Recent advances in the numerical modeling of constitutive relations

Finite Elements in Analysis and Design

Volumn 24, Issue 3, 1997, Pages 171-185

  Gadala, M S ^a  

^a UNIVERSITY OF BRITISH COLUMBIA   (Canada)

Author keywords

Anisotropy; Bubble function; Composite materials; Constitutive equations; Elastoplastic materials; Hyperelasticity; Incompressibility; Large strain; Reduced selective integration; Rubber like materials

Indexed keywords

ANISOTROPY; COMPOSITE MATERIALS; COMPRESSIBILITY; ELASTICITY; ELASTOPLASTICITY; FINITE ELEMENT METHOD; INTEGRATION; MATHEMATICAL MODELS; STRAIN;

BUBBLE FUNCTION; HYPERELASTICITY; REDUCED SELECTIVE INTEGRATION; RUBBER LIKE MATERIALS;

COMPUTER SIMULATION;

CONSTITUTIVE LAW; DEFORMATION; ELASTICITY; FINITE ELEMENT METHOD;

EID: 0030941394     PISSN: 0168874X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0168-874X(96)00048-0     Document Type: Article

References (33)

1. R.A. Brockman, "On the use of the Blatz-Ko constitutive model in nonlinear finite element analysis", Comput. Struct. 24, pp. 607-611, 1996.
2. M.S. Gadala, "Alternative methods for the solution of hyperelastic models with incompressibility", Comput. Struct. 42, pp. 1-10, 1992.
3. M.S. Gadala, "A unified numericl treatment for hyperelastic and rubber-like constitutive laws", Comm. Appl. Numer. Methods 1, pp. 581-587, 1991.
4. M.S. Gadala, "On the use of bubble functions and modified invariants for the analysis of hyperelastic and rubber-like materials", in: C.S. Desai et al. (eds.), Constitutive Laws for Engng. Materials, ASME Press, Proc. 3rd Int. Conf. on Constitutive Laws, Tucson-Arizona, pp. 101-105, 1991.
5. S.R. Swanson, "A constitutive model for high elongation elastic material", J. Eng. Mat. Tech. ASME Trans., 107, pp. 110-114, 1984.
6. J.T. Oden, "Finite Elements of Nonlinear Continua", McGraw Hill, New York, 1972.
7. H. Alexander, "A constitutive relation for rubber-like material", Int. J. Eng. Sci. 6, pp. 549-563, 1968.
8. R.S. Rivlin, "Large elastic deformations of isotropic materials; IV: Further developments of the general theory", Philos. Trans. Roy. Soc. London Ser. A241, pp. 379-397, 1948.
9. M. Mooney, "A theory for large elastic deformation", J. Appl. Phys. 11, pp. 582-597, 1940.
10. R.W. Ogden, "Large deformation isotropic elasticity: On the correlation of theory and experiment for compressibile rubber-like solids", Proc. Roy. Soc. London Ser. A328j, pp. 567-583, 1972.
11. E.G. Thompson, "Average and complete incompressibility in the finite element method", Int. J. Numer. Meth. Eng., 9, pp. 925-935, 1975.
12. B. Fraijs de Veubeke, "A new variational principle for finite elastic displacements", Int. J. Eng. Sci. 10, pp. 745-763, 1972.
13. J.T. Oden and O.P. Jacquotte, "Stability of some mixed finite element methods for stokesian flows", Comput. Meth. Appl. Mech. Eng. 43, pp. 231-247, 1984.
14. J.T. Oden and N. Kikuchi, "Finite element method for constrained problems in elasticity", Int. J. Numer. Meth. Eng. 18, pp. 701-725, 1982.
15. T.J.R. Hughes and D.S. Malkus, "A general penalty/mixed equivalence theorem for anisotropic incompressible finite elements", in: S.N. Atluri et al. (eds.), Hybrid and Mixed Finite Element Methods, Wiley, New York, pp. 487-496, 1983.
16. S. Cescotto and G. Fonder, "A finite element approach for large strains of nearly incompressible rubber-like materials", Int. J. Solids Struct. 15, pp. 589-605, 1979.
17. B. Haggblad and J.A. Sunberg, "Large strain solutions of rubber components", Comput. Struct. 17, pp. 835-843, 1983.
18. NISA Users Manual, Engineering Mechanics Research Corp. - EMRC, Troy-Michigan, 1992.
19. ANSYS Theoretical Manual, Swanson Analysis System Inc., Houston, PA-USA, 1994.
20. A.E. Green and P.M. Naghdi, "A general theory for elastoplastic continuum", Arch. Rat. Mech. Anal. 18, pp. 251-281, 1965.
21. A.E. Green and P.M. Naghdi, "Some remarks on elastoplastic deformations at finite strains", Int. J. Eng. Sci. 9, pp. 1219-1229, 1971.
22. K.J. Bathe, "Finite Element Procedure for Engineering Analysis", Prentice-Hall, Englewood Cliffs, NJ, 1995.
23. M.S. Gadala, G.A.E. Oravas and M. Dokainish, "Continuum basis and consistent numerical formulations of nonlinear continuum mechanics problems", Solid Mech. Arch. 9, pp. 1-52, 1994.
24. H.D. Hibbit, P.V. Marcal and J.R. Rice, "A finite element formulation for problems of large strain and large displacements", Int. J. Solids Struct. 6, pp. 1069-1086, 1970.
25. R. Hill, 'A theory of the yielding and plastic flow of anisotropic metals', Proc. Roy. Soc. London Ser. A 193, pp. 281-297, 1947.
26. C.F. Shih and D. Lee, "Further developments in anisotropic plasticity", J. Appl. Mech. ASME Trans. 100, pp. 294-302, 1978.
27. C.N. Chen, "An acceleration method for elastoplastic finite element computations", Comput. Struct. 44, pp. 125-132, 1992.
28. E. Orady and M.S. Gadala, "Finite element application to selected manufacturing processes", Int. J. Sci. Tech. 2, pp. 18-29, 1989.
29. A.C. Hansen, D. Blackketter and D.E. Walrath, "An invariant-based flow rule for anisotropic plasticity applied to composite material", J. Appl. Mech. 58, pp. 881-888, 1991.
30. F. Barlat, D.J. Lege and J.C. Brem, "A six-component yield function for anisotropic materials", Int. J. Plasticity 7, pp. 693-712, 1991.
31. R. De Borst and P.H. Feenstra, "Studies in anisotropic plasticity with reference to the Hill criterion", Int. J. Numer. Methods Eng. 29, pp. 315-336, 1990.
32. S. Hecker, Experimental studies of yield phenomena in biaxially loaded metals, in: J. Strickle and K. Saczalski (eds.), Constitutive Equations in Viscoplastic: Computational and Engineering Aspects, ASME, New York, 1976.
33. D.J.R. Owen and J.A. Figueries, "Anisotropic elasto-plastic finite element analysis of thick and thin plates and shells", Int. J. Numer. Methods Eng. 19, pp. 541-556, 1983.