A thermodynamically consistent nonlocal formulation for damaging materials

European Journal of Mechanics, A/Solids

Volumn 21, Issue 4, 2002, Pages 535-553

  Benvenuti, Elena ^a   Borino, Guido ^b   Tralli, Antonio ^a  

^a UNIVERSITY OF FERRARA   (Italy)

^b UNIVERSITY OF PALERMO   (Italy)

Author keywords

Complementarity problem; Damage; Nonlocal models

Indexed keywords

ALGORITHMS; INTEGRAL EQUATIONS; MATHEMATICAL MODELS; PLASTICITY; PROBLEM SOLVING; STIFFNESS; STRENGTH OF MATERIALS;

COMPLEMENTARITY PROBLEMS; NONLOCAL MODELS; QUASI-BRITTLE MATERIALS; STRAIN LOCALIZATION;

FREE ENERGY;

EID: 0038357478     PISSN: 09977538     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0997-7538(02)01220-2     Document Type: Article

References (31)

1. Bathe K.J. Finite Element Procedures. 1996;Prentice Hall.
2. Batoz J.L., Dhatt G. Incremental displacement algorithms for nonlinear problems. Internat. J. Numer. Methods Engng. 14:1979;1262-1266.
3. Bažant Z.P., Pijaudier-Cabot G. Measurement of characteristic length of nonlocal continuum. J. Eng. Mech. 115:1989;755-767.
4. Benvenuti E., Borino G., Tralli A. A thermodynamically consistent nonlocal formulation for elasto-damaging materials: theory and computations. Oñate E. Proc. ECCOMAS 2000, Barcelona. 2000;. On CD.
5. de Borst, R., 1986. Non linear analysis of frictional materials. PhD thesis, University of Technology, Delft.
6. de Borst R., Heeres O.M., Benallal A. A gradient enhanced damage model: theory and computation. Owen D.R.J., , et al. Proc. CIMNE Computational Plasticity, Barcelona. 1997;373-380.
7. Capurso M., Maier G. Incremental elastoplastic analysis and quadratic optimization. Meccanica. 4:1970;107-116.
8. Chen Z., Schreyer H.L. Secant structural solution strategy. Comput. Methods Appl. Mech. Engrg. 90:1991;869-884.
9. Comi C., Rizzi E. On bifurcation in local and nonlocal materials with tension and compression damage. Oñate E. Proc. ECCOMAS 2000, Barcelona. 2000;. on CD.
10. Comi C. A non-local model with tension and compression damage mechanisms. Eur. J. Mech. A/Solids. 20:2001;1-22.
11. Cottle R.W., Pang R.E., Stone J.-S. The Linear Complementarity Problem. 1992;Academic Press, San Diego.
12. Crisfield M.A. Non Linear Finite Element Analysis of Solids and Structures. 1996;Wiley, New York.
13. Edelen D.G.B., Laws N. On the thermodynamics of systems with nonlocality. Arch. Ration. Mech. Anal. 43:1971;24-35.
14. Eringen C.A. Continuum Physics. IV:1976;Academic Press, New York. 205-267.
15. Frémond M., Nedjar B. Damage, gradient of damage and principle of virtual power. Internat. J. Solids Structures. 8:1996;1083-1103.
16. Ganghoffer, de Borst R. A new framework in nonlocal mechanics. Internat. J. Engrg. Sci. 38:2000;453-486.
17. Germain P., Nguyen Q.S., Suquet P. Continuum Thermodynamics. J. Appl. Mech. 50:1983;1010-1021.
18. Hassanzadeh, M., 1991. Behavior of fracture process zones in concrete influenced by simultaneously applied normal and shear displacements. PhD Thesis, Institute of Technology, Lund.
19. Kolmogorov A.N., Fomin S.V. Introductory Real Analysis. 1970;Dover, New York.
20. Lemaitre J., Chaboche J.L. Mechanics of Solid Materials. 1990;Cambridge University Press, New York.
21. Maier G. A minimum principle incremental elastoplasticity with nonassociated flow laws. J. Mech. Phys. Solids. 18:1970;319-330.
22. Maier G. Incremental elastoplastic analysis in the presence of large displacement and physical instabilizing effects. Internat. J. Solids Structures. 7:1971;345-372.
23. Nedjar B. Elastoplastic-damage modelling including the gradient of damage: formulation and computational aspects. Internat. J. Solids Structures. 38:2001;5421-5451.
24. Pijaudier-Cabot G., Bažant Z.P. Nonlocal Damage Theory. J. Eng. Mech. 10:1987;1512-1533.
25. Pijaudier-Cabot G., Benallal A. Strain localization and bifurcation in a non-local continuum. Internat. J. Solids Structures. 30:1993;1761-1775.
26. Polizzotto C., Borino G. A thermodynamics-based formulation of gradient plasticity. Eur. J. Mech. A/Solids. 17:1998;741-761.
27. Polizzotto C., Borino G., Fuschi P. A thermodynamically consistent formulation of nonlocal and gradient plasticity. Mech. Res. Comm. 25:1998;75-82.
28. Rudnicki J.W., Rice J.R. Conditions for the localization of deformations in pressure-sensitive dilatant material. J. Mech. Physics Solids. 23:1975;371-394.
29. Simo J.C., Hughes T.J.R. Computational Inelasticity. 1997;Springer- Verlag, Wien.
30. Strömberg L., Ristinmaa M. F.E. formulation of a nonlocal plasticity theory. Comput. Methods Appl. Mech. Engrg. 136:1996;127-144.
31. Svedberg T., Runesson K. Thermodynamically consistent nonlocal and gradient formulations of plasticity. Euromech Colloqium. 1998;378 Muhlhouse, France.