Multisurface thermoplasticity for single crystals at large strains in terms of Eulerian vector updates

International Journal of Solids and Structures

Volumn 33, Issue 20-22, 1996, Pages 3103-3130

  Miehe, C ^a  

^a UNIVERSITY OF STUTTGART   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; CONTINUUM MECHANICS; CRYSTALLOGRAPHY; ELASTIC MODULI; ELASTOPLASTICITY; MATHEMATICAL MODELS; PLASTIC DEFORMATION; SHEAR STRESS; STRAIN RATE; SURFACE PROPERTIES; VECTORS;

CONTINUUM SLIP THEORY; CRYSTALLOGRAPHIC SLIP SYSTEMS; ELASTIC DEFORMATION GRADIENT; EULERIAN VECTOR; ISOTROPIC TAYLOR TYPE HARDENING; MULTIPLICATIVE DECOMPOSITION; MULTISURFACE THERMOPLASTICITY;

SINGLE CRYSTALS;

EID: 0030212048     PISSN: 00207683     EISSN: None     Source Type: Journal    
DOI: 10.1016/0020-7683(95)00274-X     Document Type: Article

References (53)

1. Argyris, J. H. and Doltsinis, J. St. (1981). On the natural formulation and analysis of large deformation coupled thermomechanical problems. Comput. Meth. Appl. Mech. Engng 25, 195-253.
2. Armero, F. and Simó, J. C. (1992). A new unconditionable stable fractional step method for nonlinear coupled thermomechanical problems. Int. J. Numer. Meth. Engng 35, 737.
3. Asaro, R. J. (1979). Geometrical effects in the inhomogeneous deformation of ductile single crystals. Acta Metall. 27, 445-453.
4. Asaro, R. (1983). Crystal plasticity. J. Appl. Mech. 50, 921-934.
5. Asaro, R. J. and Needleman, A. (1985). Texture development and strain hardening in rate dependent polycrystals. Acta Metall. 33, 923-953.
6. Becker, R. (1992). An analysis of shear localization during bending of a polycrystalline sheet. J. Appl. Mech. 59, 491-496.
7. Bever, M. B., Holt, D. L. and Titchener, A. L. (1973). The Stored Energy of Cold Work, Pergamon, Oxford.
8. Borja, R. I. and Wren, J. R. (1993). Discrete micromechanics of elastoplastic crystals. Int. J. Numer. Meth. Engng 36, 3815-3840.
9. Chang, Y. W. and Asaro, R. J. (1981). An experimental study of shear localization in aluminium-copper single crystals. Acta Metall. 29, 241-257.
10. Cuitiño, A. M. and Ortiz, M. (1992). Computational modeling of single crystals. Modelling Simul. Mat. Sci. Engng 1, 225-263.
11. Doltsinis, J. St. (1990). Aspects of modelling and computation in the analysis of metal forming. Engng and Comput. 7, 2-20.
12. Duszek-Perzyna, M. K. and Perzyna, P. (1993). Adiabatic shear band localization in elastic-plastic single crystals. Int. J. Solids Struct. 30, 61-89.
13. Eckart, E. (1948). The thermodynamics of irreversible processes: IV. The theory of elasticity and anelasticity. Phys. Rev. 73, 337-382.
14. Flory, R. J. (1961). Thermodynamic relations for high elastic materials. Trans. Faraday Soc. 57, 829-838.
15. Harren, S. V. and Asaro, R. (1989). Nonuniform deformations in polycrystals and aspects of the validity of the Taylor model. J. Mech. Phys. Solids 37, 191-232.
16. Havner, K. S. (1982a). The theory of finite plastic deformation of crystalline solids. In Mechanics of Solids, the Rodney Hill 60th Anniversary Volume (Edited by H. G. Hopkins and M. J. Sewell), pp. 265-302. Pergamon, Swansea.
17. Havner, K. S. (1982b). Minimum plastic work selects the highest symmetry deformation in axially-loaded F.C.C. crystals. Mech. Mater. 1, 97-111.
18. Hill, R. (1966). Generalized constitutive relations for incremental deformation of metal crystals by multislip. J. Mech. Phys. Solids 14, 95-102.
19. Hill, R. and Havner, K. S. (1972). Perspective in the mechanics of elastoplastic crystals. J. Mech. Phys. Solids 30, 5-22.
20. Hill, R. and Rice, J. R. (1972). Constitutive analysis of elasto-plastic crystals at arbitrary strain. J. Mech. Phys. Solids 20, 401-413.
21. Kalidindi, S. R., Bronkhorst, C. A. and Anand, L. (1992). Crystallographic texture development in bulk deformation processing of FCC metals. J. Mech. Phys. Solids 40, 537-569.
22. Kocks, U. F. (1970). The relation between polycrystal deformation and single crystal deformation. Metall. Trans. 1, 1121-1143.
23. Koiter, W. T. (1960). General theorems of elastic-plastic solids. In Progress in Solid Mechanics (Edited by I. N. Sneddon and R. Hill). North Holland, Amsterdam.
24. Kratochvil, J. (1973). On a finite strain theory of elastic-inelastic materials. Acta Mech. 16, 127-142.
25. Kröner, E. (1964). Plastizität und verzerrungen. In Vorlesungen über Theoretische Physik (Edited by A. Sommerfeld), p. 5. Auflage, Leipzig.
26. Kröner, E. and Teodosiu, C. (1972). Lattice defect approach to plasticity and viscoplasticity. In Problems in Plasticity (Edited by A. Sawczuk). Noordhoff, Gronige.
27. Lee, E. H. (1969). Elastic-plastic deformation of finite strains. J. Appl. Mech. ASME 36, 1-6.
28. Luenberger, D. G. (1984). Linear and Nonlinear Programming. Addison-Wesley, Reading, MA.
29. Maier, G. (1970). A matrix structural theory of piecewise linear elastoplasticity with interacting yield planes. Meccanica 5, 54-66.
30. Maier, G. and Grierson, D. (1979). Engineering Plasticity and Mathematical Programming. Pergamon Press, New York.
31. Mandel, J. (1972). Plasticité Classique et Viscoplasticité. CISM Courses and Lectures, no. 97. Springer, Berlin.
32. Mathur, K. K. and Dawson, P. R. (1989). On modeling the development of crystallographic texture in bulk forming processes. Int. J. Plasticity 5, 67-94.
33. Miehe, C. (1994a). Aspects of the formulation and finite element implementation of large strain isotropic elasticity. Int. J. Numer. Meth. Engng 37, 1981-2004.
34. Miehe, C. (1994b). On the representation of Prandtl-Reuss tensors within the framework of multiplicative elastoplasticity. Int. J. Plasticity 10, 609-621.
35. Miehe, C. (1994c). Exponential map algorithm for stress updates in anisotropic multiplicative elastoplasticity for single crystals. Int. J. Numer. Meth. Engng (in press).
36. Miehe, C. (1995). Entropic thermoelasticity at finite strains. Aspects of the formulation and numerical implementation. Comput. Meth. Appl. Mech. Engng 120, 243-269.
37. Miehe, C. and Stein, E. (1992). A canonical model of multiplicative elasto-plasticity. Formulation and aspects of the numerical implementation. Euro. J. Mech. A/Solids 11, 25-43.
38. Mohan, R., Ortiz, M. and Shih, C. F. (1992). An analysis of cracks in ductile single crystals - I. Anti-plane shear, II. Mode I loading. J. Mech. Phys. Solids 40, 291-313 and 315-337.
39. Needleman, A., Asaro, R. J., Lemonds, J. and Peirce, D. (1985). Finite element analysis of crystalline solids. Comput. Meth. Appl. Mech. Engng 52, 689-708.
40. Peirce, D., Asaro, R. J. and Needleman, A. (1982). An analysis of nonuniform and localized deformation in ductile single crystals. Acta Metall. 30, 1087-1119.
41. Peirce, D., Asaro, R. J. and Needleman, A. (1983). Material rate dependence and localized deformation in crystalline solids. Acta Metall. 31, 1951-1976.
42. Perzyna, P. (1988). Temperature and rate dependent theory of plasticity of crystalline solids. Rev. Phys. Appl. 23, 445-459.
43. Rashid, M. M. and Nemat-Nesser, S. (1992). A constitutive algorithm for rate-dependent crystal plasticity. Comput. Meth. Appl. Mech. Engng 94, 201-228.
44. Rice, J. R. (1971). Inelastic constitutive relations for solids: an internal-variable theory and its application to metal plasticity. J. Mech. Phys. Solids 19, 433-455.
45. Simó, J. C. and Armero, F. (1992). Geometrically nonlinear enhanced strain mixed methods and the method of incompatible modes. Int. J. Numer. Meth. Engng 33, 1413-1449.
46. Simó, J. C., Kennedy, J. G. and Govindjee, S. (1988). Non-smooth multisurface plasticity and viscoplasticity. Loading/unloading conditions and numerical algorithms. Int. J. Numer. Meth. Engng 26, 2161-2185.
47. Simó, J. C. and Miehe, C. (1992). Associative coupled thermoplasticity at finite strains: formulation, numerical analysis and implementation. Comput. Meth. Appl. Mech. Engng 98, 41-104.
48. Spitzig, W. A. (1981). Deformation behaviour of nitrogenated Fe-Ti-Mn and Fe-Ti single crystals. Acta Metall. 29, 1359-1377.
49. Steinmann, P. and Stein, E. (1996). On the numerical treatment and analysis of finite deformation single crystal plasticity. Comput. Meth. Appl. Mech. Engng 129, 235-254.
50. Taylor, G. I. and Quinney, M. A. (1933). The latent energy remaining in a metal after cold working. Proc. R. Soc. Lond. A143, 307.
51. Teodosiu, C. (1970). A dynamic theory of dislocations and its applications to the theory of the elastic-plastic continuum. In Fundamental Aspects of Dislocation Theory (Edited by J. A. Simmons et al.), Vol. II, pp. 837-876. National Bureau of Standards (U.S.) Special Publication.
52. Teodosiu, C. and Sidoroff, F. (1976). A finite theory of the elastoviscoplasticity of single crystals. Int. J. Engng Sci. 14, 713-723.
53. Zienkiewicz, O. C. and Taylor, R. L. (1989). The Finite Element Method, Vol. 1. McGraw-Hill, London.