H.-B.1    Oka, F.2
  • 38
    • 5644294661 scopus 로고    scopus 로고
    • Higher-order continua derived from discrete media: Continualisation aspects and boundary conditions
    • Askes H, Metrikine A. Higher-order continua derived from discrete media: continualisation aspects and boundary conditions. International Journal of Solids and Structures 2005; 42:187-202.
    • (2005) International Journal of Solids and Structures , vol.42 , pp. 187-202
    • Askes, H.1    Metrikine, A.2
  • 39
    • 0036542176 scopus 로고    scopus 로고
    • A classification of higher-order strain gradient models - Linear analysis
    • Askes H, Suiker ASJ, Sluys LJ. A classification of higher-order strain gradient models - linear analysis. Archive of Applied Mechanics 2002; 72:171-188.
    • (2002) Archive of Applied Mechanics , vol.72 , pp. 171-188
    • Askes, H.1    Suiker, A.S.J.2    Sluys, L.J.3
  • 40
    • 0034320847 scopus 로고    scopus 로고
    • Strain gradient elasticity theory for antiplane shear cracks. Part I: Oscillatory displacements
    • Unger DJ, Aifantis EC. Strain gradient elasticity theory for antiplane shear cracks. Part I: oscillatory displacements. Theoretical and Applied Fracture Mechanics 2000; 34:243-252.
    • (2000) Theoretical and Applied Fracture Mechanics , vol.34 , pp. 243-252
    • Unger, D.J.1    Aifantis, E.C.2
  • 41
    • 0034324258 scopus 로고    scopus 로고
    • Strain gradient elasticity theory for antiplane shear cracks. Part II: Monotonic displacements
    • Unger DJ, Aifantis EC. Strain gradient elasticity theory for antiplane shear cracks. Part II: monotonic displacements. Theoretical and Applied Fracture Mechanics 2000; 34:253-265.
    • (2000) Theoretical and Applied Fracture Mechanics , vol.34 , pp. 253-265
    • Unger, D.J.1    Aifantis, E.C.2
  • 42
  • 43
    • 0033524546 scopus 로고    scopus 로고
    • Dislocations in the theory of gradient elasticity
    • Gutkin MY, Aifantis EC. Dislocations in the theory of gradient elasticity. Scripta Materialia 1999; 40:559-566.
    • (1999) Scripta Materialia , vol.40 , pp. 559-566
    • Gutkin, M.Y.1    Aifantis, E.C.2
  • 44
    • 0002333071 scopus 로고    scopus 로고
    • Nanoscopics of dislocations and disclinations in gradient elasticity
    • Also available at
    • Gutkin MY. Nanoscopics of dislocations and disclinations in gradient elasticity. Reviews on Advanced Materials Science 2000; 1:27-60. Also available at http://www.ipme.ru.
    • (2000) Reviews on Advanced Materials Science , vol.1 , pp. 27-60
    • Gutkin, M.Y.1
  • 46
  • 48
    • 0035827386 scopus 로고    scopus 로고
    • Modelling of localisation and scale effect in thick-walled cylinders with gradient elastoplasticity
    • Zervos A, Papanastasiou P, Vardoulakis I. Modelling of localisation and scale effect in thick-walled cylinders with gradient elastoplasticity. International Journal of Solids and Structures 2001; 38:5081-5095.
    • (2001) International Journal of Solids and Structures , vol.38 , pp. 5081-5095
    • Zervos, A.1    Papanastasiou, P.2    Vardoulakis, I.3


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