On smooth bifurcations in non-associative elastoplasticity

Journal of the Mechanics and Physics of Solids

Volumn 44, Issue 8, 1996, Pages 1337-1351

  Bigoni, Davide ^a  

^a UNIVERSITY OF BOLOGNA   (Italy)

Author keywords

A. buckling; B. elastic plastic material; B. finite strain

Indexed keywords

BIFURCATION (MATHEMATICS); BUCKLING; DEFORMATION; PLASTIC FLOW; SOLIDS; STRAIN;

CONSTITUTIVE EQUATIONS; FINITE STRAIN; RANIECKI EXCLUSION PRINCIPLE;

ELASTOPLASTICITY;

EID: 0030214715     PISSN: 00225096     EISSN: None     Source Type: Journal    
DOI: 10.1016/0022-5096(96)00025-7     Document Type: Article

References (41)

1. Bigoni, D. and Zaccaria, D. (1992a) Strong ellipticity of comparison solids in elastoplasticity with volumetric non-associativity. Int. J. Solids Structures 29, 2123-2136.
2. Bigoni, D. and Zaccaria, D. (1992b) Loss of strong ellipticity in non-associative elastoplasticity. J. Mech. Phys. Solids 40, 1313-1331.
3. Bortzmeyer, D. (1992) Modelling ceramic powder compaction. Powder Technol. 70, 131-139.
4. Bruhns, O. T. (1982) Bounds to the critical stresses in bifurcation of cylindrical specimens in the case of non-associated flow laws. In Stability in the Mechanics of Continua (ed. F. H. Schroeder), pp. 46-56. Springer-Verlag, Berlin.
5. Capurso, M. (1979) Extremum theorems for the solution of the rate problem in elastic-plastic fracturing structures. J. Struct. Mech. 7, 411-434.
6. Chau, K.-T. and Rudnicki, J. W. (1990) Bifurcations of compressible pressure-sensitive materials in plane strain tension and compression. J. Mech. Phys. Solids 38, 875-898.
7. 2-containing ceramics: I, shear and dilatation effects. J. Am. Ceram. Soc. 69, 181-189.
8. Cheng, Y. S. and Lu, W. D. (1993) Uniqueness and bifurcation in elastic-plastic solids. Int. J. Solids Structures 30, 3073-3084.
9. Del Piero, G. (1979). Some properties of the set of fourth-order tensors, with application to elasticity. J. Elasticity 9, 245-261.
10. Gurtin, M. E. (1981) An Introduction to Continuum Mechanics. Academic Press, New York.
11. Hill, R. (1958) A general theory of uniqueness and stability in elastic-plastic solids. J. Mech. Phys. Solids 6, 236-249.
12. Hill, R. (1959) Some basic principles in the mechanics of solids without a natural time. J. Mech Phys. Solids, 7, 209-225.
13. Hill, R. (1978) Aspects of invariance in solid mechanics. In Advances in Applied Mechanics 18 (ed. Chia-Shun Yih), pp. 1-75. Academic Press, New York.
14. Hueckel, T. (1976) Coupling of elastic and plastic deformation of bulk solids. Meccanica 11, 227-235.
15. Hueckel, T. and Maier, G. (1977) Incremental boundary value problems in the presence of coupling of elastic and plastic deformations: a rock mechanics oriented theory. Int. J. Solids Structures 13, 1-15.
16. Hutchinson, J. W. (1973) Post-bifurcation behavior in the plastic range. J. Mech. Phys. Solids 21, 163-190.
17. Lade, P. V. and Kim, M. K. (1995) Single hardening constitutive model for soil, rock and concrete. Int. J. Solids Structures 32, 1963-1978.
18. Leger, A. and Potier-Ferry, M. (1988) Sur le flambage plastique. Journal de Mécanique Théorique et Appliquée 7, 819-857.
19. Léger, A. and Potier-Ferry, M. (1993) Elastic-plastic post-buckling from a heterogeneous state. J. Mech. Phys. Solids 41, 783-807.
20. Maier, G. (1970) A minimum principle for incremental elastoplasticity with non-associated flow laws. J. Mech. Phys. Solids 18, 319-330.
21. Maier, G. and Hueckel, T. (1979) Non associated and coupled flow-rules of elastoplasticity for rock-like materials. Int. J. Rock Mech. Min. Sci. 16, 77-92.
22. Mandel, J. (1966) Conditions de stabilite et postulat de Drucker. In Rehology and Soil Mechanics (ed. J. Kravtchenko and P. M. Sirieys), pp. 58-68. Springer, Berlin.
23. Mroz, Z. (1963) Non-associated flow-laws in plasticity. Journal de Mécanique Théorique et Appliquée II, 21-42.
24. Mróz, Z. (1966) On forms of constitutive laws for elastic-plastic solids. Arch. Mech. Stosowanej 18, 3-35.
25. Needleman, A. (1979) Non-normality and bifurcation in plane strain tension and compression. J. Mech. Phys. Solids 27, 231-254.
26. Nguyen, S. Q. (1987) Bifurcation and post-bifurcation analysis in plasticity and brittle fracture. J. Mech. Phys. Solids 35, 303-324.
27. Nguyen, S. Q. and Triantafyllidis, N. (1989) Plastic bifurcation and postbifurcation analysis for generalized standard continua. J. Mech. Phys. Solids 37, 545-566.
28. Petryk, H. (1993) Theory of bifurcation and instability in time-independent plasticity. In Bifurcation and Stability of Dissipative Systems (ed. Q. S. Nguyen), pp. 95-152. Springer-Verlag, Wien.
29. Petryk, H. and Thermann, K. (1985) Second-order bifurcation in elastic-plastic solids. J. Mech. Phys. Solids 33, 577-593.
30. Qin, Q. and Bassani, J. L. (1992) Non-associated plastic flow in single crystals. J. Mech. Phys. Solids 40, 835-862.
31. Raniecki, B. (1979) Uniqueness criteria in solids with non-associated plastic flow laws at finite deformations. Bull. Acad. Polon. Sci. ser. Sci. Tech. XXVII (8-9), 391-399.
32. Raniecki, B. and Bruhns, O. T. (1981) Bounds to bifurcation stresses in solids with non-associated plastic flow law at finite strain. J. Mech. Phys. Solids 29, 153-171.
33. Rice, J. R. (1977) The localization of plastic deformation. In Theoretical and Applied Mechanics (ed. W. T. Koiter), pp. 207-220. North-Holland, Amsterdam.
34. Rudnicki, J. W. and Rice, J. R. (1975) Conditions for the localization of deformations in pressure-sensitive dilatant materials. J. Mech. Phys. Solids 23, 371-394.
35. Spitzig, W. A., Sober, R. J. and Richmond, O. (1976) The effect of hydrostatic pressure on the deformation behavior of maraging and HY-80 steels and its implications for plasticity theory. Metall. Tram. A 7, 1703-1710.
36. Tomita, Y., Shindo, A. and Fatnassi, A. (1988) Bounding approach to the bifurcation point of annular plates with nonassociated flow law subjected to uniform tension at their outer edges. Int. J. Plasticity 4, 251-263.
37. Triantafyllidis, N. (1983) On the bifurcation and postbifurcation analysis of elastic-plastic solids under general prebifurcation conditions. J. Mech. Phys. Solids 31, 499-510.
38. Tvergaard, V. (1982) Influence of void nucleation on ductile shear fracture at a free surface. J. Mech. Phys. Solids 30, 399-425.
39. Tvergaard, V. and Needleman, A. (1975) On the buckling of elastic-plastic columns with asymmetric cross-sections. Int. J. Mech. Sci. 17, 419-424.
40. Vardoulakis, I. (1981) Bifurcation analysis of the plane rectilinear deformation on dry sand samples. Int. J. Solids Structures 11, 1085-1101.
41. Whitney, W. and Andrews, R. D. (1967) Yielding of glassy polymer: volume effects. J. Polym. Sci. C 16, 2981-2990.