Free Access
Issue
ESAIM: M2AN
Volume 43, Number 3, May-June 2009
Page(s) 399 - 428
DOI https://doi.org/10.1051/m2an/2009009
Published online 08 April 2009
  1. E. Acerbi and and N. Fusco, Semicontinuity problems in the calculus of variations. Arch. Ration. Mech. Anal. 86 (1984) 125–145. [CrossRef] [MathSciNet] [Google Scholar]
  2. J. Alberty and C. Carstensen, Numerical analysis of time-dependent primal elastoplasticity with hardening. SIAM J. Numer. Anal. 37 (2000) 1271–1294. [CrossRef] [MathSciNet] [Google Scholar]
  3. M. Arndt, M. Griebel and T. Roubíček, Modelling and numerical simulation of martensitic transformation in shape memory alloys. Continuum Mech. Thermodyn. 15 (2003) 463–485. [CrossRef] [MathSciNet] [Google Scholar]
  4. M. Arndt, M. Griebel, V. Novák, T. Roubíček and P. Šittner, Martensitic transformation in NiMnGa single crystals: numerical simulations and experiments. Int. J. Plasticity 22 (2006) 1943–1961. [CrossRef] [Google Scholar]
  5. F. Auricchio and L. Petrini, Improvements and algorithmical considerations on a recent three-dimensional model describing stress-induced solid phase transformations. Int. J. Numer. Meth. Engng. 55 (2002) 1255–1284. [CrossRef] [Google Scholar]
  6. F. Auricchio, A. Mielke and U. Stefanelli, A rate-independent model for the isothermal quasi-static evolution of shape-memory materials. Math. Models Methods Appl. Sci. 18 (2008) 125–164. [CrossRef] [MathSciNet] [Google Scholar]
  7. B. Bourdin, G. Francfort and J.-J. Marigo, Numerical experiments in revisited brittle fracture. J. Mech. Phys. Solids 48 (2000) 797–826. [CrossRef] [MathSciNet] [Google Scholar]
  8. J.G. Boyd and D.C. Lagoudas, A thermodynamical constitutive model for shape memory materials, Part I. The monolithic shape memory alloys. Int. J. Plasticity 12 (1996) 805–842. [CrossRef] [Google Scholar]
  9. W.F. Brown, Magnetoelastic interactions, in Springer Tracts in Natural Philosophy 9, C. Truesdel Ed., Springer (1966). [Google Scholar]
  10. P. Colli and J. Sprekels, Global existence for a three-dimensional model for the thermo-mechanical evolution of shape memory alloys. Nonlinear Anal. 18 (1992) 873–888. [CrossRef] [MathSciNet] [Google Scholar]
  11. P. Colli, M. Frémond and A. Visintin, Thermo-mechanical evolution of shape memory alloys. Quarterly Appl. Math. 48 (1990) 31–47. [Google Scholar]
  12. S. Conti and M. Ortiz, Dislocation microstructures and effective behaviour of single crystals. Arch. Ration. Mech. Anal. 176 (2005) 103–147. [CrossRef] [MathSciNet] [Google Scholar]
  13. F. Falk, Model free energy, mechanics and thermodynamics of shape memory alloys. Acta Metall. 28 (1980) 1773–1780. [CrossRef] [Google Scholar]
  14. G. Francfort and A. Mielke, An existence result for a rate-independent material model in the case of nonconvex energies. J. Reine Angew. Math. 595 (2006) 55–91. [CrossRef] [MathSciNet] [Google Scholar]
  15. M. Frémond, Matériaux à mémoire deforme. C.R. Acad. Sci. Paris Sér. II 304 (1987) 239–244. [Google Scholar]
  16. M. Frémond, Non-Smooth Thermomechanics. Springer, Berlin (2002). [Google Scholar]
  17. E. Fried and M.E. Gurtin, Dynamic solid-solid transitions with phase characterized by an order perameter. Physica D 72 (1994) 287–308. [CrossRef] [MathSciNet] [Google Scholar]
  18. A. Giacomini and M. Ponsiglione, Discontinuous finite element approximation of quasistatic crack growth in nonlinear elasticity. Math. Models Methods Appl. Sci. 16 (2006) 77–118. [CrossRef] [MathSciNet] [Google Scholar]
  19. S. Govindjee and Ch. Miehe, A multi-variant martensitic phase transformation model: formulation and numerical implementation. Comp. Meth. Appl. Mech. Engr. 191 (2001) 215–238. [CrossRef] [Google Scholar]
  20. S. Govindjee, A. Mielke and G.J. Hall, Free-energy of miixng for n-variant martensitic phase transformations using quasi-convex analysis. J. Mech. Phys. Solids 50 (2002) 1897–1922. [CrossRef] [MathSciNet] [Google Scholar]
  21. B. Halphen and Q.S. Nguyen, Sur les matériaux standards généralisés. J. Mécanique 14 (1975) 39–63. [Google Scholar]
  22. W. Han and B.D. Reddy, Plasticity. Mathematical theory and numerical analysis. Springer, New York (1999). [Google Scholar]
  23. W. Han and B.D. Reddy, Convergence of approximations to the primal problem in plasticity under conditions of minimal regularity. Numer. Math. 87 (2000) 283–315. [CrossRef] [MathSciNet] [Google Scholar]
  24. K.-H. Hoffmann, M. Niezgódka and Z. Songmu, Existence and uniqueness of global solutions to an extended model of the dynamical development in shape memory alloys. Nonlinear Anal. Theory Methods Appl. 15 (1990) 977–990. [CrossRef] [MathSciNet] [Google Scholar]
  25. J.E. Huber, N.A. Fleck, C.M. Landis and R.M. McMeeking, A constitutive model for ferroelectric polycrystals. J. Mech. Phys. Solids 47 (1999) 1663–1697. [CrossRef] [MathSciNet] [Google Scholar]
  26. R.D. James and D. Kinderlehrer, Theory of magnetostriction with applications to TbxDy1-xFe2. Phil. Mag. 68 (1993) 237–274. [Google Scholar]
  27. R.D. James and M. Wuttig, Magnetostriction of martensite. Phil. Mag. A 77 (1998) 1273. [CrossRef] [Google Scholar]
  28. Y. Jung, P. Papadopoulos and R.O. Ritchie, Constitutive modeling and numerical simulation of multivariant phase transformation in superelastic shape-memory alloys. Int. J. Numer. Meth. Engng. 60 (2004) 429–460. [CrossRef] [Google Scholar]
  29. D. Kinderlehrer and P. Pedregal, Gradient Young measures generated by sequences in Sobolev spaces. J. Geom. Anal. 4 (1994) 59–90. [CrossRef] [MathSciNet] [Google Scholar]
  30. M. Kočvara, A. Mielke and T. Roubíček, A rate-independent approach to the delamination problem. Math. Mech. Solids 11 (2006) 423–447. [CrossRef] [MathSciNet] [Google Scholar]
  31. M. Kružík, A. Mielke and T. Roubíček, Modelling of microstructure and its evolution in shape-memory-alloy single-crystals, in particular in CuAlNi. Meccanica 40 (2005) 389–418. [CrossRef] [MathSciNet] [Google Scholar]
  32. V.I. Levitas, The postulate of realizibility: formulation and applications to postbifurcational behavior and phase transitions in elastoplastic materials. Int. J. Eng. Sci. 33 (1995) 921–971. [CrossRef] [Google Scholar]
  33. A. Mainik, A rate-independent model for phase transformations in shape-memory alloys. Ph.D. Thesis, Fachbereich Mathematik, Universität Stuttgart, Germany (2004). [Google Scholar]
  34. A. Mainik and A. Mielke, Existence results for energetic models for rate-independent systems. Calc. Var. 22 (2005) 73–99. [CrossRef] [MathSciNet] [Google Scholar]
  35. A. Mainik and A. Mielke, Global existence for rate-independent gradient plasticity at finite strains. J. Nonlinear Science (2008) DOI: 10.1007/s00332-008-9033-y (published online). [Google Scholar]
  36. A. Mielke, Energetic formulation of multiplicative elasto-plasticity using dissipation distances. Cont. Mech. Thermodynamics 15 (2003) 351–382. [CrossRef] [MathSciNet] [Google Scholar]
  37. A. Mielke, Evolution of rate-independent systems, in Handbook of Differential Equations: Evolutionary Equations, C. Dafermos and E. Feireisl Eds., Elsevier, Amsterdam (2005) 461–559. [Google Scholar]
  38. A. Mielke and S. Müller, Lower semicontinuity and existence of minimizers for a functional in elastoplasticity. Z. Angew. Math. Mech. 86 (2006) 233–250. [CrossRef] [MathSciNet] [Google Scholar]
  39. A. Mielke and T. Roubíček, Rate-independent model of inelastic behaviour of shape-memory alloys. Multiscale Model. Simul. 1 (2003) 571–597. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  40. A. Mielke and T. Roubíček, Rate-independent damage processes in nonlinear inelasticity. Math. Models Methods Appl. Sci. 16 (2006) 177–209. [CrossRef] [MathSciNet] [Google Scholar]
  41. A. Mielke and F. Theil, A mathematical model for rate-independent phase transformations with hysteresis, in Models of Continuum Mech. in Anal. and Engineering, H.-D. Alber, R. Balean and R. Farwig Eds., Shaker Ver., Aachen (1999) 117–129. [Google Scholar]
  42. A. Mielke and F. Theil, On rate-independent hysteresis models. Nonlin. Diff. Eq. Appl. 11 (2004) 151–189. [Google Scholar]
  43. A. Mielke and A. Timofte, An energetic material model for time-dependent ferroelectric behavior: existence and uniqueness. Math. Meth. Appl. Sci. 29 (2006) 1393–1410. [CrossRef] [Google Scholar]
  44. A. Mielke, F. Theil and V.I. Levitas, A variational formulation of rate-independent phase transformations using an extremum principle. Arch. Ration. Mech. Anal. 162 (2002) 137–177. [CrossRef] [MathSciNet] [Google Scholar]
  45. A. Mielke, T. Roubíček and U. Stefanelli, Relaxation and Γ-limits for rate-independent evolution equations. Calc. Var. P.D.E. 31 (2008) 387–416. [CrossRef] [Google Scholar]
  46. A. Mielke, L. Paoli and A. Petrov, On the existence and approximation for a 3D model of thermally induced phase transformations in shape-memory alloys. SIAM J. Math. Anal. (submitted) (WIAS Preprint 1330). [Google Scholar]
  47. A. Mielke, T. Roubíček and J. Zeman, Complete damage in elastic and viscoelastic media and its energetics. Comput. Methods Appl. Mech. Engrg. (submitted) (WIAS preprint 1285). [Google Scholar]
  48. S. Müller, Variational models for microstructure and phase transitions, in Calculus of variations and geometric evolution problems, S. Hildebrandt et al. Eds., Lect. Notes in Math. 1713, Springer, Berlin (1999) 85–210. [Google Scholar]
  49. P. Pedregal, Parametrized Measures and Variational Principles. Birkhäuser, Basel (1997). [Google Scholar]
  50. P. Plecháč and T. Roubíček, Visco-elasto-plastic model for martensitic phase transformation in shape-memory alloys. Math. Meth. Appl. Sci. 25 (2002) 1281–1298. [CrossRef] [Google Scholar]
  51. K.R. Rajagopal and T. Roubíček, On the effect of dissipation in shape-memory alloys. Nonlinear Anal. Real World Appl. 4 (2003) 581–597. [CrossRef] [MathSciNet] [Google Scholar]
  52. H. Romanowski and J. Schröder, Modelling of the nonlinear ferroelectric hysteresis within a thermodynamically consistent framework, in Trends in Applications of Math. to Mech., Y. Wang and K. Hutter Eds., Shaker Ver., Aachen (2005) 419–428. [Google Scholar]
  53. T. Roubíček, A note on an interaction between penalization and discretization, in Proc. IFIP-IIASA Conf., Modelling and Inverse Problems of Control for Distributed Parameter Systems, A. Kurzhanski and I. Lasiecka Eds., Lect. Notes in Control and Inf. Sci. 154, Springer (1991) 145–150. [Google Scholar]
  54. T. Roubíček, Dissipative evolution of microstructure in shape memory alloys, in Lectures on Applied Mathematics, H.-J. Bungartz, R.H.W. Hoppe and C. Zenger Eds., Springer, Berlin (2000) 45–63. [Google Scholar]
  55. T. Roubíček and M. Kružík, Microstructure evolution model in micromagnetics. Z. Angew. Math. Phys. 55 (2004) 159–182. [CrossRef] [MathSciNet] [Google Scholar]
  56. T. Roubíček and M. Kružík, Mesoscopic model for ferromagnets with isotropic hardening. Z. Angew. Math. Phys. 56 (2005) 107–135. [CrossRef] [MathSciNet] [Google Scholar]
  57. T. Roubíček and M. Kružík, Mesoscopic model of microstructure evolution in shape memory alloys, its numerical analysis and computer implementation, in 3rd GAMM Seminar on microstructures, C. Miehe Ed., GAMM Mitteilungen 29 (2006) 192–214. [Google Scholar]
  58. T. Roubíček, M. Kružík and J. Koutný, A mesoscopical model of shape-memory alloys. Proc. Estonian Acad. Sci. Phys. Math. 56 (2007) 146–154. [MathSciNet] [Google Scholar]
  59. P. Rybka and M. Luskin, Existence of energy minimizers for magnetostrictive materials. SIAM J. Math. Anal. 36 (2005) 2004–2019. [CrossRef] [MathSciNet] [Google Scholar]
  60. Y. Shu, K. Bhattacharya, Domain patterns and macroscopic behaviour of ferroelectric materials. Phil. Mag. B 81 (2001) 2021–2054. [Google Scholar]
  61. J.C. Simo, Numerical analysis and simulation of plasticity, in Handbook of Numer. Anal., P.G. Ciarlet and J.L. Lions Eds., Vol. VI, Elsevier, Amsterdam (1998) 183–499. [Google Scholar]
  62. J.C. Simo and J.R. Hughes, Computational Inelasticity. Springer, Berlin (1998). [Google Scholar]
  63. R. Temam, Mathematical problems in plasticity. Gauthier-Villars, Paris (1985). [Google Scholar]
  64. R. Tickle, Ferromagnetic shape memory materials. Ph.D. Thesis, University of Minnesota, Minneapolis, USA (2000). [Google Scholar]
  65. A. Visintin, Strong convergence results related to strict convexity. Comm. Partial Diff. Eq. 9 (1984) 439–466. [CrossRef] [MathSciNet] [Google Scholar]
  66. A. Visintin, Modified Landau-Lifshitz equation for ferromagnetism. Physica B 233 (1997) 365–369. [CrossRef] [Google Scholar]
  67. A. Visintin, Maxwell's equations with vector hysteresis. Arch. Ration. Mech. Anal. 175 (2005) 1–37. [CrossRef] [MathSciNet] [Google Scholar]
  68. A. Vivet and C. Lexcellent, Micromechanical modelling for tension-compression pseudoelastic behaviour of AuCd single crystals. Eur. Phys. J. Appl. Phys. 4 (1998) 125–132. [CrossRef] [EDP Sciences] [Google Scholar]

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