Free Access
Issue
ESAIM: COCV
Volume 18, Number 1, January-March 2012
Page(s) 36 - 80
DOI https://doi.org/10.1051/cocv/2010054
Published online 23 December 2010
  1. L. Ambrosio, Minimizing movements. Rend. Accad. Naz. Sci. XL Mem. Mat. Appl. 19 (1995) 191–246. [MathSciNet]
  2. L. Ambrosio and G. Dal Maso, A general chain rule for distributional derivatives. Proc. Am. Math. Soc. 108 (1990) 691–702. [CrossRef]
  3. L. Ambrosio, N. Fusco and D. Pallara, Functions of bounded variation and free discontinuity problems. Oxford Mathematical Monographs, Clarendon Press, Oxford (2000).
  4. L. Ambrosio, N. Gigli and G. Savaré, Gradient flows in metric spaces and in the space of probability measures. Lectures in Mathematics ETH Zürich, 2nd edn., Birkhäuser Verlag, Basel (2008).
  5. F. Auricchio, A. Mielke and U. Stefanelli, A rate-independent model for the isothermal quasi-static evolution of shape-memory materials. Math. Models Meth. Appl. Sci. 18 (2008) 125–164. [CrossRef] [MathSciNet]
  6. G. Bouchitté, A. Mielke and T. Roubíček, A complete-damage problem at small strains. Z. Angew. Math. Phys. 60 (2009) 205–236. [CrossRef] [MathSciNet]
  7. M. Buliga, G. de Saxcé and C. Vallée, Existence and construction of bipotentials for graphs of multivalued laws. J. Convex Anal. 15 (2008) 87–104.
  8. P. Colli, On some doubly nonlinear evolution equations in Banach spaces. Japan J. Indust. Appl. Math. 9 (1992) 181–203. [CrossRef] [MathSciNet]
  9. P. Colli and A. Visintin, On a class of doubly nonlinear evolution equations. Commun. Partial Differ. Equ. 15 (1990) 737–756. [CrossRef] [MathSciNet]
  10. G. Dal Maso and R. Toader, A model for quasi-static growth of brittle fractures : existence and approximation results. Arch. Ration. Mech. Anal. 162 (2002) 101–135. [CrossRef] [MathSciNet]
  11. G. Dal Maso and R. Toader, A model for the quasi-static growth of brittle fractures based on local minimization. Math. Models Meth. Appl. Sci. 12 (2002) 1773–1799. [CrossRef]
  12. G. Dal Maso and C. Zanini, Quasi-static crack growth for a cohesive zone model with prescribed crack path. Proc. R. Soc. Edinb., Sect. A, Math. 137 (2007) 253–279. [CrossRef] [MathSciNet]
  13. G. Dal Maso, G. Francfort and R. Toader, Quasistatic crack growth in nonlinear elasticity. Arch. Ration. Mech. Anal. 176 (2005) 165–225. [CrossRef] [MathSciNet]
  14. G. Dal Maso, A. DeSimone and M.G. Mora, Quasistatic evolution problems for linearly elastic-perfectly plastic materials. Arch. Ration. Mech. Anal. 180 (2006) 237–291. [CrossRef] [MathSciNet]
  15. G. Dal Maso, A. DeSimone, M.G. Mora and M. Morini, Globally stable quasistatic evolution in plasticity with softening. Netw. Heterog. Media 3 (2008) 567–614. [CrossRef] [MathSciNet]
  16. G. Dal Maso, A. DeSimone, M.G. Mora and M. Morini, A vanishing viscosity approach to quasistatic evolution in plasticity with softening. Arch. Ration. Mech. Anal. 189 (2008) 469–544. [CrossRef] [MathSciNet]
  17. G. Dal Maso, A. DeSimone and F. Solombrino, Quasistatic evolution for cam-clay plasiticity : a weak formulation via viscoplastic regularization and time rescaling. Calc. Var. Partial Differential Equations (to appear).
  18. M. Efendiev and A. Mielke, On the rate-independent limit of systems with dry friction and small viscosity. J. Convex Analysis 13 (2006) 151–167.
  19. A. Fiaschi, A vanishing viscosity approach to a quasistatic evolution problem with nonconvex energy. Ann. Inst. Henri Poincaré, Anal. Non Linéaire (to appear).
  20. G. Francfort and A. Garroni, A variational view of partial brittle damage evolution. Arch. Ration. Mech. Anal. 182 (2006) 125–152. [CrossRef] [MathSciNet]
  21. G. 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. [CrossRef] [MathSciNet]
  22. J.-B. Hiriart-Urruty and C. Lemaréchal, Convex analysis and minimization algorithms. II : Advanced theory and bundle methods, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences] 306. Springer-Verlag, Berlin (1993).
  23. D. Knees, A. Mielke and C. Zanini, On the inviscid limit of a model for crack propagation. Math. Models Meth. Appl. Sci. 18 (2008) 1529–1569. [CrossRef]
  24. D. Knees, C. Zanini and A. Mielke, Crack propagation in polyconvex materials. Physica D 239 (2010) 1470–1484. [CrossRef] [MathSciNet]
  25. M. Kočvara, A. Mielke and T. Roubíček, A rate-independent approach to the delamination problem. Math. Mech. Solids 11 (2006) 423–447. [MathSciNet]
  26. P. Krejčí, Evolution variational inequalities and multidimensional hysteresis operators, in Nonlinear differential equations (Chvalatice, 1998), Res. Notes Math. 404, Chapman & Hall/CRC, Boca Raton, FL (1999) 47–110.
  27. P. Krejčí, and M. Liero, Rate independent Kurzweil processes. Appl. Math. 54 (2009) 117–145. [CrossRef] [MathSciNet]
  28. C.J. Larsen, Epsilon-stable quasi-static brittle fracture evolution. Comm. Pure Appl. Math. 63 (2010) 630–654. [MathSciNet]
  29. A. Mainik and A. Mielke, Existence results for energetic models for rate-independent systems. Calc. Var. PDEs 22 (2005) 73–99.
  30. A. Mainik and A. Mielke, Global existence for rate-independent gradient plasticity at finite strain. J. Nonlin. Sci. 19 (2009) 221–248. [CrossRef] [MathSciNet]
  31. A. Mielke, Energetic formulation of multiplicative elasto-plasticity using dissipation distances. Contin. Mech. Thermodyn. 15 (2003) 351–382. [CrossRef] [MathSciNet]
  32. A. Mielke, Evolution in rate-independent systems (Chap. 6), in Handbook of differential equations, evolutionary equations 2, C. Dafermos and E. Feireisl Eds., Elsevier B.V., Amsterdam (2005) 461–559.
  33. A. Mielke, Differential, energetic and metric formulations for rate-independent processes. Lecture Notes, Summer School Cetraro (in press).
  34. A. Mielke and T. Roubčíek, A rate-independent model for inelastic behavior of shape-memory alloys. Multiscale Model. Simul. 1 (2003) 571–597. [CrossRef] [MathSciNet] [PubMed]
  35. A. Mielke and T. Roubčíek, Rate-independent damage processes in nonlinear elasticity. M3 ! AS Math. Models Meth. Appl. Sci. 16 (2006) 177–209. [CrossRef] [MathSciNet]
  36. A. Mielke and T. Roubčíek, Rate-Independent Systems : Theory and Application. (In preparation).
  37. A. Mielke and 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 and R. Farwig Eds., Shaker-Verlag, Aachen (1999) 117–129.
  38. A. Mielke and F. Theil, On rate-independent hysteresis models. NoDEA 11 (2004) 151–189.
  39. 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]
  40. A. Mielke and S. Zelik, On the vanishing viscosity limit in parabolic systems with rate-independent dissipation terms. Ann. Sc. Norm. Sup. Pisa Cl. Sci. (submitted).
  41. 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]
  42. A. Mielke, R. Rossi and G. Savaré, Modeling solutions with jumps for rate-independent systems on metric spaces. Discrete Contin. Dyn. Syst. 25 (2009) 585–615. [CrossRef] [MathSciNet]
  43. A. Mielke, R. Rossi and G. Savaré, Nonsmooth analysis of doubly nonlinear evolution equations. (In preparation).
  44. M. Negri and C. Ortner, Quasi-static crack propagation by Griffith’s criterion. Math. Models Meth. Appl. Sci. 18 (2008) 1895–1925. [CrossRef]
  45. R.T. Rockafellar, Convex Analysis. Princeton University Press, Princeton (1970).
  46. R. Rossi and G. Savaré, Gradient flows of non convex functionals in Hilbert spaces and applications. ESAIM : COCV 12 (2006) 564–614. [CrossRef] [EDP Sciences]
  47. R. Rossi, A. Mielke and G. Savaré, A metric approach to a class of doubly nonlinear evolution equations and applications. Ann. Sc. Norm. Super. Pisa Cl. Sci. 7 (2008) 97–169. [MathSciNet]
  48. T. Roubčíek, Rate independent processes in viscous solids at small strains. Math. Methods Appl. Sci. 32 (2009) 825–862. [CrossRef] [MathSciNet]
  49. U. Stefanelli, A variational characterization of rate-independent evolution. Math. Nachr. 282 (2009) 1492–1512. [CrossRef] [MathSciNet]
  50. M. Thomas and A. Mielke, Damage of nonlinearly elastic materials at small strains – Existence and regularity results. Zeits. Angew. Math. Mech. 90 (2009) 88–112. [CrossRef] [MathSciNet]
  51. R. Toader and C. Zanini, An artificial viscosity approach to quasistatic crack growth. Boll. Unione Mat. Ital. 2 (2009) 1–35. [MathSciNet]
  52. A. Visintin, Differential models of hysteresis, Applied Mathematical Sciences 111. Springer-Verlag, Berlin (1994).

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