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Volumn 40, Issue 2, 2008, Pages 623-652

A variational principle for hardening elastoplasticity

Author keywords

Approximation; Elastoplasticity; Variational principle

Indexed keywords

APPROXIMATION; DISCRETIZATIONS; ELASTO-PLASTIC MATERIALS; LINEAR HARDENINGS; POSTERIORI ERROR CONTROLS; QUASI-STATIC EVOLUTIONS; TIME AND SPACES; VARIATIONAL PRINCIPLE;

EID: 63849300447     PISSN: 00361410     EISSN: None     Source Type: Journal    
DOI: 10.1137/070692571     Document Type: Article
Times cited : (26)

References (49)
  • 2
    • 84972497571 scopus 로고
    • Saddle-points and existence-uniqueness for evolution equations
    • G. AUCHMUTY, Saddle-points and existence-uniqueness for evolution equations, Differential Integral Equations, 6 (1993), pp. 1161-1171.
    • (1993) Differential Integral Equations , vol.6 , pp. 1161-1171
    • AUCHMUTY, G.1
  • 3
    • 63849236917 scopus 로고    scopus 로고
    • H. BREZIS AND I. EKELAND, Un principe variationnel associé a certaines équations paraboliques. Le cas dépendant du temps, C. R. Acad. Sci. Paris Ser. A-B, 282 (1976), pp. Ai, A1197-A1198.
    • H. BREZIS AND I. EKELAND, Un principe variationnel associé a certaines équations paraboliques. Le cas dépendant du temps, C. R. Acad. Sci. Paris Ser. A-B, 282 (1976), pp. Ai, A1197-A1198.
  • 4
    • 63849198539 scopus 로고    scopus 로고
    • H. BREZIS AND I. EKELAND, Un principe variationnel associé à certaines équations paraboliques. Le cas indépendant du temps, C. R. Acad. Sci. Paris Sér. A-B, 282 (1976), pp. Aii, A971-A974.
    • H. BREZIS AND I. EKELAND, Un principe variationnel associé à certaines équations paraboliques. Le cas indépendant du temps, C. R. Acad. Sci. Paris Sér. A-B, 282 (1976), pp. Aii, A971-A974.
  • 5
    • 63849307586 scopus 로고    scopus 로고
    • G. DAL MASO, An Introduction to F-Convergence, Progr. Nonlinear Differential Equations Appl. 8, Birkhauser Boston, Cambridge, MA, 1993.
    • G. DAL MASO, An Introduction to F-Convergence, Progr. Nonlinear Differential Equations Appl. 8, Birkhauser Boston, Cambridge, MA, 1993.
  • 6
    • 33644607451 scopus 로고    scopus 로고
    • Quasistatic evolution problems for linearly elastic-perfectly plastic materials
    • G. DAL MASO, A. DESIMONE, AND M. G. MORA, Quasistatic evolution problems for linearly elastic-perfectly plastic materials, Arch. Ration. Mech. Anal., 180 (2006), pp. 237-291.
    • (2006) Arch. Ration. Mech. Anal , vol.180 , pp. 237-291
    • DAL MASO, G.1    DESIMONE, A.2    MORA, M.G.3
  • 8
    • 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), pp. 151-167.
    • (2006) J. Convex Anal , vol.13 , pp. 151-167
    • EFENDIEV, M.A.1    MIELKE, A.2
  • 9
    • 53549123225 scopus 로고    scopus 로고
    • Selfdual Partial Differential Systems and Their Variational Principles, Uni-versitext, Springer-Verlag, New York
    • to appear
    • N. GHOUSSOUB, Selfdual Partial Differential Systems and Their Variational Principles, Uni-versitext, Springer-Verlag, New York, to appear.
    • GHOUSSOUB, N.1
  • 10
    • 7544240584 scopus 로고    scopus 로고
    • A variational principle for gradient flows
    • N. GHOUSSOUB AND L. TZOU, A variational principle for gradient flows, Math. Ann., 330 (2004), pp. 519-549.
    • (2004) Math. Ann , vol.330 , pp. 519-549
    • GHOUSSOUB, N.1    TZOU, L.2
  • 12
    • 36148967714 scopus 로고    scopus 로고
    • Geometric Numerical Integration
    • 2nd ed, Springer-Verlag, Berlin
    • E. HAIRER, CH. LUBICH, AND G. WANNER, Geometric Numerical Integration, Springer Ser. Comput. Math. 31, 2nd ed., Springer-Verlag, Berlin, 2006.
    • (2006) Springer Ser. Comput. Math , vol.31
    • HAIRER, E.1    CH2    LUBICH3    WANNER, G.4
  • 14
    • 0034553904 scopus 로고    scopus 로고
    • Convergence of approximations to the primal problem in plasticity under conditions of minimal regularity
    • W. HAN AND B. D. REDDY, Convergence of approximations to the primal problem in plasticity under conditions of minimal regularity, Numer. Math., 87 (2000), pp. 283-315.
    • (2000) Numer. Math , vol.87 , pp. 283-315
    • HAN, W.1    REDDY, B.D.2
  • 15
    • 0001567874 scopus 로고
    • Computational plasticity: The variational basis and numerical analysis
    • W. HAN AND B. D. REDDY, Computational plasticity: The variational basis and numerical analysis, Comput. Mech. Adv., 2 (1995), pp. 283-400.
    • (1995) Comput. Mech. Adv , vol.2 , pp. 283-400
    • HAN, W.1    REDDY, B.D.2
  • 16
    • 63849169807 scopus 로고    scopus 로고
    • P. KREJČÍ, Hysteresis, Convexity and Dissipation in Hyperbolic Equations, GAKUTO Internat.Ser. Math. Sci. Appl. 8, Gakkotosho, Tokyo, 1996.
    • P. KREJČÍ, Hysteresis, Convexity and Dissipation in Hyperbolic Equations, GAKUTO Internat.Ser. Math. Sci. Appl. 8, Gakkotosho, Tokyo, 1996.
  • 17
    • 0347211612 scopus 로고    scopus 로고
    • An asymptotical variational principle associated with the steepest descent method for a convex function
    • B. LEMAIRE, An asymptotical variational principle associated with the steepest descent method for a convex function, J. Convex Anal., 3 (1996), pp. 63-70.
    • (1996) J. Convex Anal , vol.3 , pp. 63-70
    • LEMAIRE, B.1
  • 21
    • 0141703617 scopus 로고    scopus 로고
    • Un principe variationnel pour une équation non linéaire du second ordre entemps
    • M. MABROUK, Un principe variationnel pour une équation non linéaire du second ordre entemps, C. R. Acad. Sci. Paris Ser. I Math., 332 (2001), pp. 381-386.
    • (2001) C. R. Acad. Sci. Paris Ser. I Math , vol.332 , pp. 381-386
    • MABROUK, M.1
  • 22
    • 0141503449 scopus 로고    scopus 로고
    • A variational principle for a nonlinear differential equation of second order
    • M. MABROUK, A variational principle for a nonlinear differential equation of second order, Adv. Appl. Math., 31 (2003), pp. 388-419.
    • (2003) Adv. Appl. Math , vol.31 , pp. 388-419
    • MABROUK, M.1
  • 23
    • 12844266060 scopus 로고    scopus 로고
    • A F-convergence result for variational integrators of Lagrangians with quadratic growth
    • F. MAGGI AND M. MORINI, A F-convergence result for variational integrators of Lagrangians with quadratic growth, ESAIM Control Optim. Calc. Var., 10 (2004), pp. 656-665.
    • (2004) ESAIM Control Optim. Calc. Var , vol.10 , pp. 656-665
    • MAGGI, F.1    MORINI, M.2
  • 24
    • 0032476963 scopus 로고    scopus 로고
    • Multisymplectic geometry, variational integrators, and nonlinear PDEs
    • J. E. MARSDEN, G. W. PATRICK, AND S. SHKOLLER, Multisymplectic geometry, variational integrators, and nonlinear PDEs, Comm. Math. Phys., 199 (1998), pp. 351-395.
    • (1998) Comm. Math. Phys , vol.199 , pp. 351-395
    • MARSDEN, J.E.1    PATRICK, G.W.2    SHKOLLER, S.3
  • 25
    • 84959193128 scopus 로고    scopus 로고
    • Discrete mechanics and variational integrators
    • J. E. MARSDEN AND M. WEST, Discrete mechanics and variational integrators, Acta Numer.,10 (2001), pp. 357-514.
    • (2001) Acta Numer , vol.10 , pp. 357-514
    • MARSDEN, J.E.1    WEST, M.2
  • 26
    • 66049141597 scopus 로고    scopus 로고
    • Evolution of rate-independent systems
    • C. Dafermos and E. Feireisl, eds, Elsevier, New York
    • A. MIELKE, Evolution of rate-independent systems, in Handbook of Differential Equations, Evolutionary Equations, Vol. 2, C. Dafermos and E. Feireisl, eds., Elsevier, New York, 2005, pp. 461-559.
    • (2005) Handbook of Differential Equations, Evolutionary Equations , vol.2 , pp. 461-559
    • MIELKE, A.1
  • 27
    • 46749100683 scopus 로고    scopus 로고
    • A class of minimum principles for characterizing the trajectories and the relaxation of dissipative systems
    • to appear; also available online from
    • A. MIELKE AND M. ORTIZ, A class of minimum principles for characterizing the trajectories and the relaxation of dissipative systems, ESAIM Control Optim. Calc. Var., 2008, to appear; also available online from http://www.wias-berlin.de/main/publications/wias-publ/index.cgi.en.
    • (2008) ESAIM Control Optim. Calc. Var
    • MIELKE, A.1    ORTIZ, M.2
  • 29
    • 52249103512 scopus 로고    scopus 로고
    • A metric approach to a class of doubly nonlinear evolution equations and applications
    • also available online from
    • A. MIELKE, R. Rossi, AND G. SAVARÉ, A metric approach to a class of doubly nonlinear evolution equations and applications, Ann. Sc. Norm. Super. Pisa CI. Sci., 5 (2008), pp. 97-169; also available online from http://www.wias-berlin.de/main/publications/wias- publ/index.cgi.en.
    • (2008) Ann. Sc. Norm. Super. Pisa CI. Sci , vol.5 , pp. 97-169
    • MIELKE, A.1    Rossi, R.2    SAVARÉ, G.3
  • 33
    • 0000626499 scopus 로고
    • La notion de sur-potentiel et les liaisons unilatérales en élastostatique
    • J.-J. MOREAU, La notion de sur-potentiel et les liaisons unilatérales en élastostatique, C. R. Acad. Sci. Paris Sér. A-B, 267 (1968), pp. A954-A957.
    • (1968) C. R. Acad. Sci. Paris Sér. A-B , vol.267
    • MOREAU, J.-J.1
  • 35
    • 0039308744 scopus 로고
    • Sur I'évolution d'un système élasto-visco-plastique
    • PP- A118-A121
    • J.-J. MOREAU, Sur I'évolution d'un système élasto-visco-plastique, C. R. Acad. Sci. Paris Sér. A-B, 273 (1971), PP- A118-A121.
    • (1971) C. R. Acad. Sci. Paris Sér. A-B , vol.273
    • MOREAU, J.-J.1
  • 36
    • 0010671416 scopus 로고
    • Convergence of convex sets and of solutions of variational inequalities
    • U. MOSCO, Convergence of convex sets and of solutions of variational inequalities, Adv. Math., 3 (1969), pp. 510-585.
    • (1969) Adv. Math , vol.3 , pp. 510-585
    • MOSCO, U.1
  • 37
    • 84867951207 scopus 로고    scopus 로고
    • On the F-convergence of discrete dynamics and variational integrators
    • S. MULLER AND M. ORTIZ, On the F-convergence of discrete dynamics and variational integrators, J. Nonlinear Sci., 14 (2004), pp. 279-296.
    • (2004) J. Nonlinear Sci , vol.14 , pp. 279-296
    • MULLER, S.1    ORTIZ, M.2
  • 38
    • 63849314574 scopus 로고    scopus 로고
    • B. NAYROLES, Deux théorémes de minimum pour certains systèmes dissipatifs, C. R. Acad. Sci. Paris Ser. A-B, 282 (1976), pp. Aiv, A1035-A1038.
    • B. NAYROLES, Deux théorémes de minimum pour certains systèmes dissipatifs, C. R. Acad. Sci. Paris Ser. A-B, 282 (1976), pp. Aiv, A1035-A1038.
  • 40
    • 63849177574 scopus 로고    scopus 로고
    • H. RIos, Étude de la question d'existence pour certains problèmes dévolution par minimisation d'une fonctionnelle convexe, C. R. Acad. Sci. Paris Ser. A-B, 283 (1976), pp. Ai, A83-A86.
    • H. RIos, Étude de la question d'existence pour certains problèmes dévolution par minimisation d'une fonctionnelle convexe, C. R. Acad. Sci. Paris Ser. A-B, 283 (1976), pp. Ai, A83-A86.
  • 41
    • 55549119764 scopus 로고    scopus 로고
    • Direct method for parabolic problems
    • T. ROUBÍČEK, Direct method for parabolic problems, Adv. Math. Sci. Appl., 10 (2000), pp. 57-65.
    • (2000) Adv. Math. Sci. Appl , vol.10 , pp. 57-65
    • ROUBÍČEK, T.1
  • 43
    • 67949114206 scopus 로고    scopus 로고
    • The Discrete Brezis-Ekeland Principle
    • to appear, also available online from
    • U. STEFANELLI, The Discrete Brezis-Ekeland Principle, J. Convex. Anal., to appear, also available online from http://www.imati.cnr.it/ ulisse/pubbl.html.
    • J. Convex. Anal
    • STEFANELLI, U.1
  • 45
    • 55549128580 scopus 로고    scopus 로고
    • The Brezis-Ekeland principle for doubly nonlinear equations
    • to appear; also available online from
    • U. STEFANELLI, The Brezis-Ekeland principle for doubly nonlinear equations, SIAM J. Control Optim., to appear; also available online from http://www.imati.cnr.it/ulisse/pubbl.html.
    • SIAM J. Control Optim
    • STEFANELLI, U.1
  • 49
    • 35248889454 scopus 로고    scopus 로고
    • Singular perturbations of finite dimensional gradient flows
    • C. ZANINI, Singular perturbations of finite dimensional gradient flows, Discrete Contin. Dyn. Syst., 18 (2007), pp. 657-675.
    • (2007) Discrete Contin. Dyn. Syst , vol.18 , pp. 657-675
    • ZANINI, C.1


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