On a formulation for anisotropic elastoplasticity at finite strains invariant with respect to the intermediate configuration

Journal of the Mechanics and Physics of Solids

Volumn 55, Issue 11, 2007, Pages 2406-2426

  Sansour, Carlo ^a   Karšaj, Igor ^b   Sorić, Jurica ^b  

^a UNIVERSITY OF NOTTINGHAM   (United Kingdom)

^b UNIVERSITY OF ZAGREB   (Croatia)

Author keywords

Anisotropic plasticity; Finite strains; Invariance to rotations; Multiplicative inelasticity; Orthotropic yield function

Indexed keywords

DEFORMATION; PHASE TRANSITIONS; STRAIN MEASUREMENT; TENSORS;

ANISOTROPIC PLASTICITY; FINITE STRAINS; MULTIPLICATIVE INELASTICITY; ORTHOTROPIC YIELD FUNCTION;

ELASTOPLASTICITY;

EID: 35248830317     PISSN: 00225096     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jmps.2007.03.013     Document Type: Article

References (27)

1. Bertram A. An alternative approach to finite plasticity based on material isomorphisms. Int. J. Plast. 15 (1999) 353-374
2. Besseling J. A thermodynamic approach to rheology. In: Parkus H., and Seddov L.I. (Eds). Irreversible Aspects of Continuum Mechanics (1968), Springer, Wien
3. Boehler J.P. Applications of Tensor Functions in Solid Mechanics (1987), Springer, Wien
4. Choquet-Bruhat Y., Dewitt-Morette C., and Dillard-Bleick M. Analysis, Manifolds and Physics (1977), North-Holland, Amsterdam
5. Cleja-Tigoiu S., and Maugin G. Eshelby's stress tensors in finite elastoplasticity. Acta Mech. 139 (2000) 231-249
6. Cleja-Tigoiu S., and Soos E. Elastoviscoplastic models with relaxed configurations and internal state variables. Appl. Mech. Rev. 43 (1990) 131-151
7. Dafalias Y. Plastic spin: necessity or redundancy. Int. J. Plast. 14 (1998) 909-931
8. Eidel B., and Gruttmann F. Elastoplastic orthotropy at finite strains: multiplicative formulation and numerical implementation. Comput. Mater. Sci. 28 (2003) 732-742
9. Haupt P. On the concept of an intermediate configuration and its application to a representation of viscoelastic-plastic material behaviour. Int. J. Plast. 1 (1985) 279-293
10. Itskov M., and Aksel N. A constitutive model for orthotropic elasto-plasticity at large strains. Arch. Appl. Mech. (Ingenieur Archiv) 74 (2004) 75-91
11. Kröner E. Allgemeine kontinuumstheorie der versetzungen und eigenspannungen. Arch. Ration. Mech. Anal. 4 (1960) 273-334
12. Lee E. Elastic-plastic deformation at finite strains. ASME J. Appl. Mech. 36 (1969) 1-6
13. Maugin G.A. Eshelby stress in elastoplasticity and ductile fracture. Int. J. Plast. 10 (1994) 393-408
14. Menzel A., and Steinmann P. On the spatial formulation of anisotropic multiplicative elasto-plasticity. Comput. Methods Appl. Mech. Eng. 192 (2003) 3431-3470
15. Moran B., Ortiz M., and Shih C. Formulation of implicit finite elements methods for multiplicative deformation plasticity. Int. J. Numer. Methods Eng. 29 (1990) 483-514
16. Papadopoulos P., and Lu J. On the formulation and numerical solution of problems in anisotropic finite plasticity. Comput. Methods Appl. Mech. Eng. 190 (2001) 4889-4910
17. Rubin M.B. Plasticity theory formulated in terms of physically based micro-structural variables-part I theory. Int. J. Solids Struct. 19 (1994) 2615-2634
18. Sansour C., Karšaj I., and Sorić J. A formulation of anisotropic continuum elastoplasticity at finite strains. Part I: modelling. Int. J. Plast. 22 (2006) 2346-2365
19. Scheidler M., and Wright T.W. A continuum framework for finite viscoplasticity. Int. J. Plast. 17 (2001) 1033-1085
20. Schroeder J., Gruttmann F., and Löblein J. A simple orthotropic finite elasto-plasticity model based on generalized stress-strain measures. Comput. Mech. 30 (2002) 38-64
21. Simo J.C. On the computational significance of the intermediate configuration and hyperelastic relations in finite deformation plasticity. Mech. Mater. 4 (1985) 439-451
22. Smith G. On isotropic functions of symmetric tensors, skew-symmetric tensors and vectors. Int. J. Eng. Sci. 9 (1971) 899-916
23. Spencer, A., 1971. Theory of invariants. In: Eringen, C. (Ed.), Continuum Physics, vol. I, pp. 239-353.
24. Svendsen B. On the modelling of anisotropic elastic and inelastic material behaviour at large strain. Int. J. Solids Struct. 38 (2001) 9579-9599
25. van der Giesen E. Continuum models for large deformation plasticity. Part I: large deformation plasticity and the concept of a natural reference state. Eur. J. Mech. A Solids 8 (1989) 14-34
26. Wang C. A new representation theorem for isotropic functions. Arch. Ration. Mech. Anal. 36 (1970) 166-197
27. Zheng Q.-S. Theory of representation for tensor functions-a unified invariant approach to constitutive equations. Appl. Mech. Rev. 47 (1994) 545-587