160 elements. It can be observed that the strain localization phenomenon is well regularized and, moreover, the damage band tends to shrink as the damage loading proceed. This aspect is quite remarkable, since it has been obtained without enforcing any special evolution law for the internal length parameter, which is kept constant in the analysis. To conclude, numerical tests of 2-D structures are at the moment under study. It is expected that such analysis will confirm the above discussed properties of the presented thermodynamically consistent damage model. 0 2 4 6 8 x 10 −3 0 0.5 1 1.5 u [mm] P [N] 20 F.E. 40 F.E. 80 F.E. 160 F.E. 0 50 100 0 0.2 0.4 0.6 0.8 1 x [mm] D Fig. 1 (a) Load-displacement curves obtained with 20, 40, 80 and 160 elements. (b) Evolution of the damage profile at increasing damage loading steps. Results obtained with 160 elements. REFERENCES 1. Polizzotto, C., Borino, G. and Fuschi, P. (1997), Mech. Res. Com. 25, 75–82. 2. Borino, G., Fuschi, P. and Polizzotto, C. (1999), J. Appl. Mech. 66, 952–963. 3. Lemaitre, J. and Chaboche, J.-L. (1990), Mechanics of Solids Materials, Cambridge University Press, New York. 4. Baˇzant, Z.P. and Pijaudier-Cabot, G. (1987), J. Appl. Mech. 55, 287–293. 5. Peerlings, R.H.J., de Borst, R., Brekelmans, W.A.M. and de Vree, J.H.P. (1996) Int. J. Num. Meth. Engrg. 39, 3391–3403. 6. Comi, C. (1999), Mech. Cohesive Frictional Materials 4, 17–36. 7. Pijaudier-Cabot, G. and Baˇzant, Z.P. (1987), J. Engrg. Mech. 113, 1512–1533. 8. Benvenuti, E., Borino, G. and Tralli, A. (2000), In: CD Proc. ECCOMAS 2000, Barcelona, Spain. 9. Benvenuti, E. (2001), Ph.D. Thesis, University of Ferrara, Italy. 10. Edelen, D.G.B. and Laws, N. (1971), Arch. Rat. Mech. Anal. 43, 24–35. 11. Str¨omberg, L. and Ristinmaa, M (1996), Comp. Meth. Appl. Mech. Engrg. 136, 127–144.
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