메뉴 건너뛰기




Volumn 57, Issue 11, 2009, Pages 1898-1920

Plane-strain crack problems in microstructured solids governed by dipolar gradient elasticity

Author keywords

Asymptotics; Cracks; Dipolar gradient elasticity; Hypersingular integral equations; Microstructure

Indexed keywords

ASYMPTOTIC SOLUTIONS; ASYMPTOTICS; CLASSICAL THEORY; CRACK DRIVING FORCE; CRACK PROBLEMS; CRITICAL STRESS; DIPOLAR GRADIENT ELASTICITY; ELASTIC STRAIN; ELASTIC STRESS; FINITE PART INTEGRALS; FULL-FIELD; GENERALIZED CONTINUUM THEORIES; GRADIENT ELASTICITY; GRADIENT THEORY; HADAMARD; HYPERSINGULAR INTEGRAL EQUATION; HYPERSINGULAR INTEGRAL EQUATIONS; J INTEGRAL; LINEAR EXPRESSION; LOCAL MAXIMUM; MATERIAL CONSTANT; MATERIAL MICROSTRUCTURES; MAXIMUM VALUES; MICROSTRUCTURED MATERIALS; MICROSTRUCTURED SOLIDS; MINDLIN; NUMERICAL TREATMENTS; PLANE-STRAIN; STRAIN ENERGY DENSITY; STRAIN FIELDS; STRAIN TENSOR; STRENGTHENING EFFECT; STRESS DISTRIBUTION; WILLIAMS;

EID: 70349246334     PISSN: 00225096     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jmps.2009.07.005     Document Type: Article
Times cited : (91)

References (82)
  • 1
    • 0003283056 scopus 로고
    • Handbook of Mathematical Functions. National Bureau of Standards
    • Abramowitz, M., Stegun, I.A., 1964. Handbook of Mathematical Functions. National Bureau of Standards, Applied Mathematics Series 55.
    • (1964) Applied Mathematics Series , vol.55
    • Abramowitz, M.1    Stegun, I.A.2
  • 2
    • 0036471631 scopus 로고    scopus 로고
    • Mixed finite element formulations of strain-gradient elasticity problems
    • Amanatidou E., and Aravas N. 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
  • 4
    • 70349259048 scopus 로고    scopus 로고
    • Plane asymptotic crack-tip solutions in gradient elasticity
    • submitted for publication
    • Aravas, N., Giannakopoulos, A.E., 2009. Plane asymptotic crack-tip solutions in gradient elasticity, submitted for publication.
    • (2009)
    • Aravas, N.1    Giannakopoulos, A.E.2
  • 5
    • 0003840331 scopus 로고
    • Kluwer Academic Publishers, Dordrecht
    • Barber J.R. Elasticity (1992), Kluwer Academic Publishers, Dordrecht
    • (1992) Elasticity
    • Barber, J.R.1
  • 6
    • 0032180495 scopus 로고    scopus 로고
    • The mechanics of size-dependent indentation
    • Begley M.R., and Hutchinson J.W. 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
  • 7
    • 24944552701 scopus 로고
    • A note on the boundary conditions of Toupin's strain-gradient theory
    • Bleustein J.L. 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
  • 8
    • 0034347976 scopus 로고    scopus 로고
    • Sliding contact with friction of a thermoelastic solid at subsonic, transonic and supersonic speeds
    • Brock L.M., and Georgiadis H.G. Sliding contact with friction of a thermoelastic solid at subsonic, transonic and supersonic speeds. J. Therm. Stresses 23 (2000) 629-656
    • (2000) J. Therm. Stresses , vol.23 , pp. 629-656
    • Brock, L.M.1    Georgiadis, H.G.2
  • 9
    • 33847704947 scopus 로고    scopus 로고
    • Multiple-zone sliding contact with friction on an anisotropic thermoelastic half-space
    • Brock L.M., and Georgiadis H.G. Multiple-zone sliding contact with friction on an anisotropic thermoelastic half-space. Int. J. Solids Struct. 44 (2007) 2820-2836
    • (2007) Int. J. Solids Struct. , vol.44 , pp. 2820-2836
    • Brock, L.M.1    Georgiadis, H.G.2
  • 10
    • 0017292288 scopus 로고
    • An influence function of the intensity factor in tensile fracture
    • Burridge R. An influence function of the intensity factor in tensile fracture. Int. J. Eng. Sci. 14 (1976) 725-734
    • (1976) Int. J. Eng. Sci. , vol.14 , pp. 725-734
    • Burridge, R.1
  • 11
    • 0009827517 scopus 로고
    • Note sur l' equilibre et les mouvements vibratoires des corps solides
    • Cauchy A.L. Note sur l' equilibre et les mouvements vibratoires des corps solides. CR Acad. Paris 32 (1851) 323-326
    • (1851) CR Acad. Paris , vol.32 , pp. 323-326
    • Cauchy, A.L.1
  • 12
    • 0037397139 scopus 로고    scopus 로고
    • Integral equations with hypersingular kernels-theory and applications to fracture mechanics
    • Chan Y.S., Fannjiang A.C., and Paulino G.H. Integral equations with hypersingular kernels-theory and applications to fracture mechanics. Int. J. Eng. Sci. 41 (2003) 683-720
    • (2003) Int. J. Eng. Sci. , vol.41 , pp. 683-720
    • Chan, Y.S.1    Fannjiang, A.C.2    Paulino, G.H.3
  • 13
    • 55149108497 scopus 로고    scopus 로고
    • Gradient elasticity theory for mode III fracture in functionally graded materials - Part II, Crack parallel to the material gradation
    • Chan Y.S., Paulino G.H., and Fannjiang A.C. Gradient elasticity theory for mode III fracture in functionally graded materials - Part II, Crack parallel to the material gradation. ASME J. Appl. Mech. 75 (2008) 061015-06101511
    • (2008) ASME J. Appl. Mech. , vol.75 , pp. 061015-06101511
    • Chan, Y.S.1    Paulino, G.H.2    Fannjiang, A.C.3
  • 14
    • 0032064510 scopus 로고    scopus 로고
    • Fracture analysis of cellular materials: a strain gradient model
    • Chen J.Y., Huang Y., and Ortiz M. Fracture analysis of cellular materials: a strain gradient model. J. Mech. Phys. Solids 46 (1998) 789-828
    • (1998) J. Mech. Phys. Solids , vol.46 , pp. 789-828
    • Chen, J.Y.1    Huang, Y.2    Ortiz, M.3
  • 15
    • 0033309102 scopus 로고    scopus 로고
    • The crack tip fields in strain gradient plasticity: the asymptotic and numerical analyses
    • Chen J.Y., Wei Y., Huang Y., Hutchinson J.W., and Hwang K.C. The crack tip fields in strain gradient plasticity: the asymptotic and numerical analyses. Eng. Fract. Mech. 64 (1999) 625-648
    • (1999) Eng. Fract. Mech. , vol.64 , pp. 625-648
    • Chen, J.Y.1    Wei, Y.2    Huang, Y.3    Hutchinson, J.W.4    Hwang, K.C.5
  • 17
    • 0008493098 scopus 로고
    • Strain-gradient effects around spherical inclusions and cavities
    • Cook T.S., and Weitsman Y. Strain-gradient effects around spherical inclusions and cavities. Int. J. Solids Struct. 2 (1966) 393-406
    • (1966) Int. J. Solids Struct. , vol.2 , pp. 393-406
    • Cook, T.S.1    Weitsman, Y.2
  • 18
    • 0028518649 scopus 로고
    • The influence of interface impurities on fracture energy of UHV diffusion bonded metal-ceramic bicrystals
    • Elssner G., Korn D., and Ruhle M. The influence of interface impurities on fracture energy of UHV diffusion bonded metal-ceramic bicrystals. Scripta Metall. Mater. 31 (1994) 1037-1042
    • (1994) Scripta Metall. Mater. , vol.31 , pp. 1037-1042
    • Elssner, G.1    Korn, D.2    Ruhle, M.3
  • 19
    • 0018047560 scopus 로고
    • Mixed boundary-value problems in mechanics
    • Nemat-Nasser S. (Ed), Academic Press, New York
    • Erdogan F. Mixed boundary-value problems in mechanics. In: Nemat-Nasser S. (Ed). Mechanics Today vol. 4 (1978), Academic Press, New York 1-86
    • (1978) Mechanics Today , vol.4 , pp. 1-86
    • Erdogan, F.1
  • 20
    • 0014776433 scopus 로고
    • Effects of strain-gradient on the stress-concentration at a cylindrical hole in a field of uniaxial tension
    • Eshel N.N., and Rosenfeld G. Effects of strain-gradient on the stress-concentration at a cylindrical hole in a field of uniaxial tension. J. Eng. Math. 4 (1970) 97-111
    • (1970) J. Eng. Math. , vol.4 , pp. 97-111
    • Eshel, N.N.1    Rosenfeld, G.2
  • 21
    • 0038875266 scopus 로고
    • The product of distributions
    • Fisher B. The product of distributions. Q. J. Math. Oxford 22 (1971) 291-298
    • (1971) Q. J. Math. Oxford , vol.22 , pp. 291-298
    • Fisher, B.1
  • 23
    • 0029536231 scopus 로고
    • Microbuckle initiation in fibre composites: a finite element study
    • Fleck N.A., and Shu J.Y. Microbuckle initiation in fibre composites: a finite element study. J. Mech. Phys. Solids 43 (1995) 1887-1918
    • (1995) J. Mech. Phys. Solids , vol.43 , pp. 1887-1918
    • Fleck, N.A.1    Shu, J.Y.2
  • 24
    • 77956668935 scopus 로고    scopus 로고
    • Strain gradient plasticity
    • Hutchinson J.W., and Wu T.Y. (Eds), Academic Press, New York
    • Fleck N.A., and Hutchinson J.W. Strain gradient plasticity. In: Hutchinson J.W., and Wu T.Y. (Eds). Advances in Applied Mechanics vol. 33 (1997), Academic Press, New York 295-361
    • (1997) Advances in Applied Mechanics , vol.33 , pp. 295-361
    • Fleck, N.A.1    Hutchinson, J.W.2
  • 25
    • 0002763255 scopus 로고    scopus 로고
    • A discussion of strain gradient plasticity theories and application to shear bands
    • de Borst R., and van der Giessen E. (Eds), Wiley, New York
    • Fleck N.A., and Hutchinson J.W. A discussion of strain gradient plasticity theories and application to shear bands. In: de Borst R., and van der Giessen E. (Eds). 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
  • 26
    • 34250475582 scopus 로고
    • Energy flux into the tip of an extending crack in an elastic solid
    • Freund L.B. Energy flux into the tip of an extending crack in an elastic solid. J. Elasticity 2 (1972) 341-349
    • (1972) J. Elasticity , vol.2 , pp. 341-349
    • Freund, L.B.1
  • 28
    • 0001674362 scopus 로고
    • Surface elastic waves in cubic crystals
    • Gazis D.C., Herman R., and Wallis R.F. Surface elastic waves in cubic crystals. Phys. Rev. 119 (1960) 533-544
    • (1960) Phys. Rev. , vol.119 , pp. 533-544
    • Gazis, D.C.1    Herman, R.2    Wallis, R.F.3
  • 30
    • 0000949779 scopus 로고    scopus 로고
    • Torsional surface waves in a gradient-elastic half-space
    • Georgiadis H.G., Vardoulakis I., and Lykotrafitis G. 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
  • 31
    • 0141829271 scopus 로고    scopus 로고
    • The mode-III crack problem in microstructured solids governed by dipolar gradient elasticity: static and dynamic analysis
    • Georgiadis H.G. 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
  • 32
    • 3543131809 scopus 로고    scopus 로고
    • Dispersive Rayleigh-wave propagation in microstructured solids characterized by dipolar gradient elasticity
    • Georgiadis H.G., Vardoulakis I., and Velgaki E.G. Dispersive Rayleigh-wave propagation in microstructured solids characterized by dipolar gradient elasticity. J. Elasticity 74 (2004) 17-45
    • (2004) J. Elasticity , vol.74 , pp. 17-45
    • Georgiadis, H.G.1    Vardoulakis, I.2    Velgaki, E.G.3
  • 33
    • 33745989506 scopus 로고    scopus 로고
    • Energy theorems and the J-integral in dipolar gradient elasticity
    • Georgiadis H.G., and Grentzelou C.G. Energy theorems and the J-integral in dipolar gradient elasticity. Int. J. Solids Struct. 43 (2006) 5690-5712
    • (2006) Int. J. Solids Struct. , vol.43 , pp. 5690-5712
    • Georgiadis, H.G.1    Grentzelou, C.G.2
  • 34
    • 36549027964 scopus 로고    scopus 로고
    • Problems of the Flamant-Boussinesq and Kelvin type in dipolar gradient elasticity
    • Georgiadis H.G., and Anagnostou D. Problems of the Flamant-Boussinesq and Kelvin type in dipolar gradient elasticity. J. Elasticity 90 (2008) 71-98
    • (2008) J. Elasticity , vol.90 , pp. 71-98
    • Georgiadis, H.G.1    Anagnostou, D.2
  • 35
    • 0000141747 scopus 로고
    • The method of virtual power in continuum mechanics. Part 2: microstructure
    • Germain P. 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
  • 36
    • 33947109486 scopus 로고    scopus 로고
    • Structural analysis of gradient elastic components
    • Giannakopoulos A.E., and Stamoulis K. Structural analysis of gradient elastic components. Int. J. Solids Struct. 44 (2007) 3440-3451
    • (2007) Int. J. Solids Struct. , vol.44 , pp. 3440-3451
    • Giannakopoulos, A.E.1    Stamoulis, K.2
  • 37
    • 24944483689 scopus 로고    scopus 로고
    • Uniqueness for plane crack problems in dipolar gradient elasticity and in couple-stress elasticity
    • Grentzelou C.G., and Georgiadis H.G. Uniqueness for plane crack problems in dipolar gradient elasticity and in couple-stress elasticity. Int. J. Solids Struct. 42 (2005) 6226-6244
    • (2005) Int. J. Solids Struct. , vol.42 , pp. 6226-6244
    • Grentzelou, C.G.1    Georgiadis, H.G.2
  • 38
    • 44249116867 scopus 로고    scopus 로고
    • Balance laws and energy release rates for cracks in dipolar gradient elasticity
    • Grentzelou C.G., and Georgiadis H.G. Balance laws and energy release rates for cracks in dipolar gradient elasticity. Int. J. Solids Struct. 45 (2008) 551-567
    • (2008) Int. J. Solids Struct. , vol.45 , pp. 551-567
    • Grentzelou, C.G.1    Georgiadis, H.G.2
  • 39
    • 41449109612 scopus 로고    scopus 로고
    • Distributed dislocation approach for cracks in couple-stress elasticity: shear modes
    • Gourgiotis P.A., and Georgiadis H.G. Distributed dislocation approach for cracks in couple-stress elasticity: shear modes. Int. J. Fract. 147 (2007) 83-102
    • (2007) Int. J. Fract. , vol.147 , pp. 83-102
    • Gourgiotis, P.A.1    Georgiadis, H.G.2
  • 40
    • 51249112990 scopus 로고    scopus 로고
    • An approach based on distributed dislocations and disclinations for crack problems in couple-stress elasticity
    • Gourgiotis P.A., and Georgiadis H.G. An approach based on distributed dislocations and disclinations for crack problems in couple-stress elasticity. Int. J. Solids Struct. 45 (2008) 5521-5539
    • (2008) Int. J. Solids Struct. , vol.45 , pp. 5521-5539
    • Gourgiotis, P.A.1    Georgiadis, H.G.2
  • 43
    • 0031102222 scopus 로고    scopus 로고
    • Mixed mode near tip fields for cracks in materials with strain-gradient effects
    • Huang Y., Zhang L., Guo T.F., and Hwang K.C. 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
  • 44
    • 0033332323 scopus 로고    scopus 로고
    • Analytic and numerical studies on mode I and mode II fracture in elastic-plastic materials with strain gradient effects
    • Huang Y., Chen J.Y., Guo T.F., Zhang L., and Hwang K.C. 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
  • 46
    • 0347600794 scopus 로고    scopus 로고
    • A conventional theory of mechanism-based strain gradient plasticity
    • Huang Y., Qu S., Hwang K.C., Li M., and Gao H. A conventional theory of mechanism-based strain gradient plasticity. Int. J. Plasticity 20 (2004) 753-782
    • (2004) Int. J. Plasticity , vol.20 , pp. 753-782
    • Huang, Y.1    Qu, S.2    Hwang, K.C.3    Li, M.4    Gao, H.5
  • 48
    • 0022186457 scopus 로고
    • Measurement of apparent Young's modulus in the bending of cantilever beam by heterodyne holographic interferometry
    • Kakunai S., Masaki J., Kuroda R., Iwata K., and Nagata R. Measurement of apparent Young's modulus in the bending of cantilever beam by heterodyne holographic interferometry. Exp. Mech. 21 (1985) 408-412
    • (1985) Exp. Mech. , vol.21 , pp. 408-412
    • Kakunai, S.1    Masaki, J.2    Kuroda, R.3    Iwata, K.4    Nagata, R.5
  • 49
    • 34548757877 scopus 로고    scopus 로고
    • Boundary element analysis of mode I and mixed mode (I and II) crack problems of 2-D gradient elasticity
    • Karlis G.F., Tsinopoulos S.V., Polyzos D., and Beskos D.E. Boundary element analysis of mode I and mixed mode (I and II) crack problems of 2-D gradient elasticity. Comput. Methods Appl. Mech. Eng. 196 (2007) 5092-5103
    • (2007) Comput. Methods Appl. Mech. Eng. , vol.196 , pp. 5092-5103
    • Karlis, G.F.1    Tsinopoulos, S.V.2    Polyzos, D.3    Beskos, D.E.4
  • 50
    • 0001863547 scopus 로고
    • On the solution of integral equations with strongly singular kernels
    • Kaya A.C., and Erdogan F. On the solution of integral equations with strongly singular kernels. Q. Appl. Math. XLV 1 (1987) 105-122
    • (1987) Q. Appl. Math. , vol.XLV , Issue.1 , pp. 105-122
    • Kaya, A.C.1    Erdogan, F.2
  • 52
    • 34250442580 scopus 로고
    • Uniqueness for plane crack problems in linear elastostatics
    • Knowles J.K., and Pucik T.A. Uniqueness for plane crack problems in linear elastostatics. J. Elasticity 3 (1973) 155-160
    • (1973) J. Elasticity , vol.3 , pp. 155-160
    • Knowles, J.K.1    Pucik, T.A.2
  • 53
    • 0003118069 scopus 로고
    • Experimental methods for study of Cosserat elastic solids and other generalized elastic continua
    • Muhlhaus H.-B. (Ed), Wiley, Chichester
    • Lakes L. Experimental methods for study of Cosserat elastic solids and other generalized elastic continua. In: Muhlhaus H.-B. (Ed). Continuum Models for Materials with Microstructure (1995), Wiley, Chichester 1-25
    • (1995) Continuum Models for Materials with Microstructure , pp. 1-25
    • Lakes, L.1
  • 54
    • 24644502714 scopus 로고    scopus 로고
    • Nonsingular stress and strain fields of dislocations and disclinations in first strain gradient elasticity
    • Lazar M., and Maugin G.A. Nonsingular stress and strain fields of dislocations and disclinations in first strain gradient elasticity. Int. J. Eng. Sci. 43 (2005) 1157-1184
    • (2005) Int. J. Eng. Sci. , vol.43 , pp. 1157-1184
    • Lazar, M.1    Maugin, G.A.2
  • 55
    • 0029289877 scopus 로고
    • Size dependent hardness in silver single crystals
    • Ma Q., and Clarke D.S. Size dependent hardness in silver single crystals. J. Mater. Res. 10 (1995) 853-863
    • (1995) J. Mater. Res. , vol.10 , pp. 853-863
    • Ma, Q.1    Clarke, D.S.2
  • 56
    • 0000013750 scopus 로고
    • End-point behavior of solutions to hypersingular integral equations
    • Martin P.A. End-point behavior of solutions to hypersingular integral equations. Proc. R. Soc. London A 432 (1991) 301-320
    • (1991) Proc. R. Soc. London A , vol.432 , pp. 301-320
    • Martin, P.A.1
  • 57
    • 0040366845 scopus 로고
    • Micro-structure in linear elasticity
    • Mindlin R.D. 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
  • 58
    • 0001357580 scopus 로고
    • On first-gradient theories in linear elasticity
    • Mindlin R.D., and Eshel N.N. On first-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
  • 59
    • 33947128429 scopus 로고
    • Effects of couple-stresses in linear elasticity
    • Mindlin R.D., and Tiersten H.F. 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
  • 60
    • 0028422932 scopus 로고
    • Numerical evaluation of hypersingular integrals
    • Monegato G. Numerical evaluation of hypersingular integrals. J. Comput. Appl. Math. 50 (1994) 9-31
    • (1994) J. Comput. Appl. Math. , vol.50 , pp. 9-31
    • Monegato, G.1
  • 62
    • 0030085874 scopus 로고    scopus 로고
    • Micro-hardness of annealed and work-hardened copper polycrystals
    • Poole W.J., Ashby M.F., and Fleck N.A. Micro-hardness of annealed and work-hardened copper polycrystals. Scr. Mater. 34 (1996) 559-564
    • (1996) Scr. Mater. , vol.34 , pp. 559-564
    • Poole, W.J.1    Ashby, M.F.2    Fleck, N.A.3
  • 63
    • 0041485693 scopus 로고
    • Stress wave radiation from a crack tip during dynamic initiation
    • Prakash V., Freund L.B., and Clifton R.J. Stress wave radiation from a crack tip during dynamic initiation. ASME J. Appl. Mech. 59 (1992) 356-365
    • (1992) ASME J. Appl. Mech. , vol.59 , pp. 356-365
    • Prakash, V.1    Freund, L.B.2    Clifton, R.J.3
  • 64
    • 34247473069 scopus 로고    scopus 로고
    • Effects of characteristic material lengths on mode III crack propagation in couple stress elastic-plastic materials
    • Radi E. Effects of characteristic material lengths on mode III crack propagation in couple stress elastic-plastic materials. Int. J. Plasticity 23 (2007) 1439-1456
    • (2007) Int. J. Plasticity , vol.23 , pp. 1439-1456
    • Radi, E.1
  • 65
    • 40849097475 scopus 로고    scopus 로고
    • On the effects of characteristic lengths in bending and torsion on mode III crack in couple stress elasticity
    • Radi E. On the effects of characteristic lengths in bending and torsion on mode III crack in couple stress elasticity. Int. J. Solids Struct. 45 (2008) 3033-3058
    • (2008) Int. J. Solids Struct. , vol.45 , pp. 3033-3058
    • Radi, E.1
  • 66
    • 0003077565 scopus 로고
    • Mathematical analysis in the mechanics of fracture
    • Liebowitz H. (Ed), Academic Press, New York
    • Rice J.R. Mathematical analysis in the mechanics of fracture. In: Liebowitz H. (Ed). Fracture-an Advanced Treatise vol. 2 (1968), Academic Press, New York 191-311
    • (1968) Fracture-an Advanced Treatise , vol.2 , pp. 191-311
    • Rice, J.R.1
  • 67
    • 0034559454 scopus 로고    scopus 로고
    • Fracture in the higher-order elastic continuum
    • Shi M.X., Huang Y., and Hwang K.C. 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
  • 68
    • 0032710222 scopus 로고    scopus 로고
    • Finite elements for materials with strain gradient effects
    • Shu J.Y., King W.E., and Fleck N.A. Finite elements for materials with strain gradient effects. Int. J. Numer. Methods Eng. 44 (1999) 373-391
    • (1999) Int. J. Numer. Methods Eng. , vol.44 , pp. 373-391
    • Shu, J.Y.1    King, W.E.2    Fleck, N.A.3
  • 69
    • 0032158229 scopus 로고    scopus 로고
    • A microbend test method for measuring the plasticity length scale
    • Stolken J.S., and Evans A.G. A microbend test method for measuring the plasticity length scale. Acta Mater. 46 (1998) 5109-5115
    • (1998) Acta Mater. , vol.46 , pp. 5109-5115
    • Stolken, J.S.1    Evans, A.G.2
  • 70
    • 33947180779 scopus 로고
    • Perfectly elastic materials with couple stresses
    • Toupin R.A. Perfectly elastic materials with couple stresses. Arch. Ration. Mech. Anal. 11 (1962) 385-414
    • (1962) Arch. Ration. Mech. Anal. , vol.11 , pp. 385-414
    • Toupin, R.A.1
  • 71
    • 0025463243 scopus 로고
    • Gauss quadrature rules for finite part integrals
    • Tsamasphyros G., and Dimou G. Gauss quadrature rules for finite part integrals. Int. J. Numer. Methods Eng. 30 (1990) 13-26
    • (1990) Int. J. Numer. Methods Eng. , vol.30 , pp. 13-26
    • Tsamasphyros, G.1    Dimou, G.2
  • 73
    • 0036814242 scopus 로고    scopus 로고
    • A boundary element method for solving 3D static gradient elastic problems with surface energy
    • Tsepoura K.G., Papargyri-Beskou S., and Polyzos D. 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
  • 76
    • 0031130302 scopus 로고    scopus 로고
    • SH surface waves in a homogeneous gradient elastic half-space with surface energy
    • Vardoulakis I., and Georgiadis H.G. SH surface waves in a homogeneous gradient elastic half-space with surface energy. J. Elasticity 47 (1997) 147-165
    • (1997) J. Elasticity , vol.47 , pp. 147-165
    • Vardoulakis, I.1    Georgiadis, H.G.2
  • 77
    • 70349258813 scopus 로고    scopus 로고
    • Voigt, W., 1887. Theoretische Studien uber die Elasticitatsverhaltnisse der Krystalle. Abh. Ges. Wissen. Goettingen 34.
    • Voigt, W., 1887. Theoretische Studien uber die Elasticitatsverhaltnisse der Krystalle. Abh. Ges. Wissen. Goettingen 34.
  • 78
    • 0031207889 scopus 로고    scopus 로고
    • Steady-state crack growth and work of fracture for solids characterized by strain gradient plasticity
    • Wei Y., and Hutchinson J.W. 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
  • 79
    • 33750331945 scopus 로고    scopus 로고
    • A new finite element method for strain gradient theories and applications to fracture analyses
    • Wei Y. A new finite element method for strain gradient theories and applications to fracture analyses. Eur. J. Mech. A/Solids 25 (2006) 897-913
    • (2006) Eur. J. Mech. A/Solids , vol.25 , pp. 897-913
    • Wei, Y.1
  • 80
    • 0014926080 scopus 로고
    • Surface elastic waves
    • White R.M. Surface elastic waves. Proc. IEEE 58 (1970) 1238-1276
    • (1970) Proc. IEEE , vol.58 , pp. 1238-1276
    • White, R.M.1
  • 81
    • 85124701057 scopus 로고
    • Stress singularities resulting from various boundary conditions in angular corners of plates in extension
    • Williams M.L. Stress singularities resulting from various boundary conditions in angular corners of plates in extension. ASME J. Appl. Mech. 74 (1952) 526-528
    • (1952) ASME J. Appl. Mech. , vol.74 , pp. 526-528
    • Williams, M.L.1
  • 82
    • 0009107948 scopus 로고    scopus 로고
    • The mode-III full-field solution in elastic materials with strain gradient effects
    • Zhang L., Huang Y., Chen J.Y., and Hwang K.C. 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


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.