Free Access
Volume 43, Number 3, May-June 2009
Page(s) 399 - 428
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]
  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]
  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]
  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]
  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]
  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]
  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]
  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]
  9. W.F. Brown, Magnetoelastic interactions, in Springer Tracts in Natural Philosophy 9, C. Truesdel Ed., Springer (1966).
  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]
  11. P. Colli, M. Frémond and A. Visintin, Thermo-mechanical evolution of shape memory alloys. Quarterly Appl. Math. 48 (1990) 31–47.
  12. S. Conti and M. Ortiz, Dislocation microstructures and effective behaviour of single crystals. Arch. Ration. Mech. Anal. 176 (2005) 103–147. [CrossRef] [MathSciNet]
  13. F. Falk, Model free energy, mechanics and thermodynamics of shape memory alloys. Acta Metall. 28 (1980) 1773–1780. [CrossRef]
  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]
  15. M. Frémond, Matériaux à mémoire deforme. C.R. Acad. Sci. Paris Sér. II 304 (1987) 239–244.
  16. M. Frémond, Non-Smooth Thermomechanics. Springer, Berlin (2002).
  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]
  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]
  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]
  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]
  21. B. Halphen and Q.S. Nguyen, Sur les matériaux standards généralisés. J. Mécanique 14 (1975) 39–63.
  22. W. Han and B.D. Reddy, Plasticity. Mathematical theory and numerical analysis. Springer, New York (1999).
  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]
  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]
  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]
  26. R.D. James and D. Kinderlehrer, Theory of magnetostriction with applications to TbxDy1-xFe2. Phil. Mag. 68 (1993) 237–274.
  27. R.D. James and M. Wuttig, Magnetostriction of martensite. Phil. Mag. A 77 (1998) 1273. [CrossRef]
  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]
  29. D. Kinderlehrer and P. Pedregal, Gradient Young measures generated by sequences in Sobolev spaces. J. Geom. Anal. 4 (1994) 59–90. [CrossRef] [MathSciNet]
  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]
  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]
  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]
  33. A. Mainik, A rate-independent model for phase transformations in shape-memory alloys. Ph.D. Thesis, Fachbereich Mathematik, Universität Stuttgart, Germany (2004).
  34. A. Mainik and A. Mielke, Existence results for energetic models for rate-independent systems. Calc. Var. 22 (2005) 73–99. [CrossRef] [MathSciNet]
  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).
  36. A. Mielke, Energetic formulation of multiplicative elasto-plasticity using dissipation distances. Cont. Mech. Thermodynamics 15 (2003) 351–382. [CrossRef] [MathSciNet]
  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.
  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]
  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]
  40. A. Mielke and T. Roubíček, Rate-independent damage processes in nonlinear inelasticity. Math. Models Methods Appl. Sci. 16 (2006) 177–209. [CrossRef] [MathSciNet]
  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.
  42. A. Mielke and F. Theil, On rate-independent hysteresis models. Nonlin. Diff. Eq. Appl. 11 (2004) 151–189.
  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]
  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]
  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]
  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).
  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).
  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.
  49. P. Pedregal, Parametrized Measures and Variational Principles. Birkhäuser, Basel (1997).
  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]
  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]
  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.
  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.
  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.
  55. T. Roubíček and M. Kružík, Microstructure evolution model in micromagnetics. Z. Angew. Math. Phys. 55 (2004) 159–182. [CrossRef] [MathSciNet]
  56. T. Roubíček and M. Kružík, Mesoscopic model for ferromagnets with isotropic hardening. Z. Angew. Math. Phys. 56 (2005) 107–135. [CrossRef] [MathSciNet]
  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.
  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]
  59. P. Rybka and M. Luskin, Existence of energy minimizers for magnetostrictive materials. SIAM J. Math. Anal. 36 (2005) 2004–2019. [CrossRef] [MathSciNet]
  60. Y. Shu, K. Bhattacharya, Domain patterns and macroscopic behaviour of ferroelectric materials. Phil. Mag. B 81 (2001) 2021–2054.
  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.
  62. J.C. Simo and J.R. Hughes, Computational Inelasticity. Springer, Berlin (1998).
  63. R. Temam, Mathematical problems in plasticity. Gauthier-Villars, Paris (1985).
  64. R. Tickle, Ferromagnetic shape memory materials. Ph.D. Thesis, University of Minnesota, Minneapolis, USA (2000).
  65. A. Visintin, Strong convergence results related to strict convexity. Comm. Partial Diff. Eq. 9 (1984) 439–466. [CrossRef] [MathSciNet]
  66. A. Visintin, Modified Landau-Lifshitz equation for ferromagnetism. Physica B 233 (1997) 365–369. [CrossRef]
  67. A. Visintin, Maxwell's equations with vector hysteresis. Arch. Ration. Mech. Anal. 175 (2005) 1–37. [CrossRef] [MathSciNet]
  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]

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