Abstract
The classical linear elastoplastic model with the von Mises yield criterion and an associative flow rule, postulating
yields
with the total (geometrical) strain ε and the plastic strain ε p, see e.g. Lubliner, 1990. The stresses follow as
The associated flow rule with isotropic hardening is described by
where H, y 0 are material constants, and α is an internal variable. The loading-unloading conditions can be expressed in the Kuhn-Tucker form as
The solution of the coupled elastoplastic problem is obtained by a standard return mapping algorithm (Simo and Taylor, 1986).
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Haase, G., Langer, U. and Meyer, A. (1990). A new approach to the Dirichlet domain decomposition method, Proc. “5th Multigrid Seminar”, R-MATH-09/90, Karl-Weierstrass-Institut für Mathematik, Berlin.
Klaas, O., Kreienmeyer, M. and Stein, E. (1993). Numerische Lösung ebener Probleme der linearen Elastizitätstheorie mit der direkten Randelementmethode, in Baumann, M. and Grube, D. (Eds.), Parallele Datenverarbeitung mit dem Transputer, pp. 265–274, Springer, Berlin.
Klaas, O., Kreienmeyer, M. and Stein, E. (1994). Elasto-plastic finite element analysis on a MIMD parallel-computer, Eng. Analysis — Int. J. Comp. Aided Eng. Software 11,(4), pp. 347–355.
Kreienmeyer, M. and Stein, E. (1995). Parallel implementation of the boundary element method for linear elastic problems on a MIMD parallel computer, Comp. Mech 15,(4), pp. 342–349.
Lubliner, J. (1990). Plasticity Theory, Macmillan Publishing Company, New York.
Saad, Y. and Schultz, M. H. (1986). GMRES: A generalized minimal residual method for solving nonsymmetric linear systems, SIAM J. Sci. Statist. Comput. 7, pp. 856–869.
Schwarz, H.A. (1870). Vierteljahresschrift der Naturforschenden Gesellschaft in Zürich Band 15.
Simo, J. and Taylor, R. L. (1986). A return mapping algorithm for plane stress elastoplasticity, Int. J. Numer. Meth. Eng. 22, pp. 649–670.
van der Vorst, H.A. (1992). BI-CGSTAB: A Fast and Smoothly Converging Variant of BI-CG for the solution of Nonsymmetric Linear Systems, SIAM J. Sci. Statist. Comput. 13, pp. 631–640.
Yserentant, H. (1986). On the Multi-Level Splitting of Finite Element Spaces, Numer. Math. 49, pp. 379–412.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1997 Springer Science+Business Media Dordrecht
About this paper
Cite this paper
Kreienmeyer, M., Stein, E. (1997). Parallel Algorithms for Coupled Bem-Fem with Elastoplastic Deformations in the Fe-Domain. In: Morino, L., Wendland, W.L. (eds) IABEM Symposium on Boundary Integral Methods for Nonlinear Problems. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-5706-3_20
Download citation
DOI: https://doi.org/10.1007/978-94-011-5706-3_20
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-6406-4
Online ISBN: 978-94-011-5706-3
eBook Packages: Springer Book Archive