Spatial representation of evolving anisotropy at large strains

International Journal of Solids and Structures

Volumn 44, Issue 10, 2007, Pages 3514-3532

  Harrysson, Magnus ^a   Harrysson, Anders ^a   Ristinmaa, Matti ^a  

^a LUND UNIVERSITY   (Sweden)

Author keywords

Anisotropy; Finite strains; Spatial form

Indexed keywords

ANISOTROPY; CONTINUUM MECHANICS; MATHEMATICAL MODELS; PLASTIC DEFORMATION; STRUCTURAL ANALYSIS;

ANISOTROPIC PROPERTIES; DEFORMATION GRADIENTS; FINITE STRAINS; SPATIAL FORMS;

STRAIN RATE;

EID: 33947107510     PISSN: 00207683     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ijsolstr.2006.10.002     Document Type: Article

References (47)

1. Apel, N. 2004. Appraches to the Description of Anisotropic Material Behaviour at Finite Elastic and Plastic deformations - Theory and Numerics -. Ph.D. thesis, University of Stutgart.
2. Arravas N. Finite elastoplastic transformation of transversely isotropic metals. International Journal of Solids and Structures 29 (1992) 2137-2157
3. Arravas N. Finite-strain anisotropic plasticity and the plastic spin. Modelling and Simulation in Materials Science 2 (1994) 483-504
4. Ball J. Convexity conditions and existence theorem in non-linear elasticity. Archive of Rational Mechanics and Analysis 63 (1977) 337-403
5. Ball, J. 1977b. Constitutive equalities and existence theorems in elasticity. In: Knops, R.J. (Ed.), Symposium on Non-Well Posed Problems and Logarithmic Convexity. Springer, Lecture Notes in Math 316.
6. Barlat F., and Lian K. Plastic behavior and stretchability of sheet metals. Part I: a yield function for orthotropic sheets under plane stress conditions. International Journal of Plasticity 5 1 (1989) 51-66
7. Barlat F., Lege D.J., and Brem J.C. A six-component yield function for anisotropic materials. International Journal of Plasticity 7 7 (1991) 693-712
8. Becker R., Smelser R.E., and Panchanadeeswaran S. Simulations of earing in aluminum single and polycrystals. Modelling and Simulation in Materials Science 1 (1993) 203-224
9. Bishop J.F.W., and Hill R. A theoretical derivation of the plastic properties of a polycrystalline face-centred metal. Philosophical Magazine 42 (1951) 1298-1307
10. Boehler, J. 1987. Applications of tensor functions in solid mechanics. International Center for Mechanical Sciences. No. 292, Udine, Springer Verlag.
11. Boyce M.C., Park D.M., and Weber G.G. On the kinematics of finite strain plasticity. Journal of the Mechanics and Physics of Solids 37 (1988) 647-665
12. Ciarlet, P.G. 1988. Mathematical Elasticity, vol. 1. Three Dimensional Elasticity. North-Holland, Amsterdam.
13. Dafalias Y. The plastic spin. Journal of Applied Mechanics 73 (1985) 865-871
14. Dafalias Y. Issues on the constitutive formulation at large elastoplastic deformations, part 1. Acta Mechanica 69 (1987) 119-138
15. Dafalias Y. Plastic spin: necessity or redundancy?. International Journal of Plasticity 14 (1998) 909-931
16. Darrieulat M., Fortunier R., and Montheillet F. Invariant formulation of anisotropic plastic behaviour in the case of cubic symmetry. International Journal of Plasticity 8 (1992) 763-771
17. Ekh M., Menzel A., Runesson K., and Steinmann P. Anisotropic damage with the mcr effect coupled to plasticity. International Journal of Engineering Science 41 (2003) 1535-1551
18. Fortunier, R., Orlans-Joliet, B., Montiheiller, F., Driver, J.H. 1987. Large strain multiple slip work hardening behaviour of fcc and bcc singel crystals. In: Constutive Relations and their Physical Basis. Riso National Laboratory.
19. Harrysson, M., Ristinmaa, M. 2006. Description of evolving anisotropy at large strains. Mechanics of Materials (in press), doi:10.1016/j.mechmat.2006.05.005.
20. Imatani S., and Maugin G. A constitutive model for material growth and its applications to thee-dimensional finite element analysis. Mechanics Research Communications 29 (2002) 477-483
21. Itskov M., and Aksel N. A constitutive model for orthotropic elasto-plasticity at large strains. Archive of Applied Mechanics 74 (2004) 75-91
22. Johansson G., Menzel A., and Runesson K. Modeling of anisotropic inelasticity in pearlitic steel at large strains due to deformation induced substructure evolution. European Journal of Mechanics A/Solids 24 (2005) 899-918
23. Karafillis A., and Boyce M. A general anisotropic yield criterion using bounds and a transformation weighting tensor. Journal of the Mechanics and Physics of Solids 41 12 (1993) 1859-1886
24. Kratochvil J. Finite-strain theory of crystalline elastic-inelastic material. Journal of Applied Physics 42 (1971) 1104
25. Kröner E. Allgemeine Kontinuumstheorie der Versetzungen. Archive of Rational Mechanics and Analysis 41 (1960) 273-334
26. Lee E. Elastic-plastic deformations at finite strains. Journal of Applied Mechanics 36 (1969) 1-6
27. Loret B. On the effect of plastic rotation in the finite deformation of anisotropic elastoplastic materials. Mechanics of Material 2 (1983) 287-304
28. Mandel, J. 1971. Plasticité classique et viscoplasticité. International Center for Mechanical Sciences, No. 97, Udine Springer Verlag.
29. Menzel A., and Steinmann P. On the comparison of two strategies to formulate orthotropic hyperelasticity. Journal of Elasticity 62 (2001) 171-201
30. Menzel A., and Steinmann P. On the spatial formulation of anisotropic multiplicative elasto-plasticity. Computer Methods in Applied Mechanics and Engineering 192 (2003) 3431-3470
31. Menzel A., and Steinmann P. Geometrically non-linear anisotropic inelasticity based on fictitious configurations: application to the coupling of continuum damage and multiplicative elasto-plasticity. International Journal for Numerical Methods in Engineering 56 (2003) 2233-2266
32. Montheillet F., Gilormini P., and Jonas J.J. Relation between axial stresses and texture development during torsion testing: a simplified theory. Acta Metallurgica 33 4 (1985) 705-717
33. Ortiz M., Radovitzky R., and Repetto E. The computation of the exponential and logarithmic mappings and their first and second linearizations. International Journal for the Numerical Methods in Engineering 52 (2001) 1431-1441
34. Reese S. Meso-macro modelling of fibre-reinforced rubber-like composites exhibiting large elastoplastic deformation. International Journal of Solids and Structures 40 (2003) 951-980
35. Schröder J., and Neff P. Invariant formulation of hyperelastic trensverse isotropy based on polyconvex free energy functions. International Journal of Solids and Structures 40 (2003) 401-445
36. Simmons G., and Wang H. Single Crystal Elastic Constants and Calculated Aggregate Properties: A Handbook (1971), The M.I.T. Press
37. Simo J. A framework for finite strain elastoplasticity based on maximum plastic dissipation and the multiplicative decomposition: part II computational aspects. Computer Methods in Applied Mechanics and Engineering 68 (1988) 1-31
38. Simo J., and Miehe C. Coupled associative thermoplasticity at finite strains. formulation numerical analysis and implentation. Computer Methods in Applied Mechanics and Engineering 98 (1992) 41-104
39. Simo, J.C. 1998. Numerical analysis and simulation of plasticity. In: Handbook of Numerical Analysis. vol. VI. Springer Verlag.
40. Spencer, A. 1984. Continuum theory of the mechanics of fiber-reinforced composites. International Center for Mechanical Sciences, No. 282, Udine, Springer Verlag.
41. Steigmann D. Frame-invariant polyconvex strain-energy function for some anisotropic solids. Mathematics and Mechanics of Solids 8 (2003) 497-506
42. Tsakmakis C. Description of plastic anisotropy effects at large deformation-part I: restrictions imposed by the second law and the postulate of Il'iushin. International Journal of Plasticity 20 (2004) 167-198
43. Tucker G. Texture and earing in deep drawing of aluminium. Acta Metallurgica 9 (1961) 275-286
44. van der Giessen E. Continuum model of large deformation plasticity part II: a kinematic hadening model and the concept of a plastically induced orientational structure. European Journal of Mechanics A/Solids 8 (1989) 89-108
45. van der Giessen E. Micromechanical and thermodynamic aspects of the plastic spin. International Journal of Plasticity 7 (1991) 365-386
46. Wallin M., and Ristinmaa M. Deformation gradient based kinematic hardening. International Journal of Plasticity 21 (2005) 2025-2050
47. Weber G., and Anand L. Finite deformation constitutive equations and time integration procedure for isotropic hyperelastic-viscoelastic solids. Computer Methods in Applied Mechanics and Engineering 79 (1990) 173-202