The integrability criterion in finite elastoplasticity and its constitutive implications

Acta Mechanica

Volumn 188, Issue 3-4, 2007, Pages 227-244

  Xiao, H ^a,b   Bruhns, O T ^a,b   Meyers, A ^a,b  

^a Ruhr Universität Bochum ^*

^b RUHR UNIVERSITY BOCHUM   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

INTEGRAL EQUATIONS; NUMERICAL METHODS; STRAIN RATE; STRESS ANALYSIS; STRETCHING;

ELASTIC RATE EQUATION; EULERIAN RATE FORMULATION; HYPOELASTIC TYPE; STRESS-STRAIN RELATION;

ELASTOPLASTICITY;

EID: 33846621862     PISSN: 00015970     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00707-006-0362-3     Document Type: Article

References (27)

1. Truesdell, C.: The mechanical foundations of elasticity and fluid dynamics. J. Rat. Mech. Anal. 1, 125-300 (1952).
2. Truesdell, C.: Hypo-elasticity. J. Rat. Mech. Anal. 4, 83-133 (1955).
3. Truesdell, C.: The simplest rate theory of pure elasticity. Comm. Pure Appl. Math. 8, 123-132 (1955).
4. Truesdell, C.: Hypo-elastic shear. J. Appl. Phys. 27, 441-447 (1956).
5. Truesdell, C., Noll, W.: The non-linear field theories of mechanics. In: Handbuch der Physik, Vol. III/3 (Flügge, S., ed.). Berlin: Springer 1965.
6. Bernstein, B.: Hypoelasticity and elasticity. Arch. Rat. Mech. Anal. 6, 90-104 (1960).
7. Sansour, C., Bednarczyk, H.: A study on rate-type constitutive equations and the existence of a free energy function. Acta Mech. 100, 205-221 (1993).
8. Simó, J. C., Pister, K. S.: Remarks on rate constitutive equations for finite deformation problems: computational implications. Compt. Meth. Appl. Mech. Engng. 46, 201-215 (1984).
9. Xiao, H., Bruhns, O. T., Meyers, A.: Objective stress rates, path-dependence properties and non-integrability problems. Acta Mech. 176, 135-151 (2005).
10. Hencky, H.: Über die Form des Elastizitätsgesetzes bei ideal elastischen Stoffen. Z. Techn. Phys. 9, 215-223, 457 (1928).
11. Xiao, H., Bruhns, O. T., Meyers, A.: Logarithmic strain, logarithmic spin and logarithmic rate. Acta Mech. 124, 89-105 (1997).
12. Lehmann, T., Guo, Z. H., Liang, H. Y.: The conjugacy between Cauchy stress and logarithm of the left stretch tensor. Eur. J. Mech. A/Solids 10, 395-404 (1991).
13. Reinhardt, W. D., Dubey, R. N.: Coordinate-independent representation of spin tensors in continuum mechanics. J. Elasticity 42, 133-144 (1996).
14. Xiao, H., Bruhns, O. T., Meyers, A.: Strain rates and material spins. J. Elasticity 52, 1-41 (1998).
15. Xiao, H., Bruhns, O. T., Meyers, A.: On objective corotational rates and their defining spin tensors. Int. J. Solids Struct. 35, 4001-4014 (1998).
16. Xiao, H., Bruhns, O. T., Meyers, A.: Hypo-elasticity model based upon the logarithmic stress rate. J. Elasticity 47, 51-68 (1997).
17. o* = λ(trD)I + 2λD and its significance to finite inelasticity. Acta Mech. 138, 31-50 (1999).
18. Xiao, H., Bruhns, O. T., Meyers, A.: The choice of objective rates in finite elastoplasticity: general results on the uniqueness of the logarithmic rate. Proc. Roy. Soc. London A 456, 1865-1882 (2000).
19. Bruhns, O. T., Xiao, H., Meyers, A.: Self-consistent Eulerian rate type elasto-plasticity models based upon the logarithmic stress rate. Int. J. Plasticity 15, 479-520 (1999).
20. Bruhns, O. T., Xiao, H., Meyers, A.: On non-corotational rates of Oldroyd's type and relevant issues in rate constitutive formulations. Proc. Roy. Soc. London A 460, 909-928 (2003).
21. Bruhns, O. T., Xiao, H., Meyers, A.: A weakened form of Ilyushin's postulate and the structure of self-consistent Eulerian finite elastoplasticity. Int. J. Plasticity 21, 199-219 (2005).
22. Meyers, A., Xiao, H., Bruhns, O.: Elastic stress ratchetting and corotational stress rates. Technische Mechanik 23, 92-102 (2003).
23. Naghdi, P. M.: A critical review of the state of finite plasticity. Z. Angew. Math. Phys. 41, 315-394 (1990).
24. Xiao, H., Bruhns, O. T., Meyers, A.: Elastoplasticity beyond small deformations. Acta Mech. 182, 31-111 (2006).
25. Lee, E. H., Liu, D. T.: Finite strain elastic-plastic theory with application to plane-wave analysis. J. Appl. Phys. 38, 19-27 (1967).
26. Lee, E. H.; Elastic-plastic deformation at finite strains. J. Appl. Mech. 36, 1-6 (1969).
27. Lee, E. H.: Some anomalies in the structure of elastic-plastic theory at finite strain. In: Nonlinear effects in fluids and solids (Carroll, M. M., Hayes, M., eds.), pp. 227-249. New York: Plenum Press 1996.