Variational formulations and a consistent finite-element procedure for a class of nonlocal elastic continua

International Journal of Solids and Structures

Volumn 45, Issue 14-15, 2008, Pages 4184-4202

  Marotti de Sciarra, Francesco ^a  

^a UNIVERSITY OF NAPLES FEDERICO II   (Italy)

Author keywords

Nonlocal elasticity; Nonlocal finite element method; Regularization; Variational formulations

Indexed keywords

ELASTICITY; FINITE ELEMENT METHOD; MATHEMATICAL MODELS; STATE ESTIMATION; VARIATIONAL TECHNIQUES;

NONLOCAL ELASTICITY; NONLOCAL FINITE-ELEMENT METHOD; REGULARIZATION; VARIATIONAL FORMULATIONS;

CONTINUUM MECHANICS;

EID: 43049123384     PISSN: 00207683     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ijsolstr.2008.03.003     Document Type: Article

References (23)

1. Alfano G., and Marotti de Sciarra F. Mixed finite element formulations and related limitation principles: a general treatment. Comput. Methods Appl. Mech. Eng. 138 (1996) 105-130
2. Borino G., Failla B., and Parrinello F. A symmetric nonlocal damage theory. Int. J. Solids Struct. 40 (2003) 3621-3645
3. Brezis H. Analyse Fonctionnelle. Théorie et Applications (1983), Masson Editeur, Paris
4. Edelen D.G.B., and Laws N. On the thermodynamics of systems with nonlocality. Arch. Rat. Mech. Anal. 43 (1971) 24-35
5. Eringen A.C. Nonlocal micropolar field theory. In: Eringen A.C. (Ed). Continuum Physics vol. 4 (1976), Academic Press, New York 205-267
6. Eringen A.C. Line crack subjected to shear. Int. J. Fract. 14 (1978) 367-379
7. Eringen A.C., and Kim B.S. Stress concentration at the tip of a crack. Mech. Res. Commun. 1 (1974) 233-237
8. Eringen A.C., Speziale C.G., and Kim B.S. Crack-tip problem in non-local elasticity. J. Mech. Phys. Solids 25 (1977) 339-355
9. Jirásek M., and Rolshoven S. Comparison of integral-type nonlocal plasticity models for strain-softening materials. Int. J. Eng. Sci. 41 (2003) 1553-1602
10. Kröner E. Elasticity theory of materials with long range cohesive forces. Int. J. Solids Struct. 3 (1967) 731-742
11. Lemaitre J., and Chaboche J.L. Mechanics of Solids Materials (1994), Cambridge University Press, Cambridge, UK
12. Polizzotto C. Nonlocal elasticity and related variational principles. Int. J. Solids Struct. 38 (2001) 7359-7380
13. Polizzotto C. Thermodynamics and continuum fracture mechanics for nonlocal-elastic plastic materials. Eur. J. Mech. A/Solids 21 (2002) 85-103
14. Polizzotto C., Fuschi P., and Pisano A.A. A strain-difference-based nonlocal elasticity model. Int. J. Solids Struct. 41 (2004) 2383-2401
15. Polizzotto C., Fuschi P., and Pisano A.A. A nonhomogeneous nonlocal elasticity model. Int. J. Solids Struct. 25 (2006) 308-333
16. Rockafellar R.T. Convex Analysis (1970), Princeton University Press, Princeton
17. Romano G. Scienza delle Costruzioni vol. I-II (2002), Hevelius Edizioni (in Italian)
18. Romano G., Rosati L., Marotti de Sciarra F., and Bisegna P. A potential theory for monotone multi-valued operators. Q. Appl. Math. 4 (1993) 613-631
19. Showalter R.E. Monotone Operators in Banach Space and Nonlinear Partial Differential Equations (1997), American Mathematical Society
20. Tricomi F.G. Integral Equations (1985), Dover Publications Inc., New York
21. Vainberg M.M. Variational Methods for the Study of Non-Linear Operators (1964), Holden-Day Inc., San Francisco
22. Washizu K. Variational Methods in Elasticity and Plasticity. third ed. (1982), Pergamon, New York
23. Zhou Z.G., Han J.C., and Du S.Y. Investigation of a Griffith crack subjected to anti-plane shear by using the non-local theory. Int. J. Solids Struct. 36 (1999) 3891-3901