A weak continuity condition of FEM for axisymmetric couple stress theory and an 18-DOF triangular axisymmetric element
Tài liệu tham khảo
Fleck, 1994, Strain gradient plasticity: theory and experiment, Acta Metall. Mater., 42, 475, 10.1016/0956-7151(94)90502-9
Stelmashenko, 1993, Microindentations on W and Mo oriented single crystals: an STM study, Acta. Metall. Mater., 41, 2855, 10.1016/0956-7151(93)90100-7
Stolken, 1998, A microbend test method for measuring the plasticity length scale, Acta. Metall. Mater., 46, 5109, 10.1016/S1359-6454(98)00153-0
Mindlin, 1963, Influence of couple-stresses on stress concentrations, Exp. Mech., 3, 1, 10.1007/BF02327219
Cosserat, 1909
Koiter, 1964, Couple stresses in the theory of elasticity, I & II, Proc. K. Ned. Akad. Wet., 67, 17
Mindlin, 1962, Effects of couple-stresses in linear elasticity, Arch. Ration. Mech. Anal., 11, 415, 10.1007/BF00253946
Fleck, 1997, Strain gradient plasticity, Adv. Appl. Mech., 33, 295, 10.1016/S0065-2156(08)70388-0
Gao, 1999, Mechanism-based strain gradient plasticity—I. Theory, J. Mech. Phys. Solids, 47, 1239, 10.1016/S0022-5096(98)00103-3
Aifantis, 1984, On the microstructural origin of certain inelastic models, Trans. ASME J. Eng. Mater. Technol., 106, 326, 10.1115/1.3225725
Chen, 2002, A new deformation theory with strain gradient effects, Int. J. Plast., 18, 971, 10.1016/S0749-6419(01)00020-1
Atkinson, 1977, The effect of couple stress on the tip of a crack, Int. J. Solids Struct., 13, 1103, 10.1016/0020-7683(77)90080-4
Xia, 1996, Crack tip fields in strain gradient plasticity, J. Mech. Phys. Solids, 44, 1621, 10.1016/0022-5096(96)00035-X
Zervos, 2001, Modelling of localisation and scale in thick-walled cylinders with gradient elastoplasticity, Int. J. Solids Struct., 38, 5081, 10.1016/S0020-7683(00)00337-1
Herrmann, 1993, Mixed finite elements for couple-stress analysis
Shu, 1999, Finite elements for materials with strain gradient effects, Int. J. Numer. Methods Eng., 44, 373, 10.1002/(SICI)1097-0207(19990130)44:3<373::AID-NME508>3.0.CO;2-7
Amanatidou, 2002, Mixed finite element formulations of strain-gradient elasticity problems, Comp. Meth. Appl. Mech. Engrg., 191, 1723, 10.1016/S0045-7825(01)00353-X
Engel, 2002, 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, 3669, 10.1016/S0045-7825(02)00286-4
Tenek, 2002, A two-dimensional finite element implementation of a special form of gradient elasticity, Comput. Model. Eng. Sci., 3, 731
W.J. Chen, C0 and C1 theories and test functions for FEM patch test in micromechanics, Sci. China Ser. G, (2009) in press.
Chen, 2009, The functions for patch test in finite element analysis of Mindlin plate and thin cylindrical shell, Sci. China Ser. G, 52, 762, 10.1007/s11433-009-0097-y
Shu, 1998, The prediction of a size effect in micro-indentation, Int. J. Solids Struct., 35, 1363, 10.1016/S0020-7683(97)00112-1
Ma, 1995, Size dependent hardness of silver single crystals, J. Mater. Res., 10, 853, 10.1557/JMR.1995.0853
McElhaney, 1998, Determination of indenter tip geometry and indentation contact area for depth-sensing indentation experiments, J. Mater. Res., 13, 1300, 10.1557/JMR.1998.0185
Poole, 1996, Micro-hardness of annealed and work-hardened copper polycrystals, Scr. Mater., 34, 559, 10.1016/1359-6462(95)00524-2
Soh, 2004, Finite element formulations of strain gradient theory for microstructures and the C0−1 patch test, Int. J. Numer. Methods Eng., 61, 433, 10.1002/nme.1075
G.P. Bazeley, Y.K. Cheung, B.M. Irons, O.C. Zienkiewicz, Triangular elements in bending conforming and nonconforming solution, in: Proceedings of the Conference on Matrix Methods in Structural Mechanics, Air Force Institute of Technology, Wright-Patterson A.F. Base, Ohio, 1965, pp. 547–576.
Cheung, 1995, Refined nine-parameter triangular thin plate bending element by using refined direct stiffness method, Int. J. Numer. Methods Eng., 38, 283, 10.1002/nme.1620380208
Hinton, 1975, Local least squares stress smoothing for parabolic isoparametric elements, 38, 235
Nisida, 1971
