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] [Google Scholar]
  2. L. Ambrosio and G. Dal Maso, A general chain rule for distributional derivatives. Proc. Am. Math. Soc. 108 (1990) 691–702. [Google Scholar]
  3. L. Ambrosio, N. Fusco and D. Pallara, Functions of bounded variation and free discontinuity problems. Oxford Mathematical Monographs, Clarendon Press, Oxford (2000). [Google Scholar]
  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). [Google Scholar]
  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] [Google Scholar]
  6. G. Bouchitté, A. Mielke and T. Roubíček, A complete-damage problem at small strains. Z. Angew. Math. Phys. 60 (2009) 205–236. [Google Scholar]
  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. [Google Scholar]
  8. P. Colli, On some doubly nonlinear evolution equations in Banach spaces. Japan J. Indust. Appl. Math. 9 (1992) 181–203. [CrossRef] [MathSciNet] [Google Scholar]
  9. P. Colli and A. Visintin, On a class of doubly nonlinear evolution equations. Commun. Partial Differ. Equ. 15 (1990) 737–756. [CrossRef] [MathSciNet] [Google Scholar]
  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] [Google Scholar]
  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. [Google Scholar]
  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] [Google Scholar]
  13. G. Dal Maso, G. Francfort and R. Toader, Quasistatic crack growth in nonlinear elasticity. Arch. Ration. Mech. Anal. 176 (2005) 165–225. [Google Scholar]
  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] [Google Scholar]
  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] [Google Scholar]
  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] [Google Scholar]
  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). [Google Scholar]
  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. [Google Scholar]
  19. A. Fiaschi, A vanishing viscosity approach to a quasistatic evolution problem with nonconvex energy. Ann. Inst. Henri Poincaré, Anal. Non Linéaire (to appear). [Google Scholar]
  20. G. Francfort and A. Garroni, A variational view of partial brittle damage evolution. Arch. Ration. Mech. Anal. 182 (2006) 125–152. [CrossRef] [MathSciNet] [Google Scholar]
  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] [Google Scholar]
  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). [Google Scholar]
  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. [Google Scholar]
  24. D. Knees, C. Zanini and A. Mielke, Crack propagation in polyconvex materials. Physica D 239 (2010) 1470–1484. [Google Scholar]
  25. 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]
  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. [Google Scholar]
  27. P. Krejčí, and M. Liero, Rate independent Kurzweil processes. Appl. Math. 54 (2009) 117–145. [CrossRef] [MathSciNet] [Google Scholar]
  28. C.J. Larsen, Epsilon-stable quasi-static brittle fracture evolution. Comm. Pure Appl. Math. 63 (2010) 630–654. [MathSciNet] [Google Scholar]
  29. A. Mainik and A. Mielke, Existence results for energetic models for rate-independent systems. Calc. Var. PDEs 22 (2005) 73–99. [Google Scholar]
  30. A. Mainik and A. Mielke, Global existence for rate-independent gradient plasticity at finite strain. J. Nonlin. Sci. 19 (2009) 221–248. [Google Scholar]
  31. A. Mielke, Energetic formulation of multiplicative elasto-plasticity using dissipation distances. Contin. Mech. Thermodyn. 15 (2003) 351–382. [CrossRef] [MathSciNet] [Google Scholar]
  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. [Google Scholar]
  33. A. Mielke, Differential, energetic and metric formulations for rate-independent processes. Lecture Notes, Summer School Cetraro (in press). [Google Scholar]
  34. A. Mielke and T. Roubčíek, A rate-independent model for inelastic behavior of shape-memory alloys. Multiscale Model. Simul. 1 (2003) 571–597. [Google Scholar]
  35. A. Mielke and T. Roubčíek, Rate-independent damage processes in nonlinear elasticity. M3 ! AS Math. Models Meth. Appl. Sci. 16 (2006) 177–209. [Google Scholar]
  36. A. Mielke and T. Roubčíek, Rate-Independent Systems : Theory and Application. (In preparation). [Google Scholar]
  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. [Google Scholar]
  38. A. Mielke and F. Theil, On rate-independent hysteresis models. NoDEA 11 (2004) 151–189. [Google Scholar]
  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] [Google Scholar]
  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). [Google Scholar]
  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. [Google Scholar]
  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. [Google Scholar]
  43. A. Mielke, R. Rossi and G. Savaré, Nonsmooth analysis of doubly nonlinear evolution equations. (In preparation). [Google Scholar]
  44. M. Negri and C. Ortner, Quasi-static crack propagation by Griffith’s criterion. Math. Models Meth. Appl. Sci. 18 (2008) 1895–1925. [Google Scholar]
  45. R.T. Rockafellar, Convex Analysis. Princeton University Press, Princeton (1970). [Google Scholar]
  46. R. Rossi and G. Savaré, Gradient flows of non convex functionals in Hilbert spaces and applications. ESAIM : COCV 12 (2006) 564–614. [Google Scholar]
  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] [Google Scholar]
  48. T. Roubčíek, Rate independent processes in viscous solids at small strains. Math. Methods Appl. Sci. 32 (2009) 825–862. [CrossRef] [MathSciNet] [Google Scholar]
  49. U. Stefanelli, A variational characterization of rate-independent evolution. Math. Nachr. 282 (2009) 1492–1512. [CrossRef] [MathSciNet] [Google Scholar]
  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. [Google Scholar]
  51. R. Toader and C. Zanini, An artificial viscosity approach to quasistatic crack growth. Boll. Unione Mat. Ital. 2 (2009) 1–35. [MathSciNet] [Google Scholar]
  52. A. Visintin, Differential models of hysteresis, Applied Mathematical Sciences 111. Springer-Verlag, Berlin (1994). [Google Scholar]

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