Viscoplasticity based on additive decomposition of logarithmic strain and unified constitutive equations - Theoretical and computational considerations with reference to shell applications

Computers and Structures

Volumn 81, Issue 15, 2003, Pages 1583-1594

  Sansour, Carlo ^a   Wagner, Werner ^b  

^a UNIVERSITY OF ADELAIDE   (Australia)

^b UNIVERSITY OF KARLSRUHE   (Germany)

Author keywords

Algorithmic strain; Finite elements; Shell theory; Viscoplasticity

Indexed keywords

ANISOTROPY; FINITE ELEMENT METHOD; SHELLS (STRUCTURES); STRAIN; TENSORS;

SHELL THEORY;

VISCOPLASTICITY;

EID: 0037911599     PISSN: 00457949     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0045-7949(03)00149-4     Document Type: Article

References (21)

1. Arnold S.M., Saleeb A.F., Tan H.Q., Zang Y. Explicit robust schemes for implementation of a class of principal value-based constitutive models. Int. J. Numer. Meth. Eng. 37:1994;1931-1944.
2. Bertram A. An alternative approach to finite plasticity based on material isomorphisms. Int. J. Plasticity. 15:1999;353-374.
3. Besseling J.F. A thermodynamic approach to rheology. Parkus H., Seddov L.I. Irreversible aspects of continuum mechanics. 1968;Springer, Wien.
4. Bodner S.R., Partom Y. Constitutive equations for elastic-viscoplastic strain-hardening materials. ASME J. Appl. Mech. 42:1975;385-389.
5. Eterovic A.L., Bathe K.J. A hyperelastic-based large strain elasto-plastic constitutive formulation with combined isotropic-kinematic hardening using the logarithmic stress and strain measures. Int. J. Numer. Meth. Eng. 30:1990;1099-1115.
6. Haupt P. On the concept of an intermediate configuration and its application to a representation of viscoelastic-plastic material behaviour. Int. J. Plasticity. 1:1985;279-293.
7. Ibrahimbegovic A. Equivalent spatial and material descriptions of finite deformation elastoplasticity in principal axes. Int. J. Solids Struct. 31:1994;3027-3040.
8. Kröner E. Allgemeine Kontinuumstheorie der Versetzungen und Eigenspannungen. Arch. Rat. Mech. Anal. 4:1960;273-334.
9. Lee E.H. Elastic-plastic deformation at finite strains. ASME J. Appl. Mech. 36:1969;1-6.
10. Maugin G.A. Material forces: concepts and applications. Appl. Mech. Rev. 48:1995;213-245.
11. Moran B., Ortiz M., Shih C.F. Formulation of implicit finite element methods for multiplicative finite deformation plasticity. Int. J. Numer. Meth. Eng. 29:1990;483-514.
12. Ogden R.W. Nonlinear elastic deformation. 1984;Ellis Horwood, Chichester.
13. Sansour C. A theory and finite element formulation of shells at finite deformations involving thickness change: circumventing the use of a rotation tensor. Arch. Appl. Mech. 65:1995;194-216.
14. Sansour C. On the dual variable of the logarithmic strain tensor, the dual variable of the Cauchy stress tensor, and related issues. Int. J. Solids Struct. 38:2001;9221-9232.
15. Sansour C., Kollmann F.G. On theory and numerics of large viscoplastic deformation. Comput. Meth. Appl. Mech. Eng. 146:1997;351-369.
16. Sansour C., Kollmann F.G. Large strain viscoplastic deformations of shells. Theory and finite element computation. Comput. Mech. 21:1998;512-525.
17. Sansour C., Wagner W. A model of finite strain viscoplasticity based on unified constitutive equations. Theoretical and computational considerations with applications to shells. Comput. Meth. Appl. Mech. Eng. 191:2001;423-450.
18. Simo J.C. Algorithms for static and dynamic multiplicative plasticity that preserve the classical return mapping schemes of infinitesimal theory. Comput. Meth. Appl. Mech. Eng. 99:1992;61-112.
19. Simo J.C., Rifai M.S. A class of mixed assumed strain methods and the method of incompatible modes. Int. J. Numer. Meth. Eng. 29:1990;1595-1638.
20. Simo J.C., Taylor R.L. Quasi-incompressible finite elasticity in principal stretches. Continuum basis and numerical algorithms. Comput. Meth. Appl. Mech. Eng. 85:1991;273-310.
21. Weber G., Anand L. Finite deformation constitutive equations and a time integration procedure for isotropic, hyperelastic-viscoplastic solids. Comput. Meth. Appl. Mech. Eng. 79:1990;173-202.