Multifield description of microcracked continua: A local model

Mathematics and Mechanics of Solids

Volumn 3, Issue 2, 1998, Pages 183-200

  Mariano, Paolo Maria ^a   Augusti, Giuliano ^a  

^a SAPIENZA UNIVERSITY OF ROME   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

BRITTLE FRACTURE; CONTINUUM MECHANICS; CRACK PROPAGATION; ELASTICITY; MATHEMATICAL MODELS;

CLAUSIUS-DUHEM INEQUALITY;

SOLIDS;

EID: 0032097110     PISSN: 10812865     EISSN: None     Source Type: Journal    
DOI: 10.1177/108128659800300204     Document Type: Article

References (27)

1. Krajcinovic, D.: Damage Mechanics, North-Holland, Amsterdam, 1996.
2. Capriz, G. and Giovine, P.: Remedy to omissions in a tract on continua with microstructure. Proc. XIII National Congress of the Italian Association of Theoretical and Applied Mechanics, AIMETA, Siena, 1997.
3. Di Carlo, A.: A non-standard format for continuum mechanics, in Contemporary Research in the Mechanics and Mathematics of Materials, pp. 92-104, eds., R. C. Batra and M. F. Beatty, CIMNE, Barcelona, 1996.
4. Lubarda, V. A. and Krajcinovic, D.: Damage tensors and the crack density distribution Int. J. Solids Struct., 30, 2859-2877 (1993).
5. Mariano, P.M.: Natural entropies in the state space of damaged bodies. Z. Angew. Math. Phys. ZAMP, 48, 1002-1011 (1997).
6. Liu, I.-S.: On entropy flux-heat flux relation in thermodynamics with Lagrange multipliers. Continuum Mech. Thermodyn., 8, 247-256 (1996).
7. Mariano, P. M. and Augusti, G.: Some axioms and theorems in damage mechanics and fatigue of materials. Int. J. Solids Struct., 34, 3337-3350 (1997).
8. Bazant, Z. P. and Pijauder-Cabot, G.: Nonlocal continuum damage, localization instability and convergence. ASME J. Appl. Mech., 55, 287-293 (1988).
9. Pijauder-Cabot, G. and Benallal, H.: Strain localization and bifurcation in a nonlocal continuum. Int. J. Solids Struct., 30, 1761-1775 (1993).
10. Brekelmans, W. A.: Nonlocal formulation of the evolution of damage in a one-dimensional configuration. Int. J. Solids Struct., 30, 1503-1512 (1993).
11. Xia, S., Takezono, S., and Tao, K.: Nonlocal elastic damage near crack tip. Int. J. Fract., 62, 87-95 (1993).
12. Benallal, A. and Tvergaard, V.: Nonlocal continuum effects on bifurcation in the plane strain tension-compression test, Report No. 490, Technical University of Denmark, 1994.
13. Morro, A.: A Gronwall-like inequality and its application to continuum thermodynamics. Boll. UMI, I-B, 553-562 (1981).
14. Morro, A. and Ruggeri, T.: Propagazione del Calore ed Equazioni Costitutive. Quaderni del GNFM, Bologna, 1984.
15. Segev, R.: A geometrical framework for the statics of materials with microstructure. Math. Models Meth. Appl. Sci., 4, 871-897 (1994).
16. Capriz, G. and Virga, E. G.: Interaction in general continua with microstructure. Arch. Ration. Mech. Anal., 109, 323-342 (1990).
17. Kiajcinovic, D. and Mastilovic, S.: Some fundamental issues of damage mechanics. Mech. Mat., 21, 217-230 (1995).
18. Edelen, D.G.B.: Nonlocal field theories, in Continuum Physics, IV, ed., A. C. Eringen, Academic Press, New York, 1976.
19. Noll, W.: The geometry of contact, separation and reformation of continuous bodies. Arch. Ration. Mech. Anal., 122, 197-212 (1993).
20. Mariano, P. M.: Some remarks on the variational description of microcracked bodies. Int. J. Non-Linear Mech., in press.
21. Fletcher, D. C.: Conservation laws in linear elastodynamics. Arch. Ration. Mech. Anal., 60, 329-353 (1976).
22. Nunziato, J. W. and Cowin, S. C.: A nonlinear theory of elastic materials with voids. Arch. Ration. Mech. Anal., 72, 175-201 (1979).
23. Lemaitre, J.: A Course on Damage Mechanics, Springer-Verlag, Berlin, 1992.
24. Baldacci, R.: Scienza delle Costruzioni, UTET, Torino, 1970.
25. Frémond, M. and Nedjar, B.: Damage, gradient of damage and principle of virtual power. Int. J. Solids Struct., 33, 1083-1103 (1996).
26. Mariano, P. M. and Trovalusci, P.: Constitutive relations for elastic microcracked bodies: From a lattice model to a multifield continuum description. Int. J. Damage Mech., in press.
27. Capriz, G.: Continua with latent microstructure. Arch. Ration. Mech. Anal., 90, 43-56 (1985).