Quasistatic damage evolution with spatial bv-regularization

Discrete and Continuous Dynamical Systems - Series S

Volumn 6, Issue 1, 2013, Pages 235-255

  Thomas, Marita ^a  

^a WEIERSTRASS INSTITUTE FOR APPLIED ANALYSIS AND STOCHASTICS   (Germany)

Author keywords

Convergence of rate independent systems; Damage evolution with spatial regularization; Energetic formulation; Functions of bounded variation; Partial damage

Indexed keywords

EID: 84874163850     PISSN: 19371632     EISSN: 19371179     Source Type: Journal    
DOI: 10.3934/dcdss.2013.6.235     Document Type: Article

References (23)

1. L. Ambrosio and G. Dal Maso, A general chain rule for distributional derivatives, Proceedings of the American Mathematical Society, 108 (1990), 691-702.
2. L. Ambrosio, N. Fusco and D. Pallara, \Functions of Bounded Variation and Free Discontinuity Problems," Oxford University Press, 2005.
3. G. Alberti, Variational models for phase transitions, an approach via gamma-convergence, 1998, in \Differential Equations and Calculus of Variations" (eds. G. Buttazzo et al.), Springer-Verlag, 2000.
4. B. Bourdin, G. Francfort and J. J. Marigo, The variational approach to fracture, J. Elasticity, 91 (2008), 5-148.
5. G. Francfort and A. Garroni, A variational view of partial brittle damage evolution, Arch. Rational Mech. Anal., 182 (2006), 125-152. (Pubitemid 44099676)
6. A. Fiaschi, D. Knees and U. Stefanelli, Young-measure quasi-static damage evolution, Arch. Ration. Mech. Anal., 203 (2012), 415-453.
7. G. Francfort and J.-J. Marigo, Stable damage evolution in a brittle continuous medium, Eur. J. Mech., A/Solids, 12 (1993), 149-189.
8. 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. (Pubitemid 43959232)
9. M. Fremond and B. Nedjar, Damage, gradient of damage and principle of virtual power, Internat. J. Solids Structures, 33 (1996), 1083-1103. (Pubitemid 126403143)
10. A. Giacomini, Ambrosio-Tortorelli approximation of quasi-static evolution of brittle fracture, Calc. Var. Partial Dier. Equ., 22 (2005), 129-172. (Pubitemid 40111473)
11. E. Giusti, \Minimal Surfaces and Functions of Bounded Variation," Birkh-auser, Boston, 1984.
12. A. Garroni and C. Larsen, Threshold-based quasi-static brittle damage evolution, Arch. Ration. Mech. Anal., 194 (2009), 585-609.
13. K. Hackl and H. Stumpf, Micromechanical concept for the analysis of damage evolution in thermo-viscoelastic and quasi-static brittle fracture, Int. J. Solids Structures, 30 (2003), 1567-1584. (Pubitemid 36242750)
14. A. Mielke, Evolution of rate-independent systems, in \Evolutionary Equations," (Edited by C. M. Dafermos and E. Feireisl), Handb. Dier. Equ., Elsevier/North-Holland, Amsterdam, 2 (2005), 461-559.
15. A. Mielke, Differential, energetic and metric formulations for rate-independent processes, Nonlinear PDE's and applications, 87-170, Lecture Notes in Math., 2028, Springer, Heidelberg, 2011.
16. L. Modica and S. Mortola, Un esempio di convergenza, Boll. U. Mat. Ital. B, 14 (1977), 285-299.
17. A. Mainik and A. Mielke, Existence results for energetic models for rate-independent systems, Calc. Var. PDEs, 22 (2005), 73-99. (Pubitemid 40105958)
18. L. Modica, The gradient theory of phase transitions and the minimal interface criterion, Arch. Rational Mech. Anal., 98 (1987), 123-142.
19. A. Mielke and T. Roubcek, Rate-independent damage processes in nonlinear elasticity, M3AS Math. Models Methods Appl. Sci., 16 (2006), 177-209. (Pubitemid 43244203)
20. A. Mielke, T. Roubcek and U. Stefanelli, limits and relaxations for rate-independent evo- lutionary problems, Calc. Var. Partial Dier. Equ., 31 (2008), 387-416.
21. A. Mielke, T. Roubcek and M. Thomas, From damage to delamination in nonlinearly elastic materials at small strains, J. Elasticity, 109 (2012), 235-273.
22. M. Thomas, \Rate-independent Damage Processes in Nonlinearly Elastic Materials," PhD thesis, Humboldt-Universit-at zu Berlin, 2010.
23. M. Thomas and A. Mielke, Damage of nonlinearly elastic materials at small strain: existence and regularity results, Zeit. angew. Math. Mech., 90 (2010), 88-112.