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Revisiting brittle fracture as an energy minimization problem. (English) Zbl 0966.74060
Summary: We propose a variational model of quasistatic crack evolution. Although close in spirit to Griffith’s theory of brittle fracture, the proposed model, however, frees itself from the usual constraints of that theory: a preexisting crack and a well-defined crack path. In contrast, crack initiation as well as crack path can be quantified, as demonstrated on explicitly computable examples. Furthermore, the model lends itself to numerical implementation in more complex settings.

MSC:
74R10Brittle fracture
74G65Energy minimization (equilibrium problems in solid mechanics)
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References:
[1] Ambrosio, L.: Acta appl. Math.. 17, 1 (1989)
[2] Ambrosio, L., Coscia, A. and Dal Maso, G. (to appear) Fine properties of functions with bounded deformations.
[3] Ambrosio, L.; Tortorelli, V. M.: Comm. pure appl. Math.. 43, 999 (1990)
[4] Amestoy, M. (1987) Propagations de fissures en élasticité plane. Thèse d’Etat, Paris.
[5] Amestoy, M.; Leblond, J. -B.: International journal of solids and structures. 29, 465 (1989)
[6] Ball, J. M.; James, R. D.: Archives for rational mechanics and analysis. 110, 13 (1987)
[7] Barenblatt, G. I.: Advances in applied mechanics. 7, 55 (1962)
[8] Belletini, G.; Coscia, A.: Num. funct. Anal. optim.. 15, 201 (1994)
[9] Bourdin, B. (to appear in M2AN) Image segmentation with a finite element method. · Zbl 0947.65075
[10] Carriero, M.; Leaci, A.: Nonlinear anal. Th. meth. Appls.. 15, 661 (1990)
[11] Degiorgi, E.; Carriero, M.; Leaci, A.: Archives for rational mechanics and analysis. 108, 195 (1989)
[12] Ehrlacher, A. and Fedelich, B. (1989) Stability and bifurcation of simple dissipative systems ; application to brutal damage. In Cracking and Damage : Strain Localization and Size Effect, ed. J. Mazars and Z. P. Bazant, pp. 217--227. Elsevier, New York.
[13] Evans, L. C. and Gariepy, R. F. (1992) Measure Theory and Fine Properties of Functions. CRC Press, Boca Raton. · Zbl 0804.28001
[14] Fonseca, I.; Francfort, G. A.: Calculus of variations. 3, 407 (1995)
[15] Fonseca, I. and Fusco, N. (to appear) Regularity results for anisotropic image segmentation models. · Zbl 0899.49018
[16] Francfort, G. A.; Marigo, J. J.: Eur. J. Mech. a\solids. 12, 149 (1993)
[17] Francfort, G. A. and Marigo, J. J. (to appear) Cracks in fracture mechanics : a time-indexed family of energy minimizers. In Proceedings of the International IUTAM Symposium, April 1997, Paris : Variations de domaines et frontières libres en mécanique des solides, ed. M. Fremond and Q. S. Nguyen.
[18] Griffith, A. (1920) The phenomena of rupture and flow in solids. Phil. Trans. Roy. Soc. London CCXXI-A, 163--198.
[19] Hashin, Z.: Journal of the mechanics and physics of solids. 44, 1129 (1996)
[20] James, R. and Kinderlehrer, D. (1993) Theory of magnetostriction with application to TbxDy1-xFe2. Philosophical Magazine B68, 237--274.
[21] Leblond, J. -B.: International journal of solids and structures. 25, 1311 (1989)
[22] Leguillon, D.: CR acad. Sci. Paris série II. 309, 945 (1990)
[23] Leguillon, D.: CR acad. Sci. Paris série II. 310, 155 (1990)
[24] Mumford, D.; Shah, J.: Comm. pure applied math.. 42, 577 (1989)
[25] Nguyen, Q. S.: Journal of mechanics and physics of solids. 35, 303 (1987)
[26] Sih, G. C. and Liebowitz, H. (1968) Mathematical theories of brittle fracture. In Fracture : An Advanced Treatise, Vol. II, Mathematical Fundamentals, ed. H. Liebowitz, pp. 67--190. Academic Press, New York. · Zbl 0207.24801