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Volumn 42, Issue 24-25, 2005, Pages 6226-6244

Uniqueness for plane crack problems in dipolar gradient elasticity and in couple-stress elasticity

Author keywords

Couple stress elasticity; Crack problems; Dipolar stresses; Generalized continuum theories; Gradient elasticity; Microstructure; Uniqueness

Indexed keywords

ANISOTROPY; ELASTICITY; MATHEMATICAL MODELS; MICROSTRUCTURE; PROBLEM SOLVING; STRESSES; THEOREM PROVING;

EID: 24944483689     PISSN: 00207683     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ijsolstr.2005.02.045     Document Type: Article
Times cited : (28)

References (44)
  • 1
    • 0036471631 scopus 로고    scopus 로고
    • Mixed finite element formulations of strain-gradient elasticity problems
    • E. Amanatidou, and N. Aravas Mixed finite element formulations of strain-gradient elasticity problems Comput. Methods Appl. Mech. Eng. 191 2002 1723 1751
    • (2002) Comput. Methods Appl. Mech. Eng. , vol.191 , pp. 1723-1751
    • Amanatidou, E.1    Aravas, N.2
  • 2
    • 0017674745 scopus 로고
    • The effect of couple stresses on the tip of a crack
    • C. Atkinson, and F.G. Leppington The effect of couple stresses on the tip of a crack Int. J. Solids Struct. 13 1977 1103 1122
    • (1977) Int. J. Solids Struct. , vol.13 , pp. 1103-1122
    • Atkinson, C.1    Leppington, F.G.2
  • 3
    • 0032180495 scopus 로고    scopus 로고
    • The mechanics of size-dependent indentation
    • M.R. Begley, and J.W. Hutchinson The mechanics of size-dependent indentation J. Mech. Phys. Solids 46 1998 2049 2068
    • (1998) J. Mech. Phys. Solids , vol.46 , pp. 2049-2068
    • Begley, M.R.1    Hutchinson, J.W.2
  • 4
    • 24944552701 scopus 로고
    • A note on the boundary conditions of Toupin's strain-gradient theory
    • J.L. Bleustein A note on the boundary conditions of Toupin's strain-gradient theory Int. J. Solids Struct. 3 1967 1053 1057
    • (1967) Int. J. Solids Struct. , vol.3 , pp. 1053-1057
    • Bleustein, J.L.1
  • 5
    • 0009827517 scopus 로고
    • Note sur l' equilibre et les mouvements vibratoires des corps solides
    • A.L. Cauchy Note sur l' equilibre et les mouvements vibratoires des corps solides Compt.-Rend. Acad. Paris 32 1851 323 326
    • (1851) Compt.-Rend. Acad. Paris , vol.32 , pp. 323-326
    • Cauchy, A.L.1
  • 7
    • 0037837697 scopus 로고
    • Strain-gradient effects in microlayers
    • F.D. Day, and Y. Weitsman Strain-gradient effects in microlayers ASCE J. Eng. Mech. 92 1966 67 86
    • (1966) ASCE J. Eng. Mech. , vol.92 , pp. 67-86
    • Day, F.D.1    Weitsman, Y.2
  • 8
    • 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
    • G. Engel, K. Garikipati, T.J.R. Hughes, M.G. Larson, L. Mazzei, and R.L. Taylor 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. Eng. 191 2002 3669 3750
    • (2002) Comput. Methods Appl. Mech. Eng. , 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
  • 9
    • 0002763255 scopus 로고    scopus 로고
    • A discussion of strain gradient plasticity theories and application to shear bands
    • R. de Borst E. van der Giessen Wiley New York
    • N.A. Fleck, and J.W. Hutchinson A discussion of strain gradient plasticity theories and application to shear bands R. de Borst E. van der Giessen Material Instabilities in Solids 1998 Wiley New York 507 519
    • (1998) Material Instabilities in Solids , pp. 507-519
    • Fleck, N.A.1    Hutchinson, J.W.2
  • 12
    • 0141829271 scopus 로고    scopus 로고
    • The mode-III crack problem in microstructured solids governed by dipolar gradient elasticity: Static and dynamic analysis
    • H.G. Georgiadis The mode-III crack problem in microstructured solids governed by dipolar gradient elasticity: static and dynamic analysis ASME J. Appl. Mech. 70 2003 517 530
    • (2003) ASME J. Appl. Mech. , vol.70 , pp. 517-530
    • Georgiadis, H.G.1
  • 13
    • 0028516561 scopus 로고
    • Exact elastodynamic analysis of some fracture specimen models involving strip geometries
    • H.G. Georgiadis, and L.M. Brock Exact elastodynamic analysis of some fracture specimen models involving strip geometries Int. J. Solids Struct. 31 1994 2599 2613
    • (1994) Int. J. Solids Struct. , vol.31 , pp. 2599-2613
    • Georgiadis, H.G.1    Brock, L.M.2
  • 15
    • 0030217432 scopus 로고    scopus 로고
    • Transient SIF results for a cracked viscoelastic strip under concentrated impact loading-an integral-transform/function-theoretic approach
    • H.G. Georgiadis, and A.P. Rigatos Transient SIF results for a cracked viscoelastic strip under concentrated impact loading-an integral-transform/ function-theoretic approach Wave Motion 24 1996 41 57
    • (1996) Wave Motion , vol.24 , pp. 41-57
    • Georgiadis, H.G.1    Rigatos, A.P.2
  • 16
    • 0038330386 scopus 로고    scopus 로고
    • High-frequency Rayleigh waves in materials with microstructure and couple-stress effects
    • H.G. Georgiadis, and E.G. Velgaki High-frequency Rayleigh waves in materials with microstructure and couple-stress effects Int. J. Solids Struct. 40 2003 2501 2520
    • (2003) Int. J. Solids Struct. , vol.40 , pp. 2501-2520
    • Georgiadis, H.G.1    Velgaki, E.G.2
  • 17
    • 0000949779 scopus 로고    scopus 로고
    • Torsional surface waves in a gradient-elastic half-space
    • H.G. Georgiadis, I. Vardoulakis, and G. Lykotrafitis Torsional surface waves in a gradient-elastic half-space Wave Motion 31 2000 333 348
    • (2000) Wave Motion , vol.31 , pp. 333-348
    • Georgiadis, H.G.1    Vardoulakis, I.2    Lykotrafitis, G.3
  • 18
    • 3543131809 scopus 로고    scopus 로고
    • Dispersive Rayleigh-wave propagation in microstructured solids characterized by dipolar gradient elasticity
    • H.G. Georgiadis, I. Vardoulakis, and E.G. Velgaki Dispersive Rayleigh-wave propagation in microstructured solids characterized by dipolar gradient elasticity J. Elast. 74 2004 17 45
    • (2004) J. Elast. , vol.74 , pp. 17-45
    • Georgiadis, H.G.1    Vardoulakis, I.2    Velgaki, E.G.3
  • 19
    • 0000141747 scopus 로고
    • The method of virtual power in continuum mechanics. Part 2: Microstructure
    • P. Germain The method of virtual power in continuum mechanics. Part 2: microstructure SIAM J. Appl. Math. 25 1973 556 575
    • (1973) SIAM J. Appl. Math. , vol.25 , pp. 556-575
    • Germain, P.1
  • 21
    • 0012161376 scopus 로고
    • Applications of theories of generalized Cosserat continua to the dynamics of composite materials
    • E. Kroener Springer Berlin
    • G. Herrmann, and J.D. Achenbach Applications of theories of generalized Cosserat continua to the dynamics of composite materials E. Kroener Mechanics of Generalized Continua 1968 Springer Berlin 69 79
    • (1968) Mechanics of Generalized Continua , pp. 69-79
    • Herrmann, G.1    Achenbach, J.D.2
  • 22
    • 0031102222 scopus 로고    scopus 로고
    • Mixed mode near-tip fields for cracks in materials with strain-gradient effects
    • Y. Huang, L. Zhang, T.F. Guo, and K.-C. Hwang Mixed mode near-tip fields for cracks in materials with strain-gradient effects J. Mech. Phys. Solids 45 1997 439 465
    • (1997) J. Mech. Phys. Solids , vol.45 , pp. 439-465
    • Huang, Y.1    Zhang, L.2    Guo, T.F.3    Hwang, K.-C.4
  • 23
    • 0033332323 scopus 로고    scopus 로고
    • Analytic and numerical studies on mode i and mode II fracture in elastic-plastic materials with strain gradient effects
    • Y. Huang, J.Y. Chen, T.F. Guo, L. Zhang, and K.-C. Hwang Analytic and numerical studies on mode I and mode II fracture in elastic-plastic materials with strain gradient effects Int. J. Fract. 100 1999 1 27
    • (1999) Int. J. Fract. , vol.100 , pp. 1-27
    • Huang, Y.1    Chen, J.Y.2    Guo, T.F.3    Zhang, L.4    Hwang, K.-C.5
  • 25
    • 34250442580 scopus 로고
    • Uniqueness for plane crack problems in linear elastostatics
    • J.K. Knowles, and T.A. Pucik Uniqueness for plane crack problems in linear elastostatics J. Elast. 3 1973 155 160
    • (1973) J. Elast. , vol.3 , pp. 155-160
    • Knowles, J.K.1    Pucik, T.A.2
  • 27
    • 0037938668 scopus 로고    scopus 로고
    • The effect of couple-stresses on dislocation strain energy
    • V.A. Lubarda The effect of couple-stresses on dislocation strain energy Int. J. Solids Struct. 40 2003 3807 3826
    • (2003) Int. J. Solids Struct. , vol.40 , pp. 3807-3826
    • Lubarda, V.A.1
  • 28
    • 0034159337 scopus 로고    scopus 로고
    • Conservation integrals in couple stress elasticity
    • V.A. Lubarda, and X. Markenskoff Conservation integrals in couple stress elasticity J. Mech. Phys. Solids 48 2000 553 564
    • (2000) J. Mech. Phys. Solids , vol.48 , pp. 553-564
    • Lubarda, V.A.1    Markenskoff, X.2
  • 29
    • 0040366845 scopus 로고
    • Micro-structure in linear elasticity
    • R.D. Mindlin Micro-structure in linear elasticity Arch. Ration. Mech. Anal. 16 1964 51 78
    • (1964) Arch. Ration. Mech. Anal. , vol.16 , pp. 51-78
    • Mindlin, R.D.1
  • 30
    • 0001357580 scopus 로고
    • On first strain-gradient theories in linear elasticity
    • R.D. Mindlin, and N.N. Eshel On first strain-gradient theories in linear elasticity Int. J. Solids Struct. 4 1968 109 124
    • (1968) Int. J. Solids Struct. , vol.4 , pp. 109-124
    • Mindlin, R.D.1    Eshel, N.N.2
  • 31
    • 33947128429 scopus 로고
    • Effects of couple-stresses in linear elasticity
    • R.D. Mindlin, and H.F. Tiersten Effects of couple-stresses in linear elasticity Arch. Ration. Mech. Anal. 11 1962 415 448
    • (1962) Arch. Ration. Mech. Anal. , vol.11 , pp. 415-448
    • Mindlin, R.D.1    Tiersten, H.F.2
  • 32
    • 0001667118 scopus 로고
    • The influence of couple-stresses on singular stress concentrations in elastic solids
    • R. Muki, and E. Sternberg The influence of couple-stresses on singular stress concentrations in elastic solids ZAMP 16 1965 611 618
    • (1965) ZAMP , vol.16 , pp. 611-618
    • Muki, R.1    Sternberg, E.2
  • 34
    • 0034559454 scopus 로고    scopus 로고
    • Fracture in the higher-order elastic continuum
    • M.X. Shi, Y. Huang, and K.C. Hwang Fracture in the higher-order elastic continuum J. Mech. Phys. Solids 48 2000 2513 2538
    • (2000) J. Mech. Phys. Solids , vol.48 , pp. 2513-2538
    • Shi, M.X.1    Huang, Y.2    Hwang, K.C.3
  • 35
    • 0032710222 scopus 로고    scopus 로고
    • Finite elements for materials with strain gradient effects
    • J.Y. Shu, W.E. King, and N.A. Fleck Finite elements for materials with strain gradient effects Int. J. Numer. Meth. Eng. 44 1999 373 391
    • (1999) Int. J. Numer. Meth. Eng. , vol.44 , pp. 373-391
    • Shu, J.Y.1    King, W.E.2    Fleck, N.A.3
  • 36
    • 0002091925 scopus 로고
    • The effect of couple-stresses on the stress concentration around a crack
    • E. Sternberg, and R. Muki The effect of couple-stresses on the stress concentration around a crack Int. J. Solids Struct. 3 1967 69 95
    • (1967) Int. J. Solids Struct. , vol.3 , pp. 69-95
    • Sternberg, E.1    Muki, R.2
  • 37
    • 0036814242 scopus 로고    scopus 로고
    • A boundary element method for solving 3D static gradient elastic problems with surface energy
    • K.G. Tsepoura, S. Papargyri-Beskou, and D. Polyzos A boundary element method for solving 3D static gradient elastic problems with surface energy Comput. Mech. 29 2002 361 381
    • (2002) Comput. Mech. , vol.29 , pp. 361-381
    • Tsepoura, K.G.1    Papargyri-Beskou, S.2    Polyzos, D.3
  • 38
    • 0031130302 scopus 로고    scopus 로고
    • SH surface waves in a homogeneous gradient elastic half-space with surface energy
    • I. Vardoulakis, and H.G. Georgiadis SH surface waves in a homogeneous gradient elastic half-space with surface energy J. Elast 47 1997 147 165
    • (1997) J. Elast , vol.47 , pp. 147-165
    • Vardoulakis, I.1    Georgiadis, H.G.2
  • 40
    • 0003389412 scopus 로고
    • Theoretische Studien uber die Elasticitatsverhaltnisse der Krystalle
    • Voigt, W., 1887. Theoretische Studien uber die Elasticitatsverhaltnisse der Krystalle. Abh. Ges. Wiss. Gottingen 34.
    • (1887) Abh. Ges. Wiss. Gottingen , vol.34
    • Voigt, W.1
  • 41
    • 0031207889 scopus 로고    scopus 로고
    • Steady-state crack growth and work of fracture for solids characterized by strain gradient plasticity
    • Y. Wei, and J.W. Hutchinson Steady-state crack growth and work of fracture for solids characterized by strain gradient plasticity J. Mech. Phys. Solids 45 1997 1253 1273
    • (1997) J. Mech. Phys. Solids , vol.45 , pp. 1253-1273
    • Wei, Y.1    Hutchinson, J.W.2
  • 42
    • 85014213853 scopus 로고
    • Strain-gradient effects around cylindrical inclusions and cavities in a field of cylindrically symmetric tension
    • Y. Weitsman Strain-gradient effects around cylindrical inclusions and cavities in a field of cylindrically symmetric tension ASME J. Appl. Mech. 33 1966 57 67
    • (1966) ASME J. Appl. Mech. , vol.33 , pp. 57-67
    • Weitsman, Y.1
  • 43
    • 0037150391 scopus 로고    scopus 로고
    • Couple stress based strain gradient theory for elasticity
    • F. Yang, A.C.M. Chong, D.C.C. Lam, and P. Tong Couple stress based strain gradient theory for elasticity Int. J. Solids Struct. 39 2002 2731 2743
    • (2002) Int. J. Solids Struct. , vol.39 , pp. 2731-2743
    • Yang, F.1    Chong, A.C.M.2    Lam, D.C.C.3    Tong, P.4
  • 44
    • 0009107948 scopus 로고    scopus 로고
    • The mode-III full-field solution in elastic materials with strain gradient effects
    • L. Zhang, Y. Huang, J.Y. Chen, and K.C. Hwang The mode-III full-field solution in elastic materials with strain gradient effects Int. J. Fract. 92 1998 325 348
    • (1998) Int. J. Fract. , vol.92 , pp. 325-348
    • Zhang, L.1    Huang, Y.2    Chen, J.Y.3    Hwang, K.C.4


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