A general constitutive theory for linear and nonlinear particulate media with microstructure evolution

Journal of the Mechanics and Physics of Solids

Volumn 46, Issue 3, 1998, Pages 427-465

  Kailasam, M ^a   Ponte Castaneda P ^a  

^a UNIVERSITY OF PENNSYLVANIA   (United States)

Author keywords

A. microstructures; B. constitutive behavior, principles; B. particulate reinforced material

Indexed keywords

COMPOSITE MATERIALS; DEFORMATION; HARDENING; SINGLE CRYSTALS; STRAIN; THREE DIMENSIONAL;

CONSTITUTIVE THEORY; NONLINEAR PARTICULATE MEDIA; SHEAR LOCALIZATION; STATISTICAL DISTRIBUTION FUNCTIONS;

CRYSTAL MICROSTRUCTURE;

EID: 0032016962     PISSN: 00225096     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0022-5096(97)00095-1     Document Type: Article

References (46)

1. Aravas, N. (1987) On the numerical integration of a class of pressure-dependent plasticity. International Journal of Meth. Engng. 24, 1395-1416.
2. Aravas, N. (1992) Finite elastoplastic transformations of transversely isotropic metals. International Journal of Solids and Structures 29, 2137-2157.
3. Bilby, B. A. and Kolbuszewski, M. L. (1977) The finite deformation of an inhomogeneity in two-dimensional slow viscous incompressible flow. Proceedings of the Royal Society of London A 355, 335-353.
4. Bornert, M., Stolz, C. and Zaoui, A. (1996) Morphologically representative pattern-based bounding in elasticity. Journal of the Mechanics and Physics of Solids 44, 307-331.
5. Budiansky, B., Hutchinson, J. W. and Slutsky, S. (1982) Void growth and collapse in viscous solids. In Mechanics of Solids, The Rodney Hill Anniversary Volume, ed. H. G. Hopkins and J. J. Sewell, pp. 13-45. Pergamon Press, Oxford.
6. Dafalias, Y. F. (1985) The plastic spin. Journal of Applied Mechanics 52, 865-871.
7. Dafalias, Y. F. and Rashid, M. M. (1989) The effects of plastic spin on anisotropic material behavior. International Journal of Plasticity 5, 227-246.
8. Eshelby, J. D. (1957) The determination of the elastic field of an ellipsoidal inclusion and related problems. Proceedings of the Royal Society of London A 241, 376-396.
9. Fleck, N. and Hutchinson, J. W. (1986) Void growth in shear. Proceedings of the Roval Society of London A 407, 435-458.
10. Gologanu, M., Leblond, J. B. and Devaux, J. (1993) Approximate models for ductile metals containing non-spherical voids - Case of axisymmetric prolate ellipsoidal cavities. Journal of the Mechanics and Physics of Solids 41, 1723-1754.
11. Gologanu, M., Leblond, J. B. and Devaux, J. (1994) Approximate models for ductile metals containing non-spherical voids - Case of axisymmetric oblate ellipsoidal cavities. Journal of Engng. Mater. Tech. 116, 290-297.
12. Gurson, A. L. (1977) Continuum theory of ductile rupture by void nucleation and growth. Journal of Engng. Mater. Tech. 90, 2-15.
13. Hashin, Z. and Shtrikman, S. (1963) A variational approach to the theory of the elastic behavior of multiphase materials. Journal of the Mechanics and Physics of Solids 11, 127-140.
14. Hill, R. (1963) Elastic properties of reinforced solids: some theoretical principles. Journal of the Mechanics and Physics of Solids 11, 352-357.
15. Hill, R. (1965) Continuum micromechanics of elastoplastic polycrystals. Journal of the Mechanics and Physics of Solids 13, 89-101.
16. Hill, R. (1967a) The essential structure of constitutive laws for metal composites and polycrystals. Journal of the Mechanics and Physics of Solids 15, 79-75.
17. Hill, R. (1967b) On the classical constitutive relations for elastic/plastic solids. In Recent Progress in Applied Mechanics: The Folke Odqvist Volume, ed. B. Broberg, J. Huit and F. Niordson, pp. 241-249. Almqvist and Wiksell/Gebers Förlag, Stockholm, Sweden.
18. Hu, G. K. (1996) A method of plasticity for general aligned spherical void or fiber-reinforced composites. International Journal of Plasticity 2, 439-449.
19. Jeffery, G. B. (1922) The motion of ellipsoidal particles immersed in a viscous fluid. Proceedings of the Royal Society of London A 102, 161-179.
20. Kailasam, M. (1998) A general constitutive theory for particulate composites and porous materials with microstructure evolution. Ph.D. thesis, University of Pennyslvania.
21. Kailasam, M., Ponte Castañeda, P. and Willis, J. R. (1997a) The effect of particle size, shape, distribution and their evolution on the constitutive response of nonlinearly viscous composites. I. Theory. Phil. Trans. R. Soc. Lond. A 355, 1835-1852.
22. Kailasam, M., Ponte Castañeda, P. and Willis, J. R. (1997b) The effect of particle size, shape, distribution and their evolution on the constitutive response of nonlinearly viscous composites. II. Examples. Phil. Trans. R. Soc. Lond. A. 355, 1853-1872.
23. Kailasam, M., Ponte Castañeda, P. and Willis, J. R. (1997c) Errata : The effect of particle size, shape, distribution and their evolution on the constitutive response of nonlinearly viscous composites. I. Theory. Phil. Trans. R. Soc. Lond. A, 355, 2520-2521.
24. Lee, B. J. and Mear, M. E. (1992) Axisymmetric deformation of power-law solids containing a dilute concentration of aligned spheroidal voids. Journal of the Mechanics and Physics of Solids 40, 1805-1836.
25. Li, G. and Ponte Castañeda, P. (1994) Variational estimates for the elastoplastic response of particle-reinforced metal-matrix composites. Applied Mechanics Review 47, s77-94.
26. Ogden, R. W. (1984) Non-linear Elastic Deformations. Ellis Harwood, Chichester, 1st edn. p. 130.
27. Ponte Castañeda, P. (1991) The effective mechanical properties of nonlinear isotropic solids. Journal of the Mechanics and Physics of Solids 39, 45-71.
28. Ponte Castañeda, P. (1992) New variational principles in plasticity and their application to composite materials. Journal of the Mechanics and Physics of Solids 40, 1757-1788.
29. Ponte Castañeda, P. (1996) Exact second-order estimates for the effective mechanical properties of nonlinear composite materials. Journal of the Mechanics and Physics of Solids 44, 827-862.
30. Ponte Castañeda, P. (1997) Nonlinear composite materials : effective constitutive behavior and microstructure evolution. In Continuum Micromechanics, CISM Courses and Lectures, ed. P. Suquet, Vol. 377, pp. 131-195. Springer-Verlag.
31. Ponte Castañeda, P. and Willis, J. R. (1995) The effect of spatial distribution on the effective behavior of composite materials and cracked media. Journal of the Mechanics and Physics of Solids 43, 1919-1951.
32. Ponte Castañeda, P. and Zaidman, M. (1994) Constitutive models for porous materials with evolving microstructure. Journal of the Mechanics and Physics of Solids 42, 1459-1497.
33. Ponte Castañeda, P. and Zaidman, M. (1996) On the finite deformation of nonlinear composite materials. I. Instantaneous constitutive relations. International Journal of Solids and Structures 33, 1271-1286.
34. Rice, J. R. (1976) The localization of plastic deformation. Proceedings of the 14th International Congress of Theoretical and Applied Mechanics, ed. W. T. Koiter, pp. 207-220. North-Holland.
35. Rice, J. R. and Tracey, D. M. (1969) On the ductile enlargement of voids in a triaxial field. Journal of the Mechanics and Physics of Solids 17, 201-217.
36. Spitzig, W. A., Smelser, R. E. and Richmond, O. (1988) The evolution of damage and fracture in iron compacts with various initial porosities. Acta metallica 36, 1201-1211.
37. Suquet, P. (1993) Overall potentials and extremal surfaces of power law or ideally plastic composites. Journal of the Mechanics and Physics of Solids 41, 981-1002.
38. Suquet, P. (1995) Overall properties of nonlinear composites : a modified secant moduli theory and its link with Ponte Castañeda's nonlinear variational procedure. C. R. Acad. Sc. Paris II 320, 563-571.
39. Talbot, D. R. S. and Willis, J. R. (1985) Variational principles for nonlinear inhomogeneous media. IMA J. Appl. Math. 35, 39-54.
40. Triantafyllidis, N. and Bardenhagen, S. (1996) The influence of scale size on the stability of periodic solids and the role of associated higher order continuum models. Journal of the Mechanics and Physics of Solids 44, 1891-1928.
41. Triantafyllidis, N. and Maker, B. N. (1985) On the comparison between microscopic and macroscopic instability mechanisms in a class of fiber-reinforced composites. Journal of the Applied Mechanics 52, 794-800.
42. Willis, J. R. (1977) Bounds and self-consistent estimates for the overall moduli of anisotropic composites. Journal of the Mechanics and Physics of Solids 25, 185-202.
43. Willis, J. R. (1978) Variational principles and bounds for the overall properties of composites. Continuum Models for Discrete Systems, ed. J. W. Prowan, pp. 185-215. University of Waterloo Press.
44. Willis, J. R. (1981) Variational and related methods for the overall properties of composites. Advances of Applied Mechanics, ed. C. Yih, Vol. 21, pp. 1-78. Academic Press, New York.
45. Zaidman, M. and Ponte Castañeda, P. (1996) On the finite deformation of nonlinear composite materials. II. Evolution of microstructure. International Journal of Solids and Structure 33, 1287-1303.
46. Zavaliangos, A. and Anand, L. (1993) Thermo-elasto-viscoplasticity of isotropic porous metals. J. Mech. Phys. Solids 25, 185-202.