Abstract
Computational problem of cyclic plasticity which leads to reliable results for use in engineering faces formidable difficulties. These difficulties relate to the following aspects
-
a)
The aim of computational analysis.
-
b)
The selection of the constitutive model and assessment of its reliability for the given goals.
-
c)
Mathematical formulation of the problem and analysis of its properties, such as existence and uniqueness of the solution, its dependence on the selected model, regularity of the solution, etc.
-
d)
Numerical solution of the mathematical problem, its convergence, a priori and a posteriori error estimation of the data of interest, adaptive approaches etc.
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
Eric Bonnetier, Ph.D. Dissertation, Institute for Physical Science & Technology and Department of Mathematics. The University of Maryland at College Park. 1988.
I. Babuška, K. L. Jerina, Y. Li & P. Smith, Quantitative Assessment of the Accuracy of Constitutive Laws for Plasticity with an Emphasis on Cyclic Deformation, Proceedings of the Symposium on Parameter Estimation for Modern Constitutive Equations at the 1993 ASME Winter Annual Meeting, ASME, New York, 1993.
I. Babuška & Y. Li, On High Order Finite Element Method for Plasticity Problems, TICAM Report 96–22, The University of Texas at Austin, May 1996.
I. Babuška & Y. Li, On h-p Adaptive Finite Element Method for Plasticity Problems, in preparation.
I. Babuška & P. Shi, Regularity of solutions to a one dimensional plasticity model, TICAM Report 96–16, The University of Texas at Austin, April 1996.
J. L. Chaboche, Time independent Constitutive Theories for Cyclic Plasticity, International Journal of Plasticity, Vol. 2, No. 2, pp. 149–188, 1986.
L. Gallimard, P. Ladevèze & J. Pelle, Error in constitutive relation and time error indicator for nonlinear computation, Numerical Methods in Engineering’96, John Wiley & Sons Ltd, 1996.
W. Han & B. D. Reddy, Computational plasticity: the variational basis and numerical analysis, Computational Mechanics Advances 2,No. 2, 1995.
P. Krejći, Hysteresis, Convexity and Dissipation in Hyperbolic Equations, Springer, 1996.
Y. Li & I. Babuška, A convergence analysis of a P-version FEM for 1-D elasto-plasticity problems, SIAM Journal on Numerical Analysis, Vol. 33, No.2, pp. 809–842, April 1996.
Y. Li & I. Babuska, A convergence analysis of an h-version high order FEM for 2-D elasto-plasticity problems, will appear in SIAM Journal on Numerical Analysis July 1997.
J. Lubliner, Plasticity Theory, Macmillan Publishing Company, New York, 1990.
P. Shi & I. Babuška, Analysis and computation of a cyclic plasticity model by aid of Ddassl, will appear in Computational Mechanics.
M. Zyzckowski, Combined Loading in the Theory of Plasticity, PWN-Polish Scientific Publisher, Warszawa, 1981.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1999 Springer Science+Business Media Dordrecht
About this paper
Cite this paper
Babuška, I., Li, Y. (1999). Numerical Solution of Problems of Cyclic Plasticity. In: Mang, H.A., Rammerstorfer, F.G. (eds) IUTAM Symposium on Discretization Methods in Structural Mechanics. Solid Mechanics and its Applications, vol 68. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-4589-3_36
Download citation
DOI: https://doi.org/10.1007/978-94-011-4589-3_36
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-5942-8
Online ISBN: 978-94-011-4589-3
eBook Packages: Springer Book Archive