메뉴 건너뛰기




Volumn 3, Issue 2, 2010, Pages 149-212

A comparative analysis on variational models for quasi-static brittle crack propagation

Author keywords

Brittle fracture; Quasi static propagation

Indexed keywords


EID: 77956409151     PISSN: 18648258     EISSN: 18648266     Source Type: Journal    
DOI: 10.1515/ACV.2010.008     Document Type: Article
Times cited : (30)

References (33)
  • 3
  • 5
    • 0003353189 scopus 로고    scopus 로고
    • Hysteresis and phase transitions
    • Springer-Verlag, New York
    • M. Brokate and J. Sprekels, Hysteresis and Phase Transitions, Applied Mathematical Sciences 121, Springer-Verlag, New York, 1996.
    • (1996) Applied Mathematical Sciences , vol.121
    • Brokate, M.1    Sprekels, J.2
  • 6
    • 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
  • 7
    • 0038806783 scopus 로고    scopus 로고
    • A density result in two-dimensional linearized elasticity, and applications
    • DOI 10.1007/s00205-002-0240-7
    • A. Chambolle, A density result in two-dimensional linearized elasticity and applications, Arch. Ration. Mech. Anal. 167(2003), 211-233. (Pubitemid 36737532)
    • (2003) Archive for Rational Mechanics and Analysis , vol.167 , Issue.3 , pp. 211-233
    • Chambolle, A.1
  • 9
    • 68149097899 scopus 로고    scopus 로고
    • A 1D variational formulation for quasibrittle fracture
    • C. Comi, S. Mariani, M. Negri and U. Perego, A 1D variational formulation for quasibrittle fracture, J. Mech. Mater. Struct. 1(2006), 1323-1343.
    • (2006) J. Mech. Mater. Struct. , vol.1 , pp. 1323-1343
    • Comi, C.1    Mariani, S.2    Negri, M.3    Perego, U.4
  • 10
    • 0036952081 scopus 로고    scopus 로고
    • A model for the quasi-static growth of brittle fractures based on local minimization
    • DOI 10.1142/S0218202502002331
    • G. Dal Maso and R. Toader, A model for the quasi-static growth of brittle fractures based on local minimization, Math. Models Methods Appl. Sci. 12(2002), 1773-1799. (Pubitemid 36086692)
    • (2002) Mathematical Models and Methods in Applied Sciences , vol.12 , Issue.12 , pp. 1773-1799
    • Dal Maso, G.1    Toader, R.2
  • 11
    • 0036557535 scopus 로고    scopus 로고
    • A model for the quasi-static growth of brittle fractures: Existence and approximation results
    • DOI 10.1007/s002050100187
    • -. A model for the quasi-static growth of brittle fractures: existence and approximation results, Arch. Ration. Mech. Anal. 162(2002), 101-135. (Pubitemid 36195113)
    • (2002) Archive for Rational Mechanics and Analysis , vol.162 , Issue.2 , pp. 101-135
    • Dal Maso, G.1    Toader, R.2
  • 12
    • 0019392367 scopus 로고
    • Sur une interprétation mathématique de l'intégrale de Rice en théorie de la rupture fragile
    • P. Destuynder and M. Djaoua, Sur une interprétation mathématique de l'intégrale de Rice en théorie de la rupture fragile, Math. Methods Appl. Sci. 3(1981), 70-87.
    • (1981) Math. Methods Appl. Sci. , vol.3 , pp. 70-87
    • Destuynder, P.1    Djaoua, M.2
  • 13
    • 33645145027 scopus 로고    scopus 로고
    • On the rate-independent limit of systems with dry friction and small viscosity
    • M. A. Efendiev and A. Mielke, On the rate-independent limit of systems with dry friction and small viscosity, J. Convex Anal. 13(2006), 151-167. (Pubitemid 43449198)
    • (2006) Journal of Convex Analysis , vol.13 , Issue.1 , pp. 151-167
    • Efendiev, M.A.1    Mielke, A.2
  • 15
    • 0042859940 scopus 로고    scopus 로고
    • Existence and convergence for quasi-static evolution in brittle fracture
    • G. A. Francfort and C. J. Larsen, Existence and convergence for quasi-static evolution in brittle fracture, Commun. Pure Appl. Math. 56(2003), 1465-1500.
    • (2003) Commun. Pure Appl. Math. , vol.56 , pp. 1465-1500
    • Francfort, G.A.1    Larsen, C.J.2
  • 16
    • 0032139947 scopus 로고    scopus 로고
    • Revisiting brittle fracture as an energy minimization problem
    • PII S0022509698000349
    • G. A. Francfort and J. J. Marigo, Revisiting brittle fracture as an energy minimization problem, J. Mech. Phys. Solids 46(1998), 1319-1342. (Pubitemid 128424834)
    • (1998) Journal of the Mechanics and Physics of Solids , vol.46 , Issue.8 , pp. 1319-1342
    • Francfort, G.A.1    Marigo, J.-J.2
  • 19
    • 0000357002 scopus 로고
    • The phenomena of rupture and flow in solids
    • A. A. Griffith, The phenomena of rupture and flow in solids, Phil. Trans. Roy. Soc. London 18(1920), 163-198.
    • (1920) Phil. Trans. Roy. Soc. London , vol.18 , pp. 163-198
    • Griffith, A.A.1
  • 20
    • 0003320921 scopus 로고
    • Elliptic problems in nonsmooth domains
    • Pitman Advanced Publishing Program, Boston, MA
    • P. Grisvard, Elliptic Problems in Nonsmooth Domains, Monographs and Studies in Mathematics 24, Pitman (Advanced Publishing Program), Boston, MA, 1985.
    • (1985) Monographs and Studies in Mathematics , vol.24
    • Grisvard, P.1
  • 22
    • 0032263672 scopus 로고    scopus 로고
    • Energy balance in dynamic fracture, investigated by a potential drop technique
    • J. A. Hauch and M. Marder, Energy balance in dynamic fracture, investigated by a potential drop technique, Int. J. Fracture 90(1998), 133-151.
    • (1998) Int. J. Fracture , vol.90 , pp. 133-151
    • Hauch, J.A.1    Marder, M.2
  • 23
    • 53049087113 scopus 로고    scopus 로고
    • On the inviscid limit of a model for crack propagation
    • D. Knees, A. Mielke and C. Zanini, On the inviscid limit of a model for crack propagation, Math. Models Methods Appl. Sci. 18(2008), 1529-1569.
    • (2008) Math. Models Methods Appl. Sci. , vol.18 , pp. 1529-1569
    • Knees, D.1    Mielke, A.2    Zanini, C.3
  • 24
    • 84858399169 scopus 로고    scopus 로고
    • Epsilon-stable quasi-static brittle fracture evolution, to appear in
    • C. J. Larsen, Epsilon-stable quasi-static brittle fracture evolution, to appear in Commun. Pure Appl. Math.
    • Commun. Pure Appl. Math.
    • Larsen, C.J.1
  • 25
    • 46749100683 scopus 로고    scopus 로고
    • A class of minimum principles for characterizing the trajectories and the relaxation of dissipative systems
    • A. Mielke and M. Ortiz, A class of minimum principles for characterizing the trajectories and the relaxation of dissipative systems, ESAIM Control Optim. Calc. Va r. 14(2008), 494-516.
    • (2008) ESAIM Control Optim. Calc. Va R. , vol.14 , pp. 494-516
    • Mielke, A.1    Ortiz, M.2
  • 26
    • 84858424858 scopus 로고    scopus 로고
    • Modeling solutions with jumps for rate-independent systems on metric spaces
    • A. Mielke, R. Rossi and G. Savaré, Modeling solutions with jumps for rate-independent systems on metric spaces, WIAS, Report no. 1347, 2008.
    • (2008) WIAS, Report No. 1347
    • Mielke, A.1    Rossi, R.2    Savaré, G.3
  • 27
    • 76649108874 scopus 로고    scopus 로고
    • From rate-dependent to rate-independent brittle crack propagation
    • M. Negri, From rate-dependent to rate-independent brittle crack propagation, to appear in J. Elast.
    • J. Elast.
    • Negri, M.1
  • 28
    • 84858423078 scopus 로고    scopus 로고
    • Quasi-static propagation of brittle fracture by Griffith's criterion
    • in press
    • M. Negri and C. Ortner, Quasi-static propagation of brittle fracture by Griffith's criterion, Math. Models Methods Appl. Sci. 12(2008), in press.
    • (2008) Math. Models Methods Appl. Sci. , vol.12
    • Negri, M.1    Ortner, C.2
  • 29
    • 0033611510 scopus 로고    scopus 로고
    • Confirming the continuum theory of dynamic brittle fracture for fast cracks
    • E. Sharon and J. Fineberg, Confirming the continuum theory of dynamic brittle fracture for fast cracks, Nature 397(1999).
    • (1999) Nature , vol.397
    • Sharon, E.1    Fineberg, J.2
  • 30
    • 0001064953 scopus 로고    scopus 로고
    • Energy dissipation in dynamic fracture
    • E. Sharon, S. P. Gross and J. Fineberg, Energy dissipation in dynamic fracture, Phys. Rev. Lett. 76(1996), 2117-2120. (Pubitemid 126638945)
    • (1996) Physical Review Letters , vol.76 , Issue.12 , pp. 2117-2120
    • Sharon, E.1    Gross, S.P.2    Fineberg, J.3
  • 31
    • 60749102423 scopus 로고    scopus 로고
    • An artificial viscosity approach to quasi-static crack growth
    • R. Toader and C. Zanini, An artificial viscosity approach to quasi-static crack growth, Boll. Unione Mat. Ital. Sez. B 2:1(2009), 1-35.
    • (2009) Boll. Unione Mat. Ital. Sez. B , vol.2 , Issue.1 , pp. 1-35
    • Toader, R.1    Zanini, C.2
  • 32
    • 0012659452 scopus 로고
    • Differential models of hysteresis
    • Springer-Verlag, Berlin
    • A. Visintin, Differential Models of Hysteresis, Applied Mathematical Sciences 111, Springer-Verlag, Berlin, 1994.
    • (1994) Applied Mathematical Sciences , vol.111
    • Visintin, A.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.