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Volumn 135, Issue 3, 2009, Pages 203-213

Two finite-element discretizations for gradient elasticity

Author keywords

Elastic analysis; Finite element method; Microstructures; Numerical models

Indexed keywords

BENCHMARKING; COMPUTATIONAL EFFICIENCY; DIFFERENTIAL EQUATIONS; ELASTICITY; ELASTOHYDRODYNAMICS; INTERPOLATION; MICROSTRUCTURE; NUMERICAL METHODS;

EID: 60649103606     PISSN: 07339399     EISSN: None     Source Type: Journal    
DOI: 10.1061/(ASCE)0733-9399(2009)135:3(203)     Document Type: Article
Times cited : (92)

References (29)
  • 1
    • 0021502102 scopus 로고
    • "On the microstructural origin of certain inelastic models"
    • JEMTA80094-4289
    • Aifantis, E. (1984). "On the microstructural origin of certain inelastic models." J. Eng. Mater. Technol. JEMTA80094-4289, 106(4), 326-330.
    • (1984) J. Eng. Mater. Technol. , vol.106 , Issue.4 , pp. 326-330
    • Aifantis, E.1
  • 2
    • 0036471631 scopus 로고    scopus 로고
    • "Mixed finite element formulations of strain-gradient elasticity problems"
    • CMMECC0045-7825
    • Amanatidou, E., and Aravas, N. (2002). "Mixed finite element formulations of strain-gradient elasticity problems." Comput. Methods Appl. Mech. Eng. CMMECC0045-7825, 191(15), 1723-1751.
    • (2002) Comput. Methods Appl. Mech. Eng. , vol.191 , Issue.15 , pp. 1723-1751
    • Amanatidou, E.1    Aravas, N.2
  • 3
    • 0001558920 scopus 로고
    • "The tuba family of plate elements for the matrix displacement method"
    • AENJAK0001-9240
    • Argyris, J. H., Fried, I., and Scharpf, D. W. (1968). "The tuba family of plate elements for the matrix displacement method." Aeronaut. J. AENJAK0001-9240, 72, 701-709.
    • (1968) Aeronaut. J. , vol.72 , pp. 701-709
    • Argyris, J.H.1    Fried, I.2    Scharpf, D.W.3
  • 4
    • 0036822265 scopus 로고    scopus 로고
    • "Numerical modelling of size effects with gradient elasticity-Formulation, meshless discretization and examples"
    • IJFRAP0376-9429
    • Askes, H., and Aifantis, E. C. (2002). "Numerical modelling of size effects with gradient elasticity-Formulation, meshless discretization and examples." Int. J. Fract. IJFRAP0376-9429, 117(4), 347-358.
    • (2002) Int. J. Fract. , vol.117 , Issue.4 , pp. 347-358
    • Askes, H.1    Aifantis, E.C.2
  • 5
    • 33746171292 scopus 로고    scopus 로고
    • "Implicit gradient elasticity"
    • IJNMBH0029-598110.1002/nme.1640
    • Askes, H., and Gutierrez, M. (2006). "Implicit gradient elasticity." Int. J. Numer. Methods Eng. IJNMBH0029-598110.1002/ nme.1640, 67(3), 400-416.
    • (2006) Int. J. Numer. Methods Eng. , vol.67 , Issue.3 , pp. 400-416
    • Askes, H.1    Gutierrez, M.2
  • 6
    • 0038552978 scopus 로고
    • "The generation of inter-element-compatible stiffness and mass matrices by the use of interpolation formulas"
    • Air Force Institute of Technology, Wright-Patterson AF Base, Ohio
    • Bogner, F. K., Fox, R. L., and Schmit, L. A. (1965). "The generation of inter-element-compatible stiffness and mass matrices by the use of interpolation formulas." Proc., Conf. on Matrix Methods in Structural Mechanics, Air Force Institute of Technology, Wright-Patterson AF Base, Ohio, 397-443.
    • (1965) Proc., Conf. on Matrix Methods in Structural Mechanics , pp. 397-443
    • Bogner, F.K.1    Fox, R.L.2    Schmit, L.A.3
  • 8
    • 0025469891 scopus 로고
    • "A higher-order triangular plate bending element revisited"
    • IJNMBH0029-598110.1002/nme.1620300303
    • Dasgupta, S., and Sengupta, D. (1990). "A higher-order triangular plate bending element revisited." Int. J. Numer. Methods Eng. IJNMBH0029-598110.1002/nme.1620300303, 30(3), 419-430.
    • (1990) Int. J. Numer. Methods Eng. , vol.30 , Issue.3 , pp. 419-430
    • Dasgupta, S.1    Sengupta, D.2
  • 9
    • 0026908533 scopus 로고
    • "Gradient-dependent plasticity: Formulation and algorithmic aspects"
    • IJNMBH0029-598110.1002/nme.1620350307
    • de Borst, R., and Mühlhaus, H.-B. (1992). "Gradient-dependent plasticity: Formulation and algorithmic aspects." Int. J. Numer. Methods Eng. IJNMBH0029-598110.1002/nme.1620350307, 35(3), 521-539.
    • (1992) Int. J. Numer. Methods Eng. , vol.35 , Issue.3 , pp. 521-539
    • de Borst, R.1    Mühlhaus, H.-B.2
  • 10
    • 50549221753 scopus 로고
    • "Nonlinear theory of simple microelastic solid-I"
    • IJESAN0020-722510.1016/0020-7225(64)90004-7
    • Eringen, A. C., and Suhubi, E. S. (1964). "Nonlinear theory of simple microelastic solid-I." Int. J. Eng. Sci. IJESAN0020-722510.1016/0020-7225(64)90004-7, 2(2), 189-203.
    • (1964) Int. J. Eng. Sci. , vol.2 , Issue.2 , pp. 189-203
    • Eringen, A.C.1    Suhubi, E.S.2
  • 11
    • 77956668935 scopus 로고    scopus 로고
    • "Strain gradient plasticity"
    • E. van derGiessen, T. Wu, and H. Aref, eds., Elsevier, Amsterdam, The Netherlands
    • Fleck, N. A., and Hutchinson, J. W. (1997). "Strain gradient plasticity." Advances in applied mechanics-33, E. van derGiessen, T. Wu, and H. Aref, eds., Elsevier, Amsterdam, The Netherlands, 295-361.
    • (1997) Advances in Applied Mechanics-33 , pp. 295-361
    • Fleck, N.A.1    Hutchinson, J.W.2
  • 12
    • 0037053923 scopus 로고    scopus 로고
    • "Large strain finite element analysis of a local second gradient model: Application to localization"
    • IJNMBH0029-598110.1002/nme.433
    • Matsushima, T., Chambon, R., and Caillerie, D. (2002). "Large strain finite element analysis of a local second gradient model: Application to localization." Int. J. Numer. Methods Eng. IJNMBH0029-598110.1002/nme.433, 54(4), 499-521.
    • (2002) Int. J. Numer. Methods Eng. , vol.54 , Issue.4 , pp. 499-521
    • Matsushima, T.1    Chambon, R.2    Caillerie, D.3
  • 13
    • 0040366845 scopus 로고
    • "Microstructure in linear elasticity"
    • AVRMAW0003-952710.1007/BF00248490
    • Mindlin, R. (1964). "Microstructure in linear elasticity." Arch. Ration. Mech. Anal. AVRMAW0003-952710.1007/BF00248490, 16(1), 51-78.
    • (1964) Arch. Ration. Mech. Anal. , vol.16 , Issue.1 , pp. 51-78
    • Mindlin, R.1
  • 14
    • 0001357580 scopus 로고
    • "On first strain-gradient theories in linear elasticity"
    • IJSOAD0020-768310.1016/0020-7683(68)90036-X
    • Mindlin, R., and Eshel, N. N. (1968). "On first strain-gradient theories in linear elasticity." Int. J. Solids Struct. IJSOAD0020-768310.1016/0020-7683(68)90036-X, 4(1), 109-124.
    • (1968) Int. J. Solids Struct. , vol.4 , Issue.1 , pp. 109-124
    • Mindlin, R.1    Eshel, N.N.2
  • 15
    • 0037014436 scopus 로고    scopus 로고
    • "A director theory for visco-elastic folding instabilities in multilayered rock"
    • IJSOAD0020-7683
    • Mühlhaus, H.-B., Dufour, F., Moresi, L., and Hobbs, B. (2002). "A director theory for visco-elastic folding instabilities in multilayered rock." Int. J. Solids Struct.IJSOAD0020-7683, 39(13), 3675-3691.
    • (2002) Int. J. Solids Struct. , vol.39 , Issue.13 , pp. 3675-3691
    • Mühlhaus, H.-B.1    Dufour, F.2    Moresi, L.3    Hobbs, B.4
  • 16
    • 0023404291 scopus 로고
    • "The thickness of shear bands in granular materials"
    • GTNQA80016-8505
    • Mühlhaus, H.-B., and Vardoulakis, I. (1987). "The thickness of shear bands in granular materials." Geotechnique GTNQA80016-8505, 37(3), 271-283.
    • (1987) Geotechnique , vol.37 , Issue.3 , pp. 271-283
    • Mühlhaus, H.-B.1    Vardoulakis, I.2
  • 17
    • 84903645008 scopus 로고
    • "Size dependency of castlegate and berea sandstone hollow-cylinder strength on the basis of bifurcation theory"
    • Taylor & Francis, Reno, Nev
    • Papamichos, E., and van den Hoek, P. (1995). "Size dependency of castlegate and berea sandstone hollow-cylinder strength on the basis of bifurcation theory." Proc., 35th U.S. Symp. on Rock Mechanics, Taylor & Francis, Reno, Nev., 301-306.
    • (1995) Proc., 35th U.S. Symp. on Rock Mechanics , pp. 301-306
    • Papamichos, E.1    van den Hoek, P.2
  • 18
    • 0024471043 scopus 로고
    • "Bifurcation analysis of deep boreholes. II: Scale effect"
    • IJNGDZ0363-906110.1002/nag.1610130206
    • Papanastasiou, P., and Vardoulakis, I. (1989). "Bifurcation analysis of deep boreholes. II: Scale effect." Int. J. Numer. Analyt. Meth. Geomech. IJNGDZ0363-906110.1002/nag.1610130206, 13(2), 183-198.
    • (1989) Int. J. Numer. Analyt. Meth. Geomech. , vol.13 , Issue.2 , pp. 183-198
    • Papanastasiou, P.1    Vardoulakis, I.2
  • 19
    • 0028532340 scopus 로고
    • "Isoparametric hermite elements"
    • IJNMBH0029-5981
    • Petera, J., and Pittman, J. (1994). "Isoparametric hermite elements." Int. J. Numer. Methods Eng. IJNMBH0029-5981, 37(20), 3489-3519.
    • (1994) Int. J. Numer. Methods Eng. , vol.37 , Issue.20 , pp. 3489-3519
    • Petera, J.1    Pittman, J.2
  • 20
    • 0032155920 scopus 로고    scopus 로고
    • "Finite element implementation of gradient plasticity models. Part I: Gradient-dependent yield functions"
    • CMMECC0045-782510.1016/S0045-7825(98)00028-0
    • Ramaswamy, S., and Aravas, N. (1998). "Finite element implementation of gradient plasticity models. Part I: Gradient-dependent yield functions." Comput. Methods Appl. Mech. Eng. CMMECC0045-782510.1016/S0045-7825(98)00028-0, 163(1-4), 11-32.
    • (1998) Comput. Methods Appl. Mech. Eng. , vol.163 , Issue.1-4 , pp. 11-32
    • Ramaswamy, S.1    Aravas, N.2
  • 21
    • 0032710222 scopus 로고    scopus 로고
    • "Finite elements for materials with strain gradient effects"
    • IJNMBH0029-598110.1002/ (SICI)1097-0207(19990130)44:3<373::AID-NME508>3.0.CO;2-7
    • Shu, J. Y., King, W. E., and Fleck, N. A. (1999). "Finite elements for materials with strain gradient effects." Int. J. Numer. Methods Eng. IJNMBH0029-598110.1002/ (SICI)1097-0207(19990130)44:3<373::AID-NME508>3.0.CO;2-7 44(3), 373-391.
    • (1999) Int. J. Numer. Methods Eng. , vol.44 , Issue.3 , pp. 373-391
    • Shu, J.Y.1    King, W.E.2    Fleck, N.A.3
  • 22
    • 33947180779 scopus 로고
    • "Elastic materials with couple stresses"
    • AVRMAW0003-952710.1007/BF00253945
    • Toupin, R. (1962). "Elastic materials with couple stresses." Arch. Ration. Mech. Anal. AVRMAW0003-952710.1007/BF00253945, 11(1), 385-414.
    • (1962) Arch. Ration. Mech. Anal. , vol.11 , Issue.1 , pp. 385-414
    • Toupin, R.1
  • 23
    • 0026962738 scopus 로고
    • "Micro-structure in kinematic-hardening plasticity"
    • EJASEV0997-7538
    • Vardoulakis, I., and Frantziskonis, G. (1992). "Micro-structure in kinematic-hardening plasticity." Eur. J. Mech. A/Solids EJASEV0997-7538, 11(4), 467-486.
    • (1992) Eur. J. Mech. A/Solids , vol.11 , Issue.4 , pp. 467-486
    • Vardoulakis, I.1    Frantziskonis, G.2
  • 24
    • 13844320056 scopus 로고    scopus 로고
    • "Gradient plasticity theory with a variable length scale parameter"
    • IJSOAD0020-7683
    • Voyiadjis, G., and Abu Al-Rub, R. (2005). "Gradient plasticity theory with a variable length scale parameter." Int. J. Solids Struct. IJSOAD0020-7683, 42(14), 3998-4029.
    • (2005) Int. J. Solids Struct. , vol.42 , Issue.14 , pp. 3998-4029
    • Voyiadjis, G.1    Abu Al-Rub, R.2
  • 25
    • 38349192853 scopus 로고    scopus 로고
    • "Finite elements for elasticity with microstructure and gradient elasticity"
    • IJNMBH0029-5981
    • Zervos, A. (2008). "Finite elements for elasticity with microstructure and gradient elasticity." Int. J. Numer. Methods Eng. IJNMBH0029-5981, 73(4), 564-595.
    • (2008) Int. J. Numer. Methods Eng. , vol.73 , Issue.4 , pp. 564-595
    • Zervos, A.1
  • 26
    • 0035961284 scopus 로고    scopus 로고
    • "A finite element displacement formulation for gradient elastoplasticity"
    • IJNMBH0029-598110.1002/ 1097-0207(20010228)50:6<1369::AID-NME72>3.0.CO;2-K
    • Zervos, A., Papanastasiou, P., and Vardoulakis, I. (2001a). "A finite element displacement formulation for gradient elastoplasticity." Int. J. Numer. Methods Eng. IJNMBH0029-598110.1002/ 1097-0207(20010228)50:6<1369::AID-NME72>3.0.CO;2-K, 50(6), 1369-1388.
    • (2001) Int. J. Numer. Methods Eng. , vol.50 , Issue.6 , pp. 1369-1388
    • Zervos, A.1    Papanastasiou, P.2    Vardoulakis, I.3
  • 27
    • 0035827386 scopus 로고    scopus 로고
    • "Modelling of localisation and scale effect in thick-walled cylinders with gradient elastoplasticity"
    • IJSOAD0020-768310.1016/S0020-7683(00)00337-1
    • Zervos, A., Papanastasiou, P., and Vardoulakis, I. (2001b). "Modelling of localisation and scale effect in thick-walled cylinders with gradient elastoplasticity." Int. J. Solids Struct.IJSOAD0020-768310.1016/S0020-7683(00)00337-1, 38(30-31), 5081-5095.
    • (2001) Int. J. Solids Struct. , vol.38 , Issue.30-31 , pp. 5081-5095
    • Zervos, A.1    Papanastasiou, P.2    Vardoulakis, I.3
  • 28
    • 60649084391 scopus 로고    scopus 로고
    • "Shear localisation in thick-walled cylinders under internal pressure based on gradient elastoplasticity"
    • Zervos, A., Papanastasiou, P., and Vardoulakis, I. (2008). "Shear localisation in thick-walled cylinders under internal pressure based on gradient elastoplasticity." J. Theor. Appl. Mech., 38(1-2), 81-100.
    • (2008) J. Theor. Appl. Mech. , vol.38 , Issue.1-2 , pp. 81-100
    • Zervos, A.1    Papanastasiou, P.2    Vardoulakis, I.3
  • 29
    • 33846409456 scopus 로고    scopus 로고
    • "Influence of nonassociativity on localization and failure in geomechanics based on gradient elastoplasticity"
    • IJGNAI1532-364110.1061/(ASCE)1532-3641(2007)7:1(63)
    • Zervos, A., Vardoulakis, I., and Papanastasiou, P., (2007). "Influence of nonassociativity on localization and failure in geomechanics based on gradient elastoplasticity." Int. J. Geomech. IJGNAI1532-364110.1061/(ASCE)1532-3641(2007)7:1(63), 7(1), 63-74.
    • (2007) Int. J. Geomech. , vol.7 , Issue.1 , pp. 63-74
    • Zervos, A.1    Vardoulakis, I.2    Papanastasiou, P.3


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