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All issues Volume 31 (2025) ESAIM: COCV, 31 (2025) 14 References
Open Access
Issue
ESAIM: COCV
Volume 31, 2025
Article Number 14
Number of page(s) 49
DOI https://doi.org/10.1051/cocv/2025004
Published online 14 February 2025
  1. J.-J. Marigo and K. Kazymyrenko, A micromechanical inspired model for the coupled to damage elasto-plastic behavior of geomaterials under compression. Mech. Ind. 20 (2019) 105. [CrossRef] [EDP Sciences] [Google Scholar]
  2. K. Pham and J.-J. Marigo, Approche variationnelle de l’endommagement: II. Les modèles à gradient. Comptes Rendus Mécanique 338 (2010) 199–206. [CrossRef] [Google Scholar]
  3. R. Alessi, J.-J. Marigo and S. Vidoli, Gradient damage models coupled with plasticity and nucleation of cohesive cracks. Arch. Ration. Mech. Anal. 214 (2014) 575–615. [CrossRef] [MathSciNet] [Google Scholar]
  4. V. Crismale, Energetic solutions for the coupling of associative plasticity with damage in geomaterials. Nonlinear Anal. 222 (2022) 112957. [Google Scholar]
  5. 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”, edited by H.D. Alber, R. Balean, and R. Farwig, Aachen. Shaker-Verlag (1999) 117–129. [Google Scholar]
  6. J. Ulloa, J. Wambacq, R. Alessi, E. Samaniego, G. Degrande and S. François, A micromechanics-based variational phase-field model for fracture in geomaterials with brittle-tensile and compressive-ductile behavior. J. Mech. Phys. Solids 159 (2021) 104684. [Google Scholar]
  7. E.C. Aifantis, On the microstructural origin of certain inelastic models. ASME J. Eng. Mater. Technol. 106 (1984) 326–330. [CrossRef] [Google Scholar]
  8. N.A. Fleck and J.W. Hutchinson, A reformulation of strain gradient plasticity. J. Mech. Phys. Solids 49 (2001) 2245–2271. [CrossRef] [Google Scholar]
  9. R.A.B. Engelen, M.G.D. Geers and F.P.T. Baaijens, Nonlocal implicit gradient-enhanced elasto-plasticity for the modelling of softening behaviour. Int. J. Plast. 19 (2003) 403–433. [CrossRef] [Google Scholar]
  10. R.H.J. Peerlings, On the role of moving elastic–plastic boundaries in strain gradient plasticity. Model. Simulat. Mater. Sci. Eng. 15 (2007) 109–120. [Google Scholar]
  11. S. Forest, Micromorphic approach for gradient elasticity, viscoplasticity, and damage. J. Eng. Mech. 135 (2009) 117–131. [CrossRef] [Google Scholar]
  12. L.H. Poh, R.H.J. Peerlings, M.G.D. Geers and S. Swaddiwudhipong, An implicit tensorial gradient plasticity model–formulation and comparison with a scalar gradient model. Int. J. Solids Struct. 48 (2011) 2595–2604. [CrossRef] [Google Scholar]
  13. L. Anand, O. Aslan and S.A. Chester, A large-deformation gradient theory for elastic–plastic materials: strain softening and regularization of shear bands. Int. J. Plast. 30–31 (2012) 116–143. [CrossRef] [Google Scholar]
  14. C. Miehe, F. Aldakheel and S. Mauthe, Mixed variational principles and robust finite element implementations of gradient plasticity at small strains. Int. J. Numer. Methods Eng. 94 (2013) 1037–1074. [CrossRef] [Google Scholar]
  15. I. Zreid and M. Kaliske, An implicit gradient formulation for microplane Drucker–Prager plasticity. Int. J. Plast. 83 (2016) 252–272. [CrossRef] [Google Scholar]
  16. 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]
  17. M.A. Efendiev and A. Mielke, On the rate-independent limit of systems with dry friction and small viscosity. J. Convex Anal. 13 (2006) 151–167. [Google Scholar]
  18. A. Mielke, R. Rossi and G. Savaré, BV solutions and viscosity approximations of rate-independent systems. ESAIM Control Optim. Calc. Var. 18 (2012) 36–80. [CrossRef] [EDP Sciences] [MathSciNet] [Google Scholar]
  19. A. Mielke, R. Rossi and G. Savaré, Balanced viscosity (BV) solutions to infinite-dimensional rate-independent systems. J. Eur. Math. Soc. 18 (2016) 2107–2165. [CrossRef] [MathSciNet] [Google Scholar]
  20. R. Rossi and G. Savaré, A characterization of energetic and BV solutions to one-dimensional rate-independent systems. Discrete Contin. Dyn. Syst. Ser. S 6 (2013) 167–191. [MathSciNet] [Google Scholar]
  21. G. Dal Maso, A. DeSimone, M.G. Mora and M. Morini, A vanishing viscosity approach to quasistatic evolution in plasticity with softening. Arch. Rational Mech. Anal. 189 (2008) 469–544. [CrossRef] [MathSciNet] [Google Scholar]
  22. G. Dal Maso and F. Solombrino, Quasistatic evolution for Cam-Clay plasticity: the spatially homogeneous case. Networks Heterog. Media 5 (2010) 97–132. [CrossRef] [MathSciNet] [Google Scholar]
  23. G. Dal Maso, A. DeSimone and F. Solombrino, Quasistatic evolution for Cam-Clay plasticity: a weak formulation via viscoplastic regularization and time rescaling. Calc. Var. Part. Differ. Equ. 40 (2011) 125–181. [CrossRef] [Google Scholar]
  24. J.-F. Babadjian, G.A. Francfort and M.G. Mora, Quasi-static evolution in nonassociative plasticity: the cap model. SIAM J. Math. Anal. 44 (2012) 245–292. [CrossRef] [MathSciNet] [Google Scholar]
  25. G.A. Francfort and U. Stefanelli, Quasi-static evolution for the Armstrong–Frederick hardening-plasticity model. Appl. Math. Res. Express. 2 (2013) 297–344. [Google Scholar]
  26. F. Solombrino, Quasistatic evolution in perfect plasticity for general heterogeneous materials. Arch. Ration. Mech. Anal. 212 (2014) 283–330. [Google Scholar]
  27. D. Knees, A. Mielke and C. Zanini, On the inviscid limit of a model for crack propagation. Math. Models Methods Appl. Sci. 18 (2008) 1529–1569. [CrossRef] [MathSciNet] [Google Scholar]
  28. G. Lazzaroni and R. Toader, A model for crack propagation based on viscous approximation. Math. Models Methods Appl. Sci. 21 (2011) 2019–2047. [CrossRef] [MathSciNet] [Google Scholar]
  29. D. Knees, R. Rossi and C. Zanini, A vanishing viscosity approach to a rate-independent damage model. Math. Models Methods Appl. Sci. 23 (2013) 565–616. [Google Scholar]
  30. V. Crismale and G. Lazzaroni, Viscous approximation of quasistatic evolutions for a coupled elastoplastic-damage model. Calc. Var. Part. Differ. Equ. 55 (2016) 1–54. [CrossRef] [Google Scholar]
  31. S. Almi, G. Lazzaroni and I. Lucardesi, Crack growth by vanishing viscosity in planar elasticity. Math. Eng. 2 (2020) 141–173. [CrossRef] [MathSciNet] [Google Scholar]
  32. R. Alessi, V. Crismale and G. Orlando, Fatigue effects in elastic materials with variational damage models: a vanishing viscosity approach. J. Nonlinear Sci. 29 (2019) 1041–1094. [CrossRef] [MathSciNet] [Google Scholar]
  33. V. Crismale and R. Rossi, Balanced viscosity solutions to a rate-independent coupled elasto-plastic damage system. SIAM J. Math. Anal. 53 (2021) 3420–3492. [CrossRef] [MathSciNet] [Google Scholar]
  34. V. Crismale, Globally stable quasistatic evolution for a coupled elastoplastic-damage model. ESAIM Control Optim. Calc. Var. 22 (2016) 883–912. [CrossRef] [EDP Sciences] [MathSciNet] [Google Scholar]
  35. F. Solombrino, A-priori time regularity estimates and a simplified proof of existence in perfect plasticity. Math. Nachr. 288 (2015) 1786–1800. [CrossRef] [MathSciNet] [Google Scholar]
  36. L. Ambrosio, N. Gigli and G. Savaré, Gradient Flows in Metric Spaces and in the Space of Probability Measures, Birkhäuser Verlag, Basel (2005) viii+333. [Google Scholar]
  37. G. Buttazzo, Semicontinuity, relaxation and integral representation in the calculus of variations. Pitman Research Notes in Mathematics Series, Vol. 207. Longman, Harlow, New York (1989) iv+222. [Google Scholar]

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