Abstract
The introduction of hardening into the study of elastoplastic shakedown analysis is considered in this paper, in particular in the case of non-associated plasticity. Due to the fact that the framework of Generalized Standard Materials (GSM) is not well adapted in this last case, an alternative approach, provided by the concept of Implicit Standard Materials (ISM), is then used. In particular, we study the typical example of an homogeneous constant traction and alternating torsion state; it is analyzed by using the step-by-step computations and then within the ISM framework. The obtained results for the shakedown factor as well as the back-stresses are examined. The comparison of the incremental method predictions to the analytical solution and the mathematical programming ones, built by means of the bipotential approach, shows a very good agreement.
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
Armstrong, P.-J., Frederick, C.-O.: A mathematical representation of the multiaxial Bauschinger effect. In C.E.G.B., Report No. RD/B/N731 (1966)
Bodovillé, G.: A kinematic elastic nonshakedown theorem for implicit standard materials. Arch. Appl. Mech. 72, 266–278 (2002)
Bouby, C., de Saxcé, G., Tritsch, J.-B.: A comparison between analytical calculations of the shakedown load by the bipotential approach and step-by-step computations for elastoplastic materials with non linear kinematic hardening. Int. J. Solid. Struct. 43, 2670–2692 (2006)
Bouby, C.: Adaptation élastoplastique de structures sous chargements variables avec règle d’écrouissage cinématique non linéaire et non associée. Thèse de doctorat del’Université des Sciences et Technologies de Lille (2006)
Bousshine, L., Chaaba, A., de Saxcé, G.: Plastic limit load of plane frames with frictional contact supports. Int. J. Mech. Sci. 44, 2189–2216 (2002)
Bousshine, L., Chaaba, A., de Saxcé, G.: A new approach to shakedown analysis for non standard elastoplatic material by the bipotential. Int. J. Plasticity 19, 583–598 (2003)
Fenchel, W.: On conjugate convex functions. Canadian J. Math. 1, 73–77 (1949)
Khoi, V. D., Yan, A. M., Nguyen-Dang, H.: A dual form for discretized kinematic formulation in shakedown analysis. Int. J. Solid. Struct. 41, 267–277 (2004)
Koiter, W. T.: General theorems for elastic-plastic solids. In: Sneddon, I.N., Hills, R. (eds.) Progress in Solid Mechanics. Vol. 1, North Holland, Amsterdam (1960)
Ladevèze, P.: Mécanique non linéaire des structures : unenouvelle approche et méthodes de calcul non incrémentales. Hermès, Paris (1996)
Lemaitre, J., Chaboche, J.-L.: Mechanics of Solid Materials. Cambridge University Press, Cambridge (1990)
Maier, G., Carvelli, V., Cocchetti, G.: On direct methods for shakedown and limit analysis. Eur. J. Mech. A-Solid, 19 (Special Issue), S79–S100 (2000)
Maier, G., Weichert, D.: Inelastic Behaviour of Structures under Variable Repeated Loads. CISM Courses and Lectures, No 432, Springer Wien, New-York (2002)
Marquis, D.: Modélisation et identification de l’écrouissage anisotrope des métaux. Thése de 3éme cycle del’université Pierre et Marie Curie, Paris VI (1979)
Melan, E.: Theorie statisch unbestimmter Systeme ausideal-plastischem Baustoff. Sitzber. Akad. Wiss. Wien, Abt IIA, 145, 195–218 (1936)
Nguyen, Q.-S.: On shakedown in hardening plasticity. J. Mech. Phys.Solid. 51, 101–125 (2003)
Polizzotto, C., Borino, G., Caddemi, S., Fuschi, P.: Shakedown problems for material models with internal variables. Eur. J. Mech. A-Solid. 10, 621–639 (1991)
Weichert, D., Gross-Weege, J.: Assessment of elasto-plastic sheets under variable mechanical and thermal loads using a simplified two-surface yield condition. Int. J. Mech. Sci. 30, 757–767 (1988)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer Science+Business Media B.V.
About this chapter
Cite this chapter
Bouby, C., Saxcé, G.d., Tritsch, JB. (2009). On Shakedown of Structures Under Variable Loads with a Kinematic Non-linear and Non-associated Hardening Rule. In: Dieter, W., Alan, P. (eds) Limit States of Materials and Structures. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-9634-1_9
Download citation
DOI: https://doi.org/10.1007/978-1-4020-9634-1_9
Publisher Name: Springer, Dordrecht
Print ISBN: 978-1-4020-9633-4
Online ISBN: 978-1-4020-9634-1
eBook Packages: EngineeringEngineering (R0)