Summary
An axisymmetrical shell element for large plastic strains is developed. The theory is based on the multiplicative decomposition of the material deformation gradient into an elastic and a plastic part. For quasi-Kirchhoff-type axisymmetric shells this leads to a product of the elastic and plastic stretches. By introduction of logarithmic strains the decomposition becomes additive. Plastic incompressibility is fulfilled in an exact manner.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Eberlein, R.;Wriggers, P.;Taylor, R. L.: A fully non-linear axisymmetrical quasi-Kirchhoff-type shell element for rubber-like materials. Int. J. Num. Meth. Eng. 36 (1993) 4027–4043
Eterovic, A. L.;Bathe, K. L.: A hyperelastic-based large strain elasto-plastic constitutive formulation with combined isotropic-kinematic hardening using logarithmic stresses and strain measures. Int. J. Num. Meth. Eng. 30 (1990) 1099–1115
Gruttmann, F.;Stein, E.: Tangentiale Steifigkeitsmatrizen bei Anwendung von Projektionsverfahren in der Elastoplastizitätstheorie. Ing. Arch. 58 (1988) 15–24
Hill, R.: The mathematical theory of plasticity. Oxford: University Press 1950
Hill, R.: Constitutive inequalities for isotropic elastic solids under finite strain. Proc. R. Soc. London A 314 (1970) 457–472
Hoger, A.: The stress conjugate to logarithmic strain. Int. J. Solids Struct. 23 (1987) 1645–1656
Lee, E. H.;Liu, D. T.: Finite-strain elastic-plastic theory with application to plane-wave analysis. J. Appl. Phys. 38 (1967) 19–27
Lubliner, J.: A maximum-dissipation principle in generalized plasticity. Acta Mechanica 52 (1984) 225–237
Lubliner, J.: Normality rules in large-deformation plasticity. Mech. Mater. 5 (1986) 29–34
Mattiasson, K.; Bernspång, L.; Samuelsson, A.; Hamman, T.; Schedin, E.; Melander, A.: Evaluation of a dynamic approach using explicit integration in 3-D sheet forming simulation. In: Chenot, J. L.; Wood, R. D.; Zienkiewicz, O. C. (eds.) Proc. NUMIFORM '92 Conf. 1992
Massoni, E.;Chenot, J. L.;Bellet, M.: A 3-D finite element approach for predicting the deformation of an anisotropic elasto-plastic membrane. In: Wriggers, P.; Wanger, W. (eds.) Nonlinear Computational Mechanics. Berlin: Springer 1991
Peric, D.; Owen, D. R. J.; Honnor, M. E.: A model for finite strain plasticity. In: Owen, R.; Hinton, E.; Onate, E. (eds.) Proc. 2nd Int. Conf. on Computational Plasticity, Pineridge, Swansea, 1989, pp. 111–126
Saran, M. J.;Schedin, E.;Samuelsson, A.;Melander, A.;Gustafsson, C.: Numerical and experimental investigations of deep drawing of metal sheets. J. Eng. Ind. ASME, 112 (1990) 272–277
Simo, J. C.;Taylor, R. L.: A return mapping algorithm for plane stress elastoplasticity. Int. J. Num. Meth. Eng. 22 (1986) 649–670
Simo, J. C.: A framework for finite elastoplasticity based on maximum plastic dissipation and the multiplicative decomposition: Part I. Continuum formulation. Comp. Meth. Appl. Mech. Eng. 66 (1988) 199–219
Simo, J. C.;Taylor, R. L.;Wriggers, P.: A note on finite-element implementation of pressure boundary loading. Comm. Appl. Num. Meth. 7 (1991) 513–525
Simo, J. C.: Algorithms for static and dynamic multiplicative plasticity that preserve the classical return mapping schemes of the infinitesinal theory. Comp. Meth. Appl. Mech. Eng. 99 (1992) 61–112
Wagner, W.: A finite element model for non-linear shells of revolution with finite rotations. Int. J. Num. Meth. Eng. 29 (1990) 1455–1471
Weber, G.;Anand, L.: Finite deformation constitutive equations and a time integration procedure for isotropic, hyperelastic-viscoplastic solids. Comp. Meth. Appl. Mech. Eng. 79 (1990) 173–202
Wriggers, P.;Miehe, C.: Contact constraints within coupled thermomechanical analysis-A finite element model. Comp. Meth. Appl. Mech. Eng. 113 (1994) 301–319
Wriggers, P.;Simo, J. C.: A note on tangent stiffnesses for fully nonlinear contact problems. Comm. Appl. Num. Meth. 1 (1985) 199–203
Zienkiewicz, O. C.;Taylor, R. L.: The Finite Element Method, Vol. 1. London: McGraw Hill 1988
Author information
Authors and Affiliations
Additional information
Support for this work was provided by the Deutsche Forschungsgemeinschaft (DFG) under contract Wr 19/7-1. The financial aid for the first and second author is gratefully acknowledged.
Rights and permissions
About this article
Cite this article
Wriggers, P., Eberlein, R. & Gruttmann, F. An axisymmetrical quasi-Kirchhoff-type shell element for large plastic deformations. Arch. Appl. Mech. 65, 465–477 (1995). https://doi.org/10.1007/BF00835659
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF00835659