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Volumn 12, Issue 4, 2013, Pages 1705-1729

A cohesive crack propagation model: Mathematical theory and numerical solution

Author keywords

Cohesive elements; Crack problems; Energy minimization

Indexed keywords


EID: 84873323353     PISSN: 15340392     EISSN: 15535258     Source Type: Journal    
DOI: 10.3934/cpaa.2013.12.1705     Document Type: Article
Times cited : (14)

References (40)
  • 1
    • 0000357002 scopus 로고
    • The phenomena of rupture and ow in solids
    • A. A. Griffith, The phenomena of rupture and ow in solids, Philos Trans R Soc Lond A, 221 (1921), 163-98.
    • (1921) Philos Trans R Soc Lond A , vol.221 , pp. 163-198
    • Griffith, A.A.1
  • 3
    • 77649193465 scopus 로고
    • The mathematical theory of equilibrium cracks in brittle fracture
    • G. I. Barenblatt, The mathematical theory of equilibrium cracks in brittle fracture, Advan. Appl. Mech., 7 (1962), 55-129.
    • (1962) Advan. Appl. Mech , vol.7 , pp. 55-129
    • Barenblatt, G.I.1
  • 4
    • 0025641438 scopus 로고
    • Variational principles of nonlinear fracture mechanics
    • H. Stumpf and K. Ch. Le, Variational principles of nonlinear fracture mechanics, Acta Mech, 83 (1990), 25-37.
    • (1990) Acta Mech , vol.83 , pp. 25-37
    • Stumpf, H.1    Le, K.C.H.2
  • 5
    • 0026455428 scopus 로고
    • Pseudomomentum and material forces in nonlinear elasticity: Variational formulations and application to brittle fracture
    • G. A. Maugin and C. Trimarco, Pseudomomentum and material forces in nonlinear elasticity: variational formulations and application to brittle fracture, Acta Mech, 94 (1992), 1-28.
    • (1992) Acta Mech , vol.94 , pp. 1-28
    • Maugin, G.A.1    Trimarco, C.2
  • 6
    • 20444369477 scopus 로고
    • The continuum theory of lattice defects
    • (F. Seitz and D. Turnbull eds.), New York: Academic Press, Volume
    • J. D. Eshelby, The continuum theory of lattice defects, in "Progress in Solids State Physics" (F. Seitz and D. Turnbull eds.), New York: Academic Press, Volume 3, 1956.
    • (1956) Progress in Solids State Physics , vol.3
    • Eshelby, J.D.1
  • 7
    • 84980287971 scopus 로고
    • A path independent integral and the approximate analysis of strain concentraction by notches and cracks
    • J. R. Rice, A path independent integral and the approximate analysis of strain concentraction by notches and cracks, J. Appl. Mech., 35 (1968), 379-86.
    • (1968) J. Appl. Mech , vol.35 , pp. 379-386
    • Rice, J.R.1
  • 8
    • 0032259287 scopus 로고    scopus 로고
    • Energy minimizing brittle crack propagation
    • M. Buliga, Energy minimizing brittle crack propagation, J Elast, 52 (1999), 201-238.
    • (1999) J Elast , vol.52 , pp. 201-238
    • Buliga, M.1
  • 9
    • 0003212755 scopus 로고
    • The variational approach to fracture
    • N. Kikuchi and J. T. Oden, "The Variational Approach to Fracture," SIAM, 1988.
    • (1988) SIAM
    • Kikuchi, N.1    Oden, J.T.2
  • 13
    • 49349121254 scopus 로고
    • Continuing crack-tip deformation and fracture for plane-strain crack growth in elastic-plastic solids
    • J. R. Rice and E. P. Sorensen, Continuing crack-tip deformation and fracture for plane-strain crack growth in elastic-plastic solids, J Mech Phys Solids, 26 (1978), 163-86.
    • (1978) J Mech Phys Solids , vol.26 , pp. 163-186
    • Rice, J.R.1    Sorensen, E.P.2
  • 14
  • 15
    • 0032649861 scopus 로고    scopus 로고
    • Elastic crack growth in finite elements with minimal remeshing
    • T. Belytschko and T. Black, Elastic crack growth in finite elements with minimal remeshing, Int J Numer Methods Eng, 45 (1999), 601-620.
    • (1999) Int J Numer Methods Eng , vol.45 , pp. 601-620
    • Belytschko, T.1    Black, T.2
  • 16
    • 0027544926 scopus 로고
    • Micromechanical model for comminution and granular ow of brittle material under high strain rate application to penetration of ceramic targets
    • D. R. Curran, L. Seaman, T. Cooper and D. A. Shockey, Micromechanical model for comminution and granular ow of brittle material under high strain rate application to penetration of ceramic targets, Int J Impact Eng, 13 (1993), 53-83.
    • (1993) Int J Impact Eng , vol.13 , pp. 53-83
    • Curran, D.R.1    Seaman, L.2    Cooper, T.3    Shockey, D.A.4
  • 17
    • 0023410904 scopus 로고
    • A continuum model for void nucleation by inclusion debonding
    • A. Needleman, A continuum model for void nucleation by inclusion debonding, J. Appl. Mech., 54 (1987), 525-531.
    • (1987) J. Appl. Mech , vol.54 , pp. 525-531
    • Needleman, A.1
  • 18
    • 50549180512 scopus 로고
    • Yielding of steel sheets containing slits
    • D. S. Dugdale, Yielding of steel sheets containing slits, J Mech Phys Solids, 8 (1960), 100-104.
    • (1960) J Mech Phys Solids , vol.8 , pp. 100-104
    • Dugdale, D.S.1
  • 19
    • 0141663695 scopus 로고
    • The inuence of plasticity on mixed mode interface toughness
    • V. Tvergaard and J. W. Hutchinson, The inuence of plasticity on mixed mode interface toughness, J Mech Phys Solids, 41 (1993), 1119-1135.
    • (1993) J Mech Phys Solids , vol.41 , pp. 1119-1135
    • Tvergaard, V.1    Hutchinson, J.W.2
  • 20
    • 0030212427 scopus 로고    scopus 로고
    • Computational modelling of impact damage in brittle materials
    • G. T. Camacho and M. Ortiz, Computational modelling of impact damage in brittle materials, Int J Solids Struct, 33 (1996), 2899-2938.
    • (1996) Int J Solids Struct , vol.33 , pp. 2899-2938
    • Camacho, G.T.1    Ortiz, M.2
  • 21
    • 0028497372 scopus 로고
    • Numerical simulations of fast crack growth in brittle solids
    • X.-P. Xu and A. Needleman, Numerical simulations of fast crack growth in brittle solids, Mech Phys Solids, 42 (1994), 1397-1434.
    • (1994) Mech Phys Solids , vol.42 , pp. 1397-1434
    • Xu, X.-P.1    Needleman, A.2
  • 22
    • 0033097151 scopus 로고    scopus 로고
    • Finite-deformation irreversible cohesive elements for threedimensional crack-propagation analysis
    • M. Ortiz and A. Pandolfi, Finite-deformation irreversible cohesive elements for threedimensional crack-propagation analysis, Int J Numer Methods Eng, 44 (1999), 1267-1282.
    • (1999) Int J Numer Methods Eng , vol.44 , pp. 1267-1282
    • Ortiz, M.1    Pandolfi, A.2
  • 23
    • 3843067674 scopus 로고    scopus 로고
    • Computational modeling of damage evolution in unidirectional fiber reinforced ceramic matrix composites
    • M. E. Walter, G. Ravichandran and M. Ortiz, Computational modeling of damage evolution in unidirectional fiber reinforced ceramic matrix composites, Computational Mechanics, 20 (1997), 192-198.
    • (1997) Computational Mechanics , vol.20 , pp. 192-198
    • Walter, M.E.1    Ravichandran, G.2    Ortiz, M.3
  • 24
    • 3242686284 scopus 로고    scopus 로고
    • A hybrid discontinuous Galerkin/interface method for the computational modelling of failure
    • J. Mergheim, E. Kuhl and P. Steinmann, A hybrid discontinuous Galerkin/interface method for the computational modelling of failure, Commun Numer Methods Eng, 20 (2004), 511-519.
    • (2004) Commun Numer Methods Eng , vol.20 , pp. 511-519
    • Mergheim, J.1    Kuhl, E.2    Steinmann, P.3
  • 25
    • 17244363448 scopus 로고    scopus 로고
    • Nonconvex problem for crack with nonpenetration
    • V. A. Kovtunenko, Nonconvex problem for crack with nonpenetration, ZAMM Z. Angew. Math. Mech., 85 (2005), 242-251.
    • (2005) ZAMM Z. Angew. Math. Mech , vol.85 , pp. 242-251
    • Kovtunenko, V.A.1
  • 26
    • 22944473896 scopus 로고
    • An introduction to composite materials
    • (R. W. Cahn, M. W. Thompson and I. M. Ward eds.), Cambridge University Press
    • D. Hull, An introduction to composite materials, in "Cambridge Solid State Science Series" (R. W. Cahn, M. W. Thompson and I. M. Ward eds.), Cambridge University Press, 1981, 1-246.
    • (1981) Cambridge Solid State Science Series , pp. 1-246
    • Hull, D.1
  • 27
  • 28
    • 13944279600 scopus 로고    scopus 로고
    • A rate-dependent cohesive model for simulating dynamic crack propagation in brittle materials
    • F. Zhou, J.F. Molinari and T. Shioya, A rate-dependent cohesive model for simulating dynamic crack propagation in brittle materials, Eng Fract Mech, 72 (2005), 1383-1410.
    • (2005) Eng Fract Mech , vol.72 , pp. 1383-1410
    • Zhou, F.1    Molinari, J.F.2    Shioya, T.3
  • 29
    • 72049087213 scopus 로고    scopus 로고
    • Time-dependent cohesive zone modelling for discrete fracture simulation
    • G. Geissler and M. Kaliske, Time-dependent cohesive zone modelling for discrete fracture simulation, Eng Fract Mech, 77 (2010), 153-169.
    • (2010) Eng Fract Mech , vol.77 , pp. 153-169
    • Geissler, G.1    Kaliske, M.2
  • 30
    • 0027573936 scopus 로고
    • Fundamental issues in finite element analyses of localization of deformation
    • R. De Borst, L. J. Sluys, H.-B. Mühlhaus and J. Pamin, Fundamental issues in finite element analyses of localization of deformation, Engineering Computations, 10 (1993), 99-121.
    • (1993) Engineering Computations , vol.10 , pp. 99-121
    • De Borst, R.1    Sluys, L.J.2    Mühlhaus, H.-B.3    Pamin, J.4
  • 32
    • 67649359327 scopus 로고    scopus 로고
    • Regularized formulation of the variational brittle fracture with unilateral contact: Numerical experiments
    • H. Amor, J.-J. Marigo and C. Maurini, Regularized formulation of the variational brittle fracture with unilateral contact: Numerical experiments, J. Mech. Phys. Solids, 57 (2009), 1209-1229.
    • (2009) J. Mech. Phys. Solids , vol.57 , pp. 1209-1229
    • Amor, H.1    Marigo, J.-J.2    Maurini, C.3
  • 33
    • 79953030125 scopus 로고    scopus 로고
    • Towards optimization of crack resistance of composite materials by adjustment of fiber shapes Reference
    • M. Prechtel, G. Leugering, P. Steinmann and M. Stingl, Towards optimization of crack resistance of composite materials by adjustment of fiber shapes Reference, Eng Fract Mech, 78 (2011), 944-960.
    • (2011) Eng Fract Mech , vol.78 , pp. 944-960
    • Prechtel, M.1    Leugering, G.2    Steinmann, P.3    Stingl, M.4
  • 36
    • 29144523061 scopus 로고    scopus 로고
    • On the implementation of a primal-dual interior point filter line search algorithm for large-scale nonlinear programming
    • A. Wächter and L. T. Biegler, On the implementation of a primal-dual interior point filter line search algorithm for large-scale nonlinear programming, Mathematical Programming, 106 (2006), 25-57.
    • (2006) Mathematical Programming , vol.106 , pp. 25-57
    • Wächter, A.1    Biegler, L.T.2
  • 37
    • 79960584035 scopus 로고    scopus 로고
    • Obstacle problems with cohesion: A hemivariational inequality approach and its efficient numerical solution
    • M. Hintermüller, V. A. Kovtunenko and K. Kunisch, Obstacle problems with cohesion: a hemivariational inequality approach and its efficient numerical solution, SIAM J Optim, 21 (2011), 491-516.
    • (2011) SIAM J Optim , vol.21 , pp. 491-516
    • Hintermüller, M.1    Kovtunenko, V.A.2    Kunisch, K.3
  • 38
    • 84858217734 scopus 로고    scopus 로고
    • A hemivariational inequality in crack problems
    • doi: 10.1080/02331934.2010.534477
    • V. A. Kovtunenko, A hemivariational inequality in crack problems, Optimization, doi: 10.1080/02331934.2010.534477.
    • Optimization
    • Kovtunenko, V.A.1
  • 39
    • 0037150396 scopus 로고    scopus 로고
    • Some issues in the application of cohesive zone models for metal-ceramic interfaces
    • N. Chandra, H. Li, C. Shet and H. Ghonem, Some issues in the application of cohesive zone models for metal-ceramic interfaces, Int J Solid Struct, 39 (2002), 2827-2855.
    • (2002) Int J Solid Struct , vol.39 , pp. 2827-2855
    • Chandra, N.1    Li, H.2    Shet, C.3    Ghonem, H.4
  • 40
    • 0001526041 scopus 로고
    • Origins of the universal binding-energy relation
    • A. Banerjea and J. R. Smith, Origins of the universal binding-energy relation, Phys Rev B, 37 (1988), 6632-6645.
    • (1988) Phys Rev B , vol.37 , pp. 6632-6645
    • Banerjea, A.1    Smith, J.R.2


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