Energy minimizing brittle crack propagation

Journal of Elasticity

Volumn 52, Issue 3, 1998, Pages 201-238

  Buliga, Marius ^a  

^a INSTITUTE OF MATHEMATICS   (Romania)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; BRITTLENESS; CRACK PROPAGATION; DEFORMATION; FUNCTIONS; MATHEMATICAL MODELS; OPTIMIZATION; PARAMETER ESTIMATION; PROBLEM SOLVING; VARIATIONAL TECHNIQUES;

BOUNDED DEFORMATIONS; BRITTLE FRACTURE PROPAGATION; FREE DISCONTINUITY; MINIMIZING MOVEMENTS; MUMFORD-SHAH FUNCTIONS;

ELASTICITY;

EID: 0032259287     PISSN: 03743535     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1007545213010     Document Type: Article

References (39)

1. L. Ambrosio, Variational problems in SBV and image segmentation. Acta Appl. Mathematicœ 17 (1989) 1-40.
2. L. Ambrosio, Existence theory for a new class of variational problems. Arch. Rational Mech. Anal. 111 (1990) 291-322.
3. L. Ambrosio, Movimenti minimizzanti. Rend. Accad. Naz. Sci. XL Mem. Mat. Sci. Fis. Natur. 113 (1995) 191-246.
4. L. Ambrosio and A. Braides, Energies in SBV and variational models in fracture mechanics. In: Proceedings of the EurHomogenization Congress, Nizza, Gakuto Int. Series, Math. Sci. and Appl. 9 (1997) 1-22.
5. L. Ambrosio, G. Buttazzo and I. Fonseca, Lower semicontinuity problems in Sobolev spaces with respect to a measure. J. Math. Pures Appl. 75 (1996) 211-224.
6. L. Ambrosio, A. Coscia and G. Dal Maso, Fine properties of functions in BD. Arch. Rational Mech. Anal. 139 (1997) 201-238.
7. L. Ambrosio and D. Pallara, Partial regularity of free discontinuity sets I. Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 24 (1997) 1-38.
8. L. Ambrosio, N. Fusco and D. Pallara, Partial regularity of free discontinuity sets II. Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 24 (1997) 39-62.
9. L. Ambrosio, N. Fusco and D. Pallara, Higher regularity of solutions of free discontinuity problems. Differential Integral Equations (in press).
10. L. Ambrosio, N. Fusco and D. Pallara, Functions of Bounded Variation and Free Discontinuity Problems. Oxford University Press, Oxford (in press).
11. L. Ambrosio and V.M. Tortorelli, Approximation of functionals depending on jumps by elliptic functionals via Γ-convergence. Comm. Pure Appl. Math. 43 (1990) 999-1036.
12. L. Ambrosio and V.M. Tortorelli, On the approximation of free discontinuity problems. Boll. U.M.I. 6-B (1992) 105-123.
13. F.J. Almgren, J. Taylor and L. Wang, Curvature driven flows: A variational approach. Siam J. Cont. Optim. 31 (1993) 387-438.
14. J.M. Ball, Nonlinear elasticity and materials science: A survey of some recent developments. In: P.J. Aston (ed.), Nonlinear Mathematics and Its Applications, Cambridge University Press, (1996) pp. 93-119.
15. G. Bellettini, A. Coscia and G. Dal Maso, Compactness and lower semicontinuity properties in SBD(Ω). Math. Z. 228 (1998) 337-351.
16. A. Braides, Approximation of Free Discontinuity Problems. Lecture Notes in Mathematics, Springer-Verlag, Berlin (1998).
17. M. Buliga, Variational Formulations in Brittle Fracture Mechanics. PhD Thesis, Institute of Mathematics of the Romanian Academy (1997).
18. M. Buliga, Modelisation de la décohesion d'interface fibres-matrice dans les materiaux composites. Memoire de D.E.A., Ecole Polytechnique (1995).
19. A.P. Calderon and A. Zygmund, On the differentiability of functions which are of bounded variation in Tonelli's sense. Rev. Un. Mat. Argentina 20 (1960) 102-121.
20. E. De Giorgi, New problems on minimizing movements. In: C. Baiocchi and J.L. Lions (eds), Boundary Value Problems for PDE and Applications, Masson (1993) pp. 81-98.
21. E. De Giorgi and L. Ambrosio, Un nuovo funzionale del calcolo delle variazioni. Atti Accad. Naz., Lincei Rend. Cl. Sci. Fis. Mat. Natur. 82 (1988) 199-210.
22. E. De Giorgi, G. Carriero and A. Leaci, Existence theory for a minimum problem with free discontinuity set. Arch. Rational Mech. Anal. 108 (1989) 195-218.
23. E. De Giorgi, Nuovi teoremi relativi alle misure (r - 1)-dimensionali in uno spazio a r-dimensioni. Ricerche Mat. 4 (1955) 95-113.
24. J.D. Eshelby, Energy relations and the energy-momentum tensor in continuum mechanics. In: M.F. Kanninen et al. (eds.), Inelastic Behavior of Solids, McGraw-Hill New York (1970) pp. 77-115.
25. L.C. Evans and R.F. Gariepy, Notes on measure theory and fine properties of functions. Studies in Advanced Math., CRC Press (1992).
26. G. Francfort and J.-J. Marigo, Stable damage evolution in a brittle continuous medium. Eur. J. Mech. A/Solids 12(2) (1993) 149-189.
27. A.A. Griffith, The phenomenon of rupture and flow in solids. Phil. Trans. Royal Soc. London A 221 (1920) 163-198.
28. M.E. Gurtin, On the energy release rate in quasistatic elastic crack propagation. J. Elasticity 9(2) (1979) 187-195.
29. M.E. Gurtin, Thermodynamics and the Griffith criterion for brittle fracture. Int. J. Solids Structures 15 (1979) 553-560.
30. G.R. Irwin, Structural Mechanics. Pergamon Press, London, England (1960).
31. R.V. Kohn, PhD Thesis. Princeton University (1979).
32. T.J. Richardson and S.K. Mitter, Approximation, computation, and distortion in the variational formulation. In: Bart M. ter Haar Romeny (ed.), Geometry-Driven Diffusion in Computer Vision, Kluwer Academic Publishers, Dordrecht (1994) pp. 169-190.
33. D. Mumford and J. Shah, Optimal approximation by piecewise smooth functions and associated variational problems. Comm. on Pure and Appl. Math. 42(5) (1989) 577-685.
34. K. Ohtsuka, Generalized J-integral and its applications I. Basic theory. Japan J. Appl. Math. 2 (1985) 21-52.
35. K. Ohtsuka, Generalized J-integral and three-dimensional fracture mechanics I. Hiroshima Math. J. 11 (1981) 329-350.
36. K. Ohtsuka, Generalized J-integral and three-dimensional fracture mechanics II. Hiroshima Math. J. 16 (1986) 327-352.
37. K. Ohtsuka, Generalized J-integral and its applications. RIMS Kokyuroku A 62, 149-165.
38. J.R. Rice, Mathematical analysis in the mechanics of fracture. In: H. Liebowitz (ed.), Fracture: An Advanced Treatise, Vol. II, Academic Press, New York (1969) 191-311.
39. H. Stumpf and K. Ch. Le, Variational principles of nonlinear fracture mechanics. Acta Mechanica 83 (1990) 25-37.