Linearized plastic plate models as Γ-limits of 3D finite elastoplasticity
ESAIM: Control, Optimisation and Calculus of Variations (2014)
- Volume: 20, Issue: 3, page 725-747
- ISSN: 1292-8119
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top- [1] E. Acerbi, G. Buttazzo and D. Percivale, A variational definition for the strain energy of an elastic string. J. Elasticity25 (1991) 137–148. Zbl0734.73094MR1111364
- [2] A. Bertram, An alternative approach to finite plasticity based on material isomorphisms. Int. J. Plasticity15 (1999) 353–374. Zbl1016.74009
- [3] C. Carstensen, K. Hackl and A. Mielke, Non-convex potentials and microstructures in finite-strain plasticity. R. Soc. London Proc. Ser. A Math. Phys. Eng. Sci.458 (2002) 299–317. Zbl1008.74016MR1889770
- [4] G. Dal Maso, An introduction to Γ-convergence. Boston, Birkhäuser (1993). Zbl0816.49001MR1201152
- [5] G. Dal Maso and G. Lazzaroni, Quasistatic crack growth in finite elasticity with non-interpenetration. Ann. Inst. Henri Poincaré Anal. Non Linéaire27 (2010) 257–290. Zbl1188.35205MR2580510
- [6] E. Davoli, Quasistatic evolution models for thin plates arising as low energy Γ-limits of finite plasticity. Preprint SISSA (2012), Trieste. Zbl06322950MR3211118
- [7] G.A. Francfort and A. Mielke, Existence results for a class of rate-independent material models with nonconvex elastic energies. J. Reine Angew. Math.595 (2006) 55–91. Zbl1101.74015MR2244798
- [8] G. Friesecke, R.D. James and S. Müller, A theorem on geometric rigidity and the derivation of nonlinear plate theory from three-dimensional elasticity. Comm. Pure Appl. Math.55 (2002) 1461–1506. Zbl1021.74024MR1916989
- [9] G. Friesecke, R.D. James and S. Müller, A hierarchy of plate models derived from nonlinear elasticity by Gamma-convergence. Arch. Rational Mech. Anal.180 (2006) 183–236. Zbl1100.74039MR2210909
- [10] M. Lecumberry and S. Müller, Stability of slender bodies under compression and validity of the Von Kármán theory. Arch. Ration. Mech. Anal.193 (2009) 255–310. Zbl1200.74060MR2525119
- [11] H. Le Dret and A. Raoult, The nonlinear membrane model as variational limit of nonlinear three-dimensional elasticity. J. Math. Pures Appl.74 (1995) 549–578. Zbl0847.73025MR1365259
- [12] E.H. Lee, Elastic-plastic deformation at finite strains. J. Appl. Mech.36 (1969) 1–6. Zbl0179.55603
- [13] M. Liero and A. Mielke, An evolutionary elastoplastic plate model derived via Γ-convergence. Math. Models Methods Appl. Sci.21 (2011) 1961–1986. Zbl1232.35165MR2843026
- [14] M. Liero and T. Roche, Rigorous derivation of a plate theory in linear elastoplasticity via Γ-convergence. NoDEA Nonlinear Differ. Eqs. Appl.19 (2012) 437–457. Zbl1253.35180MR2949627
- [15] A. Mainik and A. Mielke, Global existence for rate-independent gradient plasticity at finite strain. J. Nonlinear Sci.19 (2009) 221–248. Zbl1173.49013MR2511255
- [16] J. Mandel, Equations constitutive et directeur dans les milieux plastiques et viscoplastique. Int. J. Sol. Struct.9 (1973) 725–740. Zbl0255.73004
- [17] A. Mielke, Energetic formulation of multiplicative elasto-plasticity using dissipation distances. Contin. Mech. Thermodyn.15 (2003) 351–382. Zbl1068.74522MR1999280
- [18] A. Mielke, Finite elastoplasticity, Lie groups and geodesics on SL(d), Geometry, Dynamics, and Mechanics. Springer, New York (2002) 61–90. Zbl1146.74309MR1919826
- [19] A. Mielke and U. Stefanelli, Linearized plasticity is the evolutionary Gamma-limit of finite plasticity. J. Eur. Math. Soc.15 (2013) 923–948. Zbl1334.74021MR3085096
- [20] P.M. Naghdi, A critical review of the state of finite plasticity. Z. Angew. Math. Phys.41 (1990) 315–394. Zbl0712.73032MR1058818