On the continuum formulation of higher gradient plasticity for single and polycrystals

Journal of the Mechanics and Physics of Solids

Volumn 48, Issue 8, 2000, Pages 1777-1796

  Menzel, A ^a   Steinmann, P ^a  

^a RPTU in Kaiserslautern   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

DISLOCATIONS (CRYSTALS); GEOMETRY; PLASTIC DEFORMATION; PLASTICITY; POLYCRYSTALLINE MATERIALS; POLYCRYSTALS; SINGLE CRYSTALS; STRAIN;

ELASTIC-PLASTIC MATERIAL; HIGHER GRADIENT PLASTICITY;

CONTINUUM MECHANICS;

EID: 0033728964     PISSN: 00225096     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0022-5096(99)00024-1     Document Type: Article

References (25)

1. Aifantis E.C. On the microstructural origin of certain inelastic models. J. . Mater. Technol. 106:1984;326-330.
2. Aifantis E.C. The physics of plastic deformations. Int. J. Plasticity. 3:1987;211-247.
3. Aifantis E.C. On the role of gradients in the localization of deformation and fracture. Int. J. Engng. Sci. 30:1992;1279-1299.
4. Aifantis E.C. Pattern formation in plasticity. Int. J. Engng Sci. 33:1995;2161-2178.
5. Anthony K.H. Die Reduktion von nichteuklidischen geometrischen Objekten in eine eulkidische Form und physikalische Deutung der Reduktion durch Eigenspannungszustände in Kristallen. Arch. Rat. Mech. Anal. 37:1970;161-180.
6. Anthony K.H. Die Theorie der Disklinationen. Arch. Rat. Mech. Anal. 39:1970;43-88.
7. Anthony K.H. Die Theorie der nichtmetrischen spannungen in Kristallen. Arch. Rat. Mech. Anal. 40:1970;50-78.
8. Bilby B.A., Bullough R., Smith E. Continuous distributions of dislocations: a new application of the methods of non-Riemannian geometry. Proc. Roy. Soc. A231:1955;263-273.
9. de Borst R., Mühlhaus H.B. Gradient-dependent plasticity: formulation and algorithmic aspects. Int. J. Numer. Methods Eng. 35:1992;521-539.
10. Fleck N.A., Hutchinson J.W. A phenomenological theory for strain gradient effects in plasticity. J. Mech. Phys. Solids. 41:1993;1825-1857.
11. Fleck N.A., Muller G.M., Ashby M.F., Hutchinson J.W. Strain gradient plasticity: theory and experiment. Acta Metall. Mater. 42:1994;475-487.
12. Huerta A., Pijaudier-Cabot G. Discretization influence on regularization by two localization limiters. ASCE J. Engng. Mech. 120:1994;1198-1218.
13. Kondo K. On the geometrical and physical foundations of the theory of yielding. Proceedings of the Second Japanese National Congress on Applied Mechanics. 1952.
14. Kröner, E. Kontinuumstheorie der Versetzungen und Eigenspannungen. Erg. Angew. Math. 3:1958;1-179.
15. Kröner E. Allgemeine Kontinuumstheorie der Versetzungen und Eigenspannungen. Arch. Rat. Mech. Anal. 4:1960;273-334.
16. Kröner E., Seeger A. Nichtlineare Elastizitätstheorie der Versetzungen und Eigenspannungen. Arch. Rat. Mech. Anal. 3:1959;97-119.
17. Maugin G.A. Material Inhomogeneities in Elasticity. 1993;Chapman & Hall, London.
18. Nye J.F. Some geometrical relations in dislocated crystals. Acta Metallurgica. 1:1953;153-162.
19. Pamin J.K. Gradient-Dependent Plasticity in Numerical Simulation of Localization Phenomena. 1994;University Press, Delft.
20. Seeger A. Neure mathematische Methoden und physikalische Ergebnisse zur Kristallplastizität. Proceedings of the IUTAM Colloquium on Deformation and Flow of Solids (Madrid), Springer, Berlin. 1955.
21. Sluys L.J., de Borst R., Mühlhaus H.B. Wave propagation, localization and dispersion in a gradient-dependent medium. Int. J. Solids & Structures. 30:1993;1153-1171.
22. Steinmann P. Views on multiplicative elstoplacticity and the continuum theory of dislocations. Int. J. Engng. Sci. 34:1996;1717-1735.
23. Svedberg T., Runesson K. An algorithm for gradient-regularized plasticity coupled to damage based on a dual mixed FE-formulation. Comp. Meth. Appl. Mech. Engrg. 161:1998;49-65.
24. de Wit R. A view of the relation between the continuum theory of lattice defects and non-Euclidian geometry in the linear approximation. Int. J. Engng. Sci. 19:1981;1475-1506.
25. Zbib, H.M., Aifantis, E.C. 1988 On the localization and postlocalization behavior of plastic deformation, I, II, III, Res. Mechanica 23, 261-277, 279-292, 292-305.