메뉴 건너뛰기




Volumn 13, Issue 1, 2006, Pages 151-167

On the rate-independent limit of systems with dry friction and small viscosity

Author keywords

Arc length parameterization; Differential inclusion; Dry friction; Nonconvex energy; Rate independence; Viscous slip

Indexed keywords


EID: 33645145027     PISSN: 09446532     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article
Times cited : (133)

References (27)
  • 1
    • 0003282411 scopus 로고
    • Opérateurs Maximaux Monotones et Semi-Groupes de Contractions dans les Espaces de Hilbert
    • [Bre73] Notas de Matemática (50), North-Holland, Amsterdam
    • [Bre73] H. Brezis: Opérateurs Maximaux Monotones et Semi-Groupes de Contractions dans les Espaces de Hilbert, North-Holland Mathematics Studies 5, Notas de Matemática (50), North-Holland, Amsterdam (1973).
    • (1973) North-Holland Mathematics Studies , vol.5
    • Brezis, H.1
  • 3
    • 0001630191 scopus 로고
    • On a class of doubly nonlinear evolution equations
    • [CoV90]
    • [CoV90] P. Colli, A. Visintin: On a class of doubly nonlinear evolution equations, Commun. Partial Differ. Equations 15(5) (1990) 737-756.
    • (1990) Commun Partial Differ. Equations , vol.15 , Issue.5 , pp. 737-756
    • Colli, P.1    Visintin, A.2
  • 4
    • 0003197193 scopus 로고
    • Weak continuity and weak lower semicontinuity of nonlinear functionals
    • [Dac82] Springer, Berlin
    • [Dac82] B. Dacorogna: Weak Continuity and Weak Lower Semicontinuity of Nonlinear Functionals, Lecture Notes in Math. 922, Springer, Berlin (1982).
    • (1982) Lecture Notes in Math. , vol.922
    • Dacorogna, B.1
  • 5
    • 12144274208 scopus 로고    scopus 로고
    • On the compactness of the stable set for rate-independent processes
    • [Efe03]
    • [Efe03] M. Efendiev: On the compactness of the stable set for rate-independent processes, Comm. Pure Applied Analysis 2 (2003) 495-509.
    • (2003) Comm. Pure Applied Analysis , vol.2 , pp. 495-509
    • Efendiev, M.1
  • 7
    • 33644926777 scopus 로고    scopus 로고
    • Existence results for a class of rate-independent material models with nonconvex elastic energies
    • [FrM05] to appear
    • [FrM05] G. Francfort, A. Mielke: Existence results for a class of rate-independent material models with nonconvex elastic energies, J. Reine Angew. Math., 2005, to appear.
    • (2005) J. Reine Angew. Math.
    • Francfort, G.1    Mielke, A.2
  • 8
    • 0032144210 scopus 로고    scopus 로고
    • Mathematical analysis of a two degree-of-freedom frictional contact problem with discontinuous solutions
    • [GMM98]
    • [GMM98] F. Gastaldi, M. D. P. M. Marques, J. A. C. Martins: Mathematical analysis of a two degree-of-freedom frictional contact problem with discontinuous solutions, Math. Comput. Modelling 28 (1998) 247-261.
    • (1998) Math. Comput. Modelling , vol.28 , pp. 247-261
    • Gastaldi, F.1    Marques, M.D.P.M.2    Martins, J.A.C.3
  • 9
    • 0001567874 scopus 로고
    • Computational plasticity: The variational basis and numerical analysis
    • [HaR95]
    • [HaR95] W. Han, B. D. Reddy: Computational plasticity: The variational basis and numerical analysis, Comput. Mech. Adv. 2(4) (1995) 283-400.
    • (1995) Comput. Mech. Adv. , vol.2 , Issue.4 , pp. 283-400
    • Han, W.1    Reddy, B.D.2
  • 11
    • 22644452642 scopus 로고    scopus 로고
    • Flow properties for Young-measure solutions of semilinear hyperbolic problems
    • [Mie99]
    • [Mie99] A. Mielke: Flow properties for Young-measure solutions of semilinear hyperbolic problems, Proc. R. Soc. Edinb., Sect. A 129 (1999) 85-123.
    • (1999) Proc. R. Soc. Edinb., Sect. A , vol.129 , pp. 85-123
    • Mielke, A.1
  • 12
    • 8644238070 scopus 로고    scopus 로고
    • Deriving new evolution equations for microstructures via relaxation of variational incremental problems
    • [Mie04]
    • [Mie04] A. Mielke: Deriving new evolution equations for microstructures via relaxation of variational incremental problems, Comput. Methods Appl. Mech. Eng. 193 (2004) 5095-5127.
    • (2004) Comput. Methods Appl. Mech. Eng. , vol.193 , pp. 5095-5127
    • Mielke, A.1
  • 13
    • 66049141597 scopus 로고    scopus 로고
    • Evolution in rate-independent systems
    • [Mie05] (Ch. 6), C. Dafermos, E. Feireisl (eds.), Elsevier B.V.
    • [Mie05] A. Mielke: Evolution in rate-independent systems (Ch. 6), in: Handbook of Differential Equations, Evolutionary Equations, Vol. 2, C. Dafermos, E. Feireisl (eds.), Elsevier B.V. (2005) 461-559.
    • (2005) Handbook of Differential Equations, Evolutionary Equations , vol.2 , pp. 461-559
    • Mielke, A.1
  • 14
    • 33846216461 scopus 로고    scopus 로고
    • Existence and uniqueness results for general rate-independent hysteresis problems
    • [MiR05] submitted
    • [MiR05] A. Mielke, R. Rossi: Existence and uniqueness results for general rate-independent hysteresis problems, M3AS Model. Math. Meth. Appl. Sci., 2005, submitted.
    • (2005) M3AS Model. Math. Meth. Appl. Sci.
    • Mielke, A.1    Rossi, R.2
  • 15
    • 0002902403 scopus 로고    scopus 로고
    • A mathematical model for rate-independent phase transformations with hysteresis
    • [MiT99] H.-D. Alber, R. Balean, R. Farwig (eds.), Shaker
    • [MiT99] A. Mielke, F. Theil: A mathematical model for rate-independent phase transformations with hysteresis, in: Proceedings of the Workshop on "Models of Continuum Mechanics in Analysis and Engineering", H.-D. Alber, R. Balean, R. Farwig (eds.), Shaker (1999) 117-129.
    • (1999) Proceedings of the Workshop on "Models of Continuum Mechanics in Analysis and Engineering" , pp. 117-129
    • Mielke, A.1    Theil, F.2
  • 16
    • 3042535426 scopus 로고    scopus 로고
    • On rate-independent hysteresis models, NoDEA
    • [MiT04] (accepted July 2001)
    • [MiT04] A. Mielke, F. Theil: On rate-independent hysteresis models, NoDEA, Nonl. Diff. Eqns. Appl. 11 (2004) 151-189, (accepted July 2001).
    • (2004) Nonl. Diff. Eqns. Appl. , vol.11 , pp. 151-189
    • Mielke, A.1    Theil, F.2
  • 17
    • 0000356994 scopus 로고
    • On an example of nonexistence of solution to a quasistatic frictional contact problem
    • [MMG94]
    • [MMG94] J. A. C. Martins, M. D. P. Monteiro Marques, F. Gastaldi: On an example of nonexistence of solution to a quasistatic frictional contact problem, Eur. J. Mech., A 13 (1994) 113-133.
    • (1994) Eur. J. Mech., A , vol.13 , pp. 113-133
    • Martins, J.A.C.1    Marques, M.D.P.M.2    Gastaldi, F.3
  • 19
    • 0003215925 scopus 로고
    • Application of convex analysis to the treatment of elastoplastic systems
    • [Mor76] P. Germain, B. Nayroles (eds.), Lecture Notes in Mathematics 503, Springer
    • [Mor76] J.-J. Moreau: Application of convex analysis to the treatment of elastoplastic systems, in: Applications of Methods of Functional Analysis to Problems in Mechanics, P. Germain, B. Nayroles (eds.), Lecture Notes in Mathematics 503, Springer (1976) 56-89.
    • (1976) Applications of Methods of Functional Analysis to Problems in Mechanics , pp. 56-89
    • Moreau, J.-J.1
  • 20
    • 0000003251 scopus 로고
    • Evolution problem associated with a moving convex set in a Hilbert space
    • [Mor77]
    • [Mor77] J.-J. Moreau: Evolution problem associated with a moving convex set in a Hilbert space, J. Differ. Equations 26(3) (1977) 347-374.
    • (1977) J. Differ. Equations , vol.26 , Issue.3 , pp. 347-374
    • Moreau, J.-J.1
  • 21
    • 0000644733 scopus 로고
    • On nonconvex subdifferential calculus in Banach spaces
    • [MoS95]
    • [MoS95] B. S. Mordukhovich, Y. H. Shao: On nonconvex subdifferential calculus in Banach spaces, J. Convex Analysis 2 (1995) 211-227.
    • (1995) J. Convex Analysis , vol.2 , pp. 211-227
    • Mordukhovich, B.S.1    Shao, Y.H.2
  • 22
    • 0000342069 scopus 로고
    • Dissipative graph solutions for a 2 degree-of-freedom quasistatic frictional contact problem
    • [MSGM95]
    • [MSGM95] J. A. C. Martins, F. M. F. Simões, F. Gastaldi, M. D. P. Monteiro Marques: Dissipative graph solutions for a 2 degree-of-freedom quasistatic frictional contact problem, Int. J. Eng. Sci. 33 (1995) 1959-1986.
    • (1995) Int. J. Eng. Sci. , vol.33 , pp. 1959-1986
    • Martins, J.A.C.1    Simões, F.M.F.2    Gastaldi, F.3    Marques, M.D.P.M.4
  • 23
    • 0036012128 scopus 로고    scopus 로고
    • A variational formulation of rate-independent phase transformations using an extremum principle
    • [MTL02]
    • [MTL02] A. Mielke, F. Theil, V. Levitas: A variational formulation of rate-independent phase transformations using an extremum principle, Arch. Ration. Mech. Anal. 162 (2002) 137-177.
    • (2002) Arch. Ration. Mech. Anal. , vol.162 , pp. 137-177
    • Mielke, A.1    Theil, F.2    Levitas, V.3
  • 24
    • 0038299240 scopus 로고    scopus 로고
    • The evolution and rate problems and the computation of all possible evolutions in quasi-static frictional contact
    • [PiM03]
    • [PiM03] A. Pinto da Costa, J. A. C. Martins: The evolution and rate problems and the computation of all possible evolutions in quasi-static frictional contact, Comput. Methods Appl. Mech. Eng. 192 (2003) 2791-2821.
    • (2003) Comput. Methods Appl. Mech. Eng. , vol.192 , pp. 2791-2821
    • Da Costa, A.P.1    Martins, J.A.C.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.