Abstract
A static shakedown theorem is presented using a micromechanical overlay model which simulates elastic-plastic material behaviour with nonlinear kinematic hardening. It is a generalization of the Melan theorem for unlimited, linear kinematic hardening material. The new model is an extension of the one-dimensional Masing overlay model. It is shown that the necessary shakedown conditions for general nonlinear kinematic hardening materials are also sufficient ones for the proposed material model. Numerical solutions of 2-D problems were developed using finite element discretization and advanced optimization techniques. Three examples for plates and shells show the influence of the type of strainhardening on the magnitude of shakedown loads and the behaviour of failure.
This is a preview of subscription content, log in via an institution to check access.
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
Belytschko, T.: Plane stress shakedown analysis by finite elements, Int. J. Mech. Sci. 14 (1972), 619–625.
Bree, J.: Elastic-plastic behaviour of thin tubes subjected to internal pressure and intermittent high-heat fluxes with application to fast-nuclear-reactor fuel elements, Journal of Strain Analysis 2 (1967), 226–238.
Besseling, J.F.: Models of metal plasticity: theory and experiment, in Sawczuk and Bianchi (ed.): Plasticity Today, Elsevier, Appl. Sci. Publ. London-New York (1985), 97–113.
Corradi, L., Zavelani, I.: A linear programming approach to shakedown analysis of structures, Comp. Mech. Appl. Mech. Eng. 3 (1974), 37–53.
Gross-Weege, J.: Zum Einspielverhalten von Flächentragwerken Dissertation, Inst. für Mech., Ruhr-Universität Bochum (1988).
Koiter, W.T.: General theorems for elastic-plastic solids, In: Progress in Solid Mechanics, North Holland, Amsterdam (1960), 165–221.
König, J.A.: On shakedown of structures in a material exhibiting strainhardening (in Polish), IPPT Reports, No. 18 (1971).
König, J.A.: Shakedown of Elastic-Plastic Structures, Elsevier PWN-Polish Scientific Publishers, Warsaw 1987.
Maier, G.: A shakedown matrix theory allowing for worhardening and second-order geometric effects, In Proc. Symp. Foundations of Plasticity (ed. Sawczuk), Noordhoof, Leyden (1972), 417–433.
Masing, G.: Zur Heyn’schen Theorie der Verfestigung der Metalle durch verborgen elastische Spannungen, Wissenschaftliche Veröffentlichungen aus dem Siemens-Konzern 3 (1924), 231–239.
Melan, E.: Der Spannungszustand eines Mises-Henckyschen Kontinuums bei veränderlicher Belastung, Sitzber. Akad. Wiss. Wien IIa 147 (1938), 73–78.
Neal, B.G.: Plastic collapse und shake-down theorems for structures of strain-hardening material, J. Aero. Sci. 17 (1950), 297–306.
Schittkowski, K.: The nonliear programming method of Wilson, Han, and Powell with an augmented Larangian type line search function, Numer. Math. 38 (1981), 83–127.
Stein, E., Zhang, G., Mahnken, R., König, J.A.: Micromechanical modelling and computation of shakedown with nonlinear kinematic hardening including examples for 2-D probems, In Proc. CSME Mechanical Engineering Forum, Toronto (1990).
Weichert, D., Gross-Weege, J.: The numerical assessment of elastic-plastic sheets under variable mechanical and thermal loads using a simplified two-surface yield condition, Int. J. Mech. Sci. 30 (1988), 757–767.
Zhang, G., Stein, E., König, J.A.: Shakedown with nonlinear strainhardening including structural computation using finite element method, to appear.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1991 Springer-Verlag Berlin, Heidelberg
About this paper
Cite this paper
Stein, E., Zhang, G., König, J.A. (1991). Micromechanical Modelling and Computation of Shakedown with Nonlinear Kinematic Hardening — Including Examples for 2D-Problems. In: Axelrad, D.R., Muschik, W. (eds) Recent Developments in Micromechanics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-84332-7_8
Download citation
DOI: https://doi.org/10.1007/978-3-642-84332-7_8
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-84334-1
Online ISBN: 978-3-642-84332-7
eBook Packages: Springer Book Archive