Two-dimensional rigid polycrystals whose grains have one ductile direction

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

Volumn 459, Issue 2036, 2003, Pages 1949-1968

  Goldsztein, Guillermo H ^a  

^a GEORGIA INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

Macroscopic behaviour; Plasticity; Polycrystals; Strength domain

Indexed keywords

ANISOTROPY; ARTICLE; CRYSTAL STRUCTURE; GRAIN; MATHEMATICAL ANALYSIS; PLASTICITY; RIGIDITY; STRENGTH;

EID: 1542407691     PISSN: 13645021     EISSN: 14712946     Source Type: Journal    
DOI: 10.1098/rspa.2002.1099     Document Type: Article

References (33)

1. Bhattacharya, K., Kohn, R. V. & Kozlov, S. 1999 Some examples of nonlinear homogenization involving nearly degenerate energies. Proc. R. Soc. Lond. A 455, 567-583.
2. Bishop, J. & Hill, R. 1951 A theory for the plastic distortion of a polycrystalline aggregate under combined stresses. Phil. Mag. 42, 414-427.
3. Bolton, W. 1996 Materials and their uses. Oxford: Butterworth-Heinemann.
4. Bouchitté, G. & Suquet, P. 1991 Homogenization, plasticity and yield design. In Composite media and homogenization (ed. G. D. Maso & G. Dell'Antonio), pp. 107-133. Birkhäuser.
5. de Buhan, P. 1986 Approche fondamentale du calcul à la rupture des ouvreges en sols renforcés. Thèse d'Etat, Université de Paris-VI, France.
6. de Buhan, P. & Taliercio, A. 1991 A homogenization approach to the yield strength of composite materials. Eur. J. Mech. A 10, 129-154.
7. deBotton, G. & Ponte Castañeda, P. 1995 Variational estimates for the creep behavior of polycrystals. Proc. R. Soc. Lond. A 488, 121-142.
8. Demengel, F. & Qi, T. 1990 Convex functions of a measure obtained by homogenization. SIAM J. Math. Analysis 21, 409-435.
9. Dendievel, R., Bonnet, G. & Willis, J. R. 1991 Bounds for the creep behavior of polycrystalline materials. In Inelastic deformations of composite materials (ed. G. J. Dvorak), pp. 175-192. Springer.
10. Goldsztein, G. H. 2001 Rigid perfectly plastic two-dimensional polycrystals. Proc. R. Soc. Lond. A 457, 2789-2798.
11. Hirth, J. P. & Lothe, J. 1982 Theory of dislocations. New York: McGraw-Hill.
12. Hutchinson, J. W. 1976 Bounds and self-consistent estimates for creep of polycrystalline materials. Proc. R. Soc. Lond. A 348, 101-127.
13. Jikov, V., Kozlov, S. & Oleinik, O. 1994 Homogenization of differential operations and integral functionals. Springer.
14. Kohn, R. V. & Little, T. D. 1998 Some model problems of polycrystal plasticity with deficient basic crystals. SIAM J. Appl. Math. 59, 172-197.
15. Lebensohn, R. 1993 A self-consistent anisotropic approach for the simulation of plastic-deformation and texture development of polycrystals: application to zirconium alloys. Acta Metall. Mater. 41, 2611-2624.
16. Lebensohn, R. 1999 Modeling the role of local correlations in polycrystal plasticity using viscoplastic self-consistent schemes. Model. Simul. Mater. Sci. Engng 7, 739-746.
17. Lubliner, J. 1990 Plasticity theory. New York: Macmillan.
18. Nesi, V., Smyshlyaev, V. P. & Willis, J. R. 2000 Improved bounds for the yield stress of a model polycrystalline material. J. Mech. Phys. Solids 48, 1799-1825.
19. Olson, T. 1994 Improvements on Taylor's upper bound for rigid-plastic composites. Mater. Sci. Engng A 175, 15-20.
20. Ponte Castañeda, P. 1991 The effective mechanical properties of nonlinear isotropic composites. J. Mech. Phys. Solids 39, 45-71.
21. Ponte Castañeda, P. 1996 Exact second-order estimates for the effective mechanical properties of nonlinear composite materials. J. Mech. Phys. Solids 44, 827-862.
22. Ponte Castañeda, P. & Nebozhyn, M. 1997 Variational estimates of the self consistent type for some model nonlinear polycrystals. Proc. R. Soc. Lond. A 453, 2715-2724.
23. Ponte Castañeda, P. & Suquet, P. 1997 Nonlinear composites. Adv. Appl. Mech. 34, 171-302.
24. Sab, K. 1994 Homogenization of non-linear random media by a duality method. Application to plasticity. Asymp. Analysis 9, 311-336.
25. Sachs, G. 1928 Zur Ableitung einer Fleissbedingung. Z. Ver. Deutsche Ing. 72, 734-736.
26. Suquet, P. 1982 Plasticité et homogénéisation. Thèse d'Etat, Université Pierre et Marie Curie, Paris, France.
27. Suquet, P. 1983 Analyse limite et homogénéisation. C. R. Acad. Sci. Paris Sér. II 296, 1355-1358.
28. Suquet, P. 1987 Elements of homogenization for inelastic solid mechanics. In Homogenization techniques for composite media (ed. E. Sanchez-Palencia & A. Zaoui). Lecture Notes in Physics, vol. 272, pp. 193-278. Springer.
29. Suquet, P. 1988 Discontinuities and plasticity. In Nonsmooth mechanics and applications (ed. J. J. Moreau & P. D. Panagiotopoulos), pp. 278-340. Springer.
30. Suquet, P. 1993 Overall potentials and extremal surfaces of power law or ideally plastic materials. J. Mech. Phys. Solids 41, 981-1002.
31. Talbot, D. R. S. & Willis, J. R. 1985 Variational principles for inhomogeneous nonlinear media. IMA J. Appl. Math. 35, 39-54.
32. Taylor, G. 1938 Plastic strains in metals. J. Inst. Metals 62, 307-324.
33. Willis, J. R. 1983 The overall elastic response of composite materials. J. Appl. Mech. 50, 1202-1209.