Constitutive equations for micropolar hyper-elastic materials

International Journal of Solids and Structures

Volumn 46, Issue 14-15, 2009, Pages 2765-2773

  Ramezani, S ^a   Naghdabadi, R ^a   Sohrabpour, S ^a  

^a SHARIF UNIVERSITY OF TECHNOLOGY   (Iran)

Author keywords

Constitutive equations; Hyper elasticity; Micropolar continuum; Mooney Rivlin materials; Neo Hookean materials

Indexed keywords

ELASTICITY TENSORS; FINITE ELEMENT FORMULATIONS; FOURTH ORDERS; HOMOGENEOUS STATE; HYPER ELASTICS; HYPER-ELASTICITY; LAGRANGIAN; LINEAR ELASTICITY THEORIES; LOADING CONDITIONS; MICRON LEVELS; MICROPOLAR; MICROPOLAR CONTINUUM; MICROPOLAR EFFECTS; MOONEY-RIVLIN MATERIALS; NEO-HOOKEAN MATERIALS; REPRESENTATION THEOREMS;

CHANNEL FLOW; CONTINUUM MECHANICS; DEFORMATION; ELASTICITY; MATERIALS;

CONSTITUTIVE EQUATIONS;

EID: 65549100441     PISSN: 00207683     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ijsolstr.2008.10.009     Document Type: Article

References (31)

1. Bathe K.J., Ramm E., and Wilson E.L. Finite element formulation for large deformation dynamic analysis. Int. J. Numer. Meth. Eng. 9 (1975) 353-386
2. Belytschko T., Liu W.K., and Moran B. Nonlinear Finite Elements for Continua and Structures (2000), Wiley, New York
3. 2-flow theory for polar continua. Comp. Meth. Appl. Mech. Eng. 103 (1993) 347-362
4. Dyszlewicz J. Micropolar Theory of Elasticity (2004), Springer Verlag, Berlin
5. Eringen A.C. Theory of micropolar elasticity. In: Leibowitz H. (Ed). Fracture vol. II (1968), Academic Press, London 621-629
6. Eringen A.C., and Kafadar C.B. Polar field theories. In: Eringen A.C. (Ed). Continuum Physics vol. IV (1976), Academic Press, London 1-73
7. Eringen A.C., and Suhubi E.S. Nonlinear theory of simple microelastic solids, I and II. Int. J. Eng. Sci. 2 (1964) 189-203 389-404
8. Forest S., and Sievert R. Elastoviscoplastic constitutive frameworks for generalized continua. Acta Mech. 160 (2003) 71-111
9. Grammenoudis P., and Tsakmakis C. Hardening rules for finite deformation micropolar plasticity: restrictions imposed by the second law of thermodynamics and the postulate of Il'iushin. Cont. Mech. Thermodyn. 13 (2001) 325-363
10. Grammenoudis P., and Tsakmakis C. Micropolar plasticity theories and their classical limits. Part I: Resulting model. Acta Mech. 189 (2007) 151-175
11. Grammenoudis P., Sator C., and Tsakmakis C. Micropolar plasticity theories and their classical limits. Part II: Comparison of responses predicted by the limiting and a standard classical model. Acta Mech. 189 (2007) 177-191
12. Iordache M.-M., and Willam K. Localization failure analysis in elastoplastic Cosserat continua. Comp. Meth. Appl. Mech. Eng. 151 (1998) 559-586
13. Kafadar C.B., and Eringen A.C. Micropolar media, I and II. Int. J. Eng. Sci. 9 (1971) 271-307
14. Marsden J.E., and Hughes T.J.R. Mathematical Foundations of Elasticity (1983), Prentice-Hall, Englewood Cliffs, NJ
15. Mühlhaus H.B., and Vardoulakis I. The thickness of shear bands in granular materials. Geotechnology 37 (1987) 271-283
16. Nowak W. Theory of Micropolar Elasticity (1976), Springer Verlag, Berlin
17. Ramezani S., and Naghdabadi R. Energy pairs in the micropolar continuum mechanics. Int. J. Solids Struct. 44 (2007) 4810-4818
18. Rubin M.B. Cossetat Theories, Points, Rods, Shells (2000), Kluwer Academic Publishers, Dordrecht
19. Sharbati E., and Naghdabadi R. Computational aspects of the Cosserat finite element analysis of localization phenomena. Comput. Mater. Sci. 38 (2006) 303-315
20. Simo J.C., and Pister K.S. Remarks on rate constitutive equation for finite deformation problems: computational implications. Comp. Meth. Appl. Mech. Eng. 46 (1984) 201-215
21. Simo J.C., Taylor R.L., and Pister K.S. Variational and projection methods for the volume constraintin finite deformation elasto-plasticity. Comp. Meth. Appl. Mech. Eng. 51 (1985) 177-208
22. Spencer A.J.M. Theory of invariants. In: Eringen A.C. (Ed). Continuum Physics vol. I (1971), Academic Press, London 239-353
23. Steinmann P. A micropolar theory of finite deformation and finite rotation multiplicative elastoplasticity. Int. J. Solids Struct. 31 8 (1994) 1063-1084
24. Steinmann P., and Willam K. Localization within the framework of micropolar elasto-plasticity. In: Bruller O., Mannl V., and Najar J. (Eds). Advances in Continuum Mechanics (1991), Springer, Berlin
25. Tejchman J. Influence of a characteristic length on shear zone formation in hypoplasticity with different enhancements. Comput. Geotech. 31 (2004) 595-611
26. Tejchman J., and Wu W. Modeling of textural anisotropy in granular materials with stochastic micropolar hypoplasticity. Int. J. Nonlinear Mech. 42 (2007) 882-894
27. Toupin RA. Theories of elasticity with couple stress. Arch. Rat. Mech. Anal. 17 (1964) 85-112
28. Truesdell C.A., and Noll W. The non-linear field theories of mechanics. S. Flugge's Handbuch der Physik vol. III/3 (1965), Springer, Berlin
29. Truesdell C.A., and Toupin R. The classical field theories of mechanics. S. Flugge's Handbuch der Physik vol. III/1 (1960), Springer, Berlin
30. Wang C.C. A new representation theorem for isotropic functions, Part 1: Scalar-valued isotropic functions. Arch. Rat. Mech. Anal. 36 (1970) 166-197
31. Zheng Q.S. Theory of representations for tensor functions. Appl. Mech. Rev. 47 (1994) 554-587