Two different approaches to model evolving directional properties at finite deformations

Acta Mechanica

Volumn 199, Issue 1-4, 2008, Pages 97-116

  Harrysson, M ^a   Ristinmaa, M ^a  

^a LUND UNIVERSITY   (Sweden)

Author keywords

[No Author keywords available]

Indexed keywords

CANNING; DEFORMATION; GRADIENT METHODS; PLASTICS; THERMODYNAMICS; VECTORS;

A-PLANE; ANISOTROPIC MATERIALS; DEFORMATION PROCESSING; DIRECTIONAL PROPERTIES; EVOLUTION LAW; FINITE DEFORMATIONS; KIRCHHOFF STRESS; PLASTIC VELOCITY; SECOND LAW OF THERMODYNAMICS; SIMPLE SHEAR;

LAWS AND LEGISLATION;

EID: 50649116199     PISSN: 00015970     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00707-007-0559-0     Document Type: Article

References (42)

1. Arravas N. (1992). Finite elastoplastic transformation of transversely isotropic metals. Int. J. Solids Struct. 29: 2137-2157
2. Arravas N. (1994). Finite-strain anisotropic plasticity and the plastic spin. Model. Simul. Mater. Sci. 2: 483-504
3. Ball J. (1977). Convexity conditions and existence theorem in non-linear elasticity. Arch. Ration. Mech. Anal. 63: 337-403
4. Ball, J.: Constitutive equlities and existence theorems in elasticity. In: Knops, R.J. (ed.) Symposium on Non-Well Posed Problems and Logarithmic Convexity. Lecture Notes in Mathematics, vol. 316. Springer, Heidelberg (1977)
5. Boehler, J.: Applications of Tensor Functions in Solid Mechanics. Springer, Heidelberg (1987)
6. Ciarlet, P.G.: Mathematical Elasticity, Volume 1: Three-dimensional Elasticity. North-Holland, Amsterdam (1988)
7. Dafalias Y. (1985). The plastic spin. J. Appl. Mech. 73: 865-871
8. Dafalias Y. (1987). Issues on the constitutive formulation at large elastoplastic deformations, part 1. Acta Mech. 69: 119-138
9. Dafalias Y. (1998). Plastic spin: Necessity or redundancy?. Int. J. Plast. 14: 909-931
10. Dafalias Y. (2000). Orientational evolution of plastic orthotropy in sheet metals. J. Mech. Phys. Solids 48: 2231-2255
11. Darrieulat M., Fortunier R. and Montheillet F. (1992). Invariant formulation of anisotropic plastic behaviour in the case of cubic symmetry. Int. J. Plast. 8: 763-771
12. Han C.-S., Choi Y., Lee J.-K. and Wagoner R.H. (2002). A fe formulation for elasto-plastic materials with planar anisotropic yield functions and plastic spin. Int. J. Solids Struct. 39: 5123-5141
13. Harrysson M. and Ristinmaa M. (2007). Description of evolving anisotropy at large strains. Mech. Mater. 39: 267-282
14. Harrysson M., Harrysson A. and Ristinmaa M. (2007). Spatial representation of evolving anisotropy at large strains. Int. J. Solids Struct. 44: 3514-3532
15. Imatani S. and Maugin G. (2002). A constitutive model for material growth and its applications to three-dimensional finite element analysis. Mech. Res. Commun. 29: 477-483
16. Itskov M. and Aksel N. (2004). A class of orthotropic and transversely isotropic hyperelastic constitutive models based on a polyconvex strain energy function. Int. J. Solids Struct. 41: 3833-3848
17. Itskov M. and Aksel N. (2004). A constitutive model for orthotropic elasto-plasticity at large strains. Arch. Appl. Mech. 74: 75-91
18. Kowalczyk K. and Gambin W. (2004). Model of plastic anisotropy evolution with texture-dependent yield surface. Int. J. Plast. 20: 19-54
19. Kröner, E.: Allgemeine Kontinuumstheorie der Versetzungen. Arch. Ration. Mech. Anal. 4, 273-334 (1960)
20. Kuroda M. (1997). Interpretation of the behavior of metals under large plastic shear deformations: A macroscopic approach. Int. J. Plast. 13: 359-383
21. Kuroda M. and Tvergaard V. (2001). Plastic spin associated with a non-normality theory of plasticity. Eur. J. Mech. A Solids 20: 893-905
22. Lee, E.: Thermo-elastic-plastic analysis at finite strain. In: Boley, B. (ed.) Thermoinelasticity. International Union of Theoretical and Applied Mechanics, pp. 157-169. Springer, Heidelberg (1968)
23. Liu I. (1982). On representation of anisotropic invariants. Int. J. Engng. Sci. 20: 1099-1109
24. Loret B. (1983). On the effects of plastic rotation in the finite deformation of anisotropic elastoplastic materials. Mech. Mater. 2: 287-304
25. Mandel, J.: Plasticitè classique et viscoplasticitè. International Center for Mechanical Sciences, Udine, no 97. Springer, Heidelberg (1971)
26. Menzel A. (2005). Modelling of anisotropic growth in biological tissues. Biomech. Model. Mechanobiol. 3: 147-171
27. Menzel A. and Steinmann P. (2003). On the spatial formulation of anisotropic multiplicative elasto-plasticity. Comput. Meth. Appl. Mech. Engng. 192: 3431-3470
28. Reese S. (2003). Meso-macro modelling of fibre-reinforced rubber-like composites exhibiting large elastoplastic deformation. Int. J. Solids Struct. 40: 951-980
29. Sansour C., Karsaj I. and Soric J. (2007). On anisotropic flow rules in multiplicative elastoplasticity at finite strains. Comput. Meth. Appl. Mech. Engng. 196: 1294-1309
30. Schröder J. and Neff P. (2003). Invariant formulation of hyperelastic trensverse isotropy based on polyconvex free energy functions. Int. J. Solids Struct. 40: 401-445
31. Spencer, A.: Continuum theory of the mechanics of fiber-reinforced composites. International Center for Mechanical Sciences, Udine, no 282. Springer, Heidelberg (1984)
32. Steigmann D. (2003). Frame-invariant polyconvex strain-energy function for some anisotropic solids. Math. Mech. Solids 8: 497-506
33. Stumpf H. and Badur J. (1990). On missing links of rate-independent elasto-plasticity at finite strains. Mech. Res. Commun. 17: 353-364
34. Svendsen B. (2001). On the modelling of anisotropic elastic and inelastic material behaviour at large deformation. Int. J. Solids Struct. 38: 9579-9599
35. Svendsen B., Levkovitch V., Wang J., Reusch F. and Reese S. (2006). Application of the concept of evolving structure tensors to the modeling of initial and induced anisotropy at large deformation. Comput. Struct. 84: 1077-1085
36. Truesdell, C., Noll, W.: The non-linear field theories of mechanics. In: Flugge, S.S. (ed.) Handbuch der Physik. Springer, Heidelberg (1965)
37. Tsakmakis C. (2004). Description of plastic anisotropy effects at large deformation - part I: Restrictions imposed by the second law and the postulate of Il'iushin. Int. J. Plast. 20: 167-198
38. Van der Giessen E. (1989). Continum model of large deformation plasticity part I: Large deformation plasticity and the concept of a natural reference state. Eur. J. Mech. A Solids 8: 15-34
39. Van der Giessen E. (1991). Micromechanical and thermodynamic aspects of the plastic spin. Int. J. Plast. 7: 365-386
40. Wallin M. and Ristinmaa M. (2005). Deformation gradient based kinematic hardening model. Int. J. Plast. 21: 2025-2050
41. Wallin M., Ristinmaa M. and Ottosen N. (2003). Kinematic hardening in large strain plasticity. Eur. J. Mech. A Solids 22: 341-356
42. Zbib H. and Aifantis E. (1988). On the concept of relative and plastic spin and its implications to large deformation theories. Part I: Hypoelasticity and vertex-type plasticity. Acta Mech. 75: 15-33