Free Access
Issue |
ESAIM: M2AN
Volume 50, Number 1, January-February 2016
|
|
---|---|---|
Page(s) | 77 - 91 | |
DOI | https://doi.org/10.1051/m2an/2015032 | |
Published online | 16 November 2015 |
- L. Ambrosio and V. Tortorelli, Approximation of functionals depending on jumps by elliptic functionals via Γ-convergence. Commun. Pure Appl. Math. 43 (1990) 999–1036. [Google Scholar]
- B. Bourdin, G.A. Francfort and J.-J. Marigo, Numerical experiments in revisited brittle fracture. J. Mech. Phys. Solids 48 (2000) 797–826. [CrossRef] [MathSciNet] [Google Scholar]
- B. Bourdin, C.J. Larsen and C. Richardson, A time-discrete model for dynamic fracture based on crack regularization. Int. J. Fracture 168 (2011) 133–143. [CrossRef] [Google Scholar]
- A. Braides, Γ-convergence for beginners. Vol. 22 of Oxford Lect. Ser. Math. Appl. Oxford University Press, Oxford (2002). [Google Scholar]
- A. Chambolle, A density result in two-dimensional linearized elasticity, and applications. Arch. Rational. Mech. Anal. 167 (2003) 211–233. [CrossRef] [MathSciNet] [Google Scholar]
- G. Dal Maso, and R. Toader, A model for the quasi-static growth of brittle fractures based on local minimization. Math. Models Methods Appl. Sci. 12 (2002) 1773–1799. [CrossRef] [MathSciNet] [Google Scholar]
- G. Dal Maso and R. Toader, A model for the quasi-static growth of brittle fractures: existence and approximation results. Arch. Rational. Mech. Anal. 162 (2002) 101–135. [Google Scholar]
- G. Dal Maso, G.A. Francfort and R. Toader, Quasistatic crack growth in nonlinear elasticity. Arch. Rational. Mech. Anal. 176 (2005) 165–225. [CrossRef] [MathSciNet] [Google Scholar]
- E. De Giorgi and G. Dal Maso, Γ-convergence and calculus of variations. In Mathematical theories of optimization (Genova, 1981). Vol. 979 of Lect. Notes Math. Springer, Berlin (1983) 121–143. [Google Scholar]
- G.A. Francfort and J.-J. Marigo, Revisiting brittle fracture as an energy minimization problem. J. Mech. Phys. Solids 46 (1998) 1319–1342. [CrossRef] [MathSciNet] [Google Scholar]
- G.A. Francfort and C.J. Larsen, Existence and convergence for quasi-static evolution in brittle fracture. Commun. Pure Appl. Math. 56 (2003) 1465–1500. [Google Scholar]
- A. Giacomini, Ambrosio–Tortorelli approximation of quasi-static evolution of brittle fractures. Calc. Var. Partial Differ. Equ. 22 (2005) 129–172. [Google Scholar]
- A. Griffith, The phenomena of rupture and flow in solids. Philos. Trans. Roy. Soc. London (1920) 163–198. [Google Scholar]
- 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]
- C.J. Larsen, Epsilon-stable quasi-static brittle fracture evolution. Commun. Pure Appl. Math. 63 (2010) 630–654. [Google Scholar]
- C.J. Larsen, C. Ortner and E. Süli, Existence of solutions to a regularized model of dynamic fracture. Math. Models Methods Appl. Sci. 20 (2010) 1021–1048. [CrossRef] [Google Scholar]
- A. Mielke, Differential, energetic, and metric formulations for rate-independent processes. In Nonlin. Partial Differ. Equ. Appl. Vol. 2028 of Lect. Notes Math. Springer, Heidelberg (2011) 87–170. [Google Scholar]
- M. Negri and C. Ortner, Quasi-static crack propagation by Griffith’s criterion. Math. Models Methods Appl. Sci. 18 (2008) 1895–1925. [CrossRef] [MathSciNet] [Google Scholar]
- T. Roubíček, Adhesive contact of visco-elastic bodies and defect measures arising by vanishing viscosity. SIAM J. Math. Anal. 45 (2013) 101–126. [CrossRef] [MathSciNet] [Google Scholar]
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.