Unified thermodynamic framework for nonlocal/gradient continuum theories

European Journal of Mechanics, A/Solids

Volumn 22, Issue 5, 2003, Pages 651-668

  Polizzotto, Castrenze ^a  

^a UNIVERSITY OF PALERMO   (Italy)

Author keywords

Gradient elasticity; Gradient plasticity; Nonlocal continua; Nonstandard boundary conditions

Indexed keywords

BOUNDARY CONDITIONS; BOUNDARY VALUE PROBLEMS; ELASTICITY; FINITE ELEMENT METHOD; PLASTICITY; STRAIN; THERMODYNAMICS;

GRADIENT ELASTICITY; GRADIENT PLASTICITY; NONLOCAL CONTINUA;

CONTINUUM MECHANICS;

EID: 2942552905     PISSN: 09977538     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0997-7538(03)00075-5     Document Type: Conference Paper

References (45)

1. Aifantis E.C. Update on a class of gradient theories. Mech. Mater. 35:2003;259-280.
2. Altan B.S., Aifantis E.C. On some aspects in the special theory of gradient elasticity. J. Mech. Behavior Mater. 8:1997;231-282.
3. Bažant Z.P., Cedolin L. Stability of Structures. 1991;Oxford University Press, New York.
4. Bažant Z.P., Planas J. Fracture and Size Effects in Concrete and Other Quasibrittle Materials. 1998;CRC Press LLC, Boston.
5. Bažant Z.P., Jirásek M. Nonlocal integral formulations of plasticity and damage: survey of progress. J. Engrg. Mech. ASCE. 128:2002;1119-1149.
6. Benvenuti E., Borino G., Tralli A. A thermodynamically consistent nonlocal formulation of damaging materials. Eur. J. Mech. A Solids. 21:2002;535-553.
7. Borino, G., Failla, B., Parrinello, F., 2003. A symmetric nonlocal damage theory. Int. J. Solids Structures, in press.
8. Borino G., Fuschi P., Polizzotto C. A thermodynamic approach to nonlocal plasticity and related variational principles. ASME J. Appl. Mech. 66:1999;952-963.
9. de Borst R., van der Giessen E. Material Instabilities in Solids. 1998;Wiley, Chichester.
10. de Borst R., Mühlhaus H.-B. Gradient dependent plasticity: formulation and algorithmic aspects. Int. J. Numer. Methods Engrg. 35:1992;539-541.
11. Capurso M. Minimum principle in elastic-plastic incremental analysis problems. Atti Accad. Naz. Lincei (8). XLIV:(4-5):1969;552-560. (in Italian).
12. Capurso M., Maier G. Incremental elastoplastic analysis and quadratic optimization. Meccanica. V:1970;107-116.
13. Colemann B.D., Gurtin M.E. Thermodynamics with internal variables. J. Chem. Phys. 47:1967;597-613.
14. Dunn J.E., Serrin J. On the thermodynamics of interstitial working. Arch. Rational Mech. Anal. 88:1985;95-133.
15. Edelen D.G.B., Laws N. Thermodynamics with internal variables. J. Chem. Phys. 47:1971;597-613.
16. Edelen D.G.B., Green A.E., Laws N. Nonlocal continuum mechanics. Arch. Rational Mech. Anal. 43:1971;24-35.
17. Eringen A.C. Nonlocal polar elastic continua. Int. J. Engrg. Sci. 10:1972;1-16.
18. Eringen A.C. Nonlocal micropolar field theory. Eringen A.C. Continuum Phys. 4:1976;205-267 Academic Press, New York.
19. Eringen A.C. Line crack subjected to shear. Int. J. Fracture. 14:1978;367-379.
20. Eringen A.C. Line crack subjected to antiplane shear. Engrg. Fract. Mech. 12:1979;211-219.
21. Eringen A.C. On nonlocal plasticity. Int. J. Engrg. Sci. 12:1981;1461-1474.
22. Eringen A.C. Theory of nonlocal elasticity and some applications. Res. Mech. 21:1987;313-342.
23. Eringen A.C., Edelen D.G.B. Nonlocal elasticity. Int. J. Engrg. Sci. 10:1972;233-248.
24. Germain P., Nguyen Q.S., Suquet P. Continuum thermodynamics. ASME J. Appl. Mech. 50:1983;1010-1021.
25. Gurtin M.E. Thermodynamics and the possibility of spatial interaction on elastic materials. Arch. Rational Mech. Anal. 19:1965;339-352.
26. Kröner E. Elasticity theory of materials with long range cohesive forces. Int. J. Solids Structures. 3:1967;731-742.
27. Lemaitre J., Chaboche J.-L. Mechanics of Solid Materials. 1990;Cambridge University Press, Cambridge.
28. Liebe T., Steinmann P., Benallal A. Theoretical and computational aspects of a thermodynamically consistent framework of geometrically linear gradient damage. Comput. Methods Appl. Mech. Engrg. 190:2001;6555-6576.
29. Malvern L.E. Introduction to the Mechanics of Continuous Media. 1969;Prentice-Hall, Englewood Cliffs, NJ.
30. Maugin G.A. Internal variables and dissipative structures. J. Non-Equilib. Thermodyn. 15:1990;173-192.
31. Mindlin R.D. Second gradient of strain and surface-tension in linear elasticity. Int. J. Solids Structures. 1:1965;417-438.
32. Mindlin R.D., Eshel N.N. On first strain-gradient theories in linear elasticity. Int. J. Solids Structures. 4:1968;109-124.
33. Mühlhaus H.-B., Aifantis E.C. A variational principle for gradient plasticity. Int. J. Solids Structures. 28:1991;845-858.
34. Mühlhaus H.B. Continuum Models for Materials with Microstructure. 1995;Wiley, Chichester.
35. Pijaudier-Cabot G., Bažant Z.P. Nonlocal damage theory. J. Engrg. Mech. 113:1987;1512-1533.
36. Polizzotto C. Nonlocal elasticity and related variational principles. Int. J. Solids Structures. 38:2001;7359-7380.
37. Polizzotto C. Thermodynamics and continuum fracture mechanics for nonlocal-elastic plastic materials. Eur. J. Mech. A Solids. 21:2002;85-103.
38. Polizzotto C. Remarks on some aspects of nonlocal theories in solid mechanics. Proc. of the 6th National Congress SIMAI. 2002;Chia Laguna, Italy.
39. Polizzotto, C., 2003. Gradient elasticity and nonstandard boundary conditions. Int. J. Solids Structures, in press.
40. Polizzotto C., Borino G., Fuschi P. A thermodynamically consistent formulation of nonlocal and gradient plasticity. Mech. Res. Commun. 25:1998;75-82.
41. Polizzotto C., Borino G. A thermodynamics-based formulation of gradient-dependent plasticity. Eur. J. Mech. A Solids. 17:1998;741-761.
42. Rogula D. Introduction to nonlocal theory of material media. Rogula D. Nonlocal Theory of Material Media. 1982;125-222 Springer, Berlin.
43. Toupin R. Elastic materials with couple stresses. Arch. Rational Mech. Anal. 11:1962;385-414.
44. Vardulakis I., Exadaktylos G., Aifantis E.C. Gradient elasticity with surface energy: mode III crack problem. Int. J. Solids Structures. 33:1996;4531-4559.
45. Wu C.H. Cohesive elasticity and surface phenomena. Quart. Appl. Math. L:(1):1992;73-103.