On the numerical implications of multiplicative inelasticity with an anisotropic elastic constitutive law

International Journal for Numerical Methods in Engineering

Volumn 58, Issue 14, 2003, Pages 2131-2160

  Sansour, Carlo ^a   Bocko, Jozef ^b  

^a UNIVERSITY OF ADELAIDE   (Australia)

^b TECHNICAL UNIVERSITY OF KO ICE   (Slovakia)

Author keywords

Anisotropy; Finite strain; Multiplicative inelasticity; Shells; Unified constitutive models

Indexed keywords

ANISOTROPY; DECOMPOSITION; ELASTICITY; TENSORS; THERMODYNAMIC PROPERTIES;

MULTIPLICATIVE STRUCTURES;

NUMERICAL METHODS;

ELASTICITY;

EID: 0346783198     PISSN: 00295981     EISSN: None     Source Type: Journal    
DOI: 10.1002/nme.848     Document Type: Article

References (20)

1. Hill R. A theory of yielding and plastic flow of anisotropic metals. Proceedings of the Royal Society 1948; A 193:281-297.
2. Papadopoulos P, Lu J. On the formulation and numerical solution of problems in anisotropic finite plasticity. Computer Methods in Applied Mechanics and Engineering 2001; 190:4889-4910.
3. Sansour C, Kollmann FG. On the formulation of anisotropic elastic laws within multiplicative finite strain viscoplasticity, preprint.
4. Haupt P, Kersten Th. On the modelling of anisotropic material behaviour in viscoplasticity. International Journal of Plasticity 2003; 19:1885-1915.
5. Menzel A, Steinmann P. On spatial formulation of anisotropic multiplicative elasto-plasticity. Computer Methods in Applied Mechanics and Engineering 2003; 192:3431-3470.
6. Reese S. Meso-macro modelling of fibre-reinforced rubber-like composites exhibiting large elastoplastic deformations. International Journal of Solids and Structures 2003; 40:951-980.
7. Tsakmakis Ch. Description of Plastic Anisotropy Effects at Large Deformations. Part I: Restrictions Imposed by the Second Law and the Postulate of Il'iushin. 2001, preprint.
8. Besseling JF. A thermodynamic approach to rheology. In Parkus H, Seddov LI (eds). Irreversible Aspects of Continuum Mechanics. Springer: Wien, 1968.
9. Kröner E. Allgemeine Kontinuumstheorie der Versetzungen und Eigenspannungen. Archive for Rational Mechanics and Analysis 1960; 4:273-334.
10. Lee EH. Elastic-plastic deformation at finite strains. Journal of Applied Mechanics (ASME) 1969; 36:1-6.
11. Bodner SR, Partom Y. Constitutive equations for elastic-viscoplastic strain-hardening materials. Journal of Applied Mechanics (ASME) 1975; 42:385-389.
12. Sansour C, Kollmann FG. Large viscoplastic deformations of shells. Theory and finite element formulation. Computational Mechanics 1998; 21:512-525.
13. Sansour C, Wagner W. A model of finite strain viscoplasticity based on unified constitutive equations. Theoretical and computational considerations with applications to shells. Computer Methods in Applied Mechanics and Engineering 2001; 191:423-450.
14. Boehler JP (ed.). Applications of Tensor Functions in Solid Mechanics. Springer: Wien, 1987.
15. Smith GF. On isotropic functions of symmetric tensors, skew-symmetric tensors and vectors. International Journal of Engineering Science 1971; 9:899-916.
16. Spencer AJM. Theory of invariants. In: Continuum Physics, vol. I. Eringen C (Ed.). Academic Press: New York, 1971; 239-353.
17. Zheng Q-S. Theory of representations for tensor functions-A unified invariant approach to constitutive equations. Applied Mechanics Reviews 1994; 47:545-587.
18. Sansour C, Kollmann FG. On theory and numerics of large viscoplastic deformation. Computer Methods in Applied Mechanics and Engineering 1997; 146:351-369.
19. Dubrovin BA, Fomenko AT, Novikov SP. Modern Geometry-Methods and Applications, Part I. Springer-Verlag: New York, 1984.
20. Mandel J. Equations constitutives et directeurs dans les milieux plastiques et viscoplastiques. International Journal of Solids and Structures 1973; 9:725-740.