strain-hardening modulus, say a = 0.5, 0.18 = D at 0.016 max1 = = w w f (dot line in Figure 4, 0.006 = h , 0.004 =δ ). In this case the fracture condition is nowhere satisfied at max w fw = and the solution cannot be extended for . max w w f > r k τrz (elastic solution) k or τrz kmax 0 r f Rmax rm Figure 3: Schematic diagram illustrating non-existence of solution 0,00 0,10 0,20 0,30 0,00 0,02 0,04 0,06 0,08 0,10 0,12 0,14 fr = Dc D wmax2 wmax1 wf Figure 4: Evolution of the damage variable at r Acknowledgement This research was supported by the Russian Foundation for Basic Research (Grants 99-01-00926, 00-1596066). References 1. Panin, V.E. (1998). Physical mesomechanics, 5,22. 2. Alexandrov, S. and Goldstein, R.V. (1999). Sov. Phys. Dok. 368(6), 768 [in Russian]. 3. Lemaitre, J. (1987). In: Continuum Damage Mechanics: Theory and Applications, pp. 37-89, Krajcinovic, D. and Lemaitre, J. (Eds). Springer, Wien - New York. 4. Prahl, U., Aboutayeb, M., Achenbach, U. and Wang, X. (1999). Comp. Mater. Sci. 16, 206. 5. Alexandrov, S. and Goldstein, R.V. (1999). C. R. Acad. Sci. Ser. IIb 327, 193. 6. Alexandrov, S. and Goldstein, R.V. (2000). J. Appl. Math. Mech. 64, 155.
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