Abstract
— A class of elastic-viscoplastic materials with dual internal variables, thermodynamic potential and temperature-dependent plastic and creep data is considered. For solids (or structures) of such materials, subjected to cyclic loads and temperature variations, the existence of a steady-state response is ascertained and its periodicity characteristics established. Particular steady-state responses, like, elastic and inelastic shakedown, are addressed. By means of a sensitivity analysis of the steady cycle with respect to the load parameter changes, a number of basic features of inelastic shakedown (the viscoplastic counterpart of plastic shakedown) are also addressed.
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
1960 Koiter, W.T., “General Theorems of Elastic-Plastic Solids”, in Sneddon, J.N., and Hill, R. (eds.),Progress in Solid Mechanics, Vol. 1, North Holland, Amsterdam, pp. 167–221.
1966 Frederick, C.O. and Armstrong, P.J., “Convergent Internal Stresses and Steady Cyclic State of Stress”, J. Strain Analysis 1, 154.
1972 MrÓZ, Z., “On the Theory of Steady Plastic Cycles in Structures”, In: Proc. of the First Int. Conf. on Structural Mechanics in Reactor Technology, Vol. 6, Part L, pp. 489–501.
1972 Ponter, A.R.S., “Deformation, Displacement and Work Bounds for Structure in a State of Creep and Subjected to Variable Loading”, J. Appl. Mech. 39, 953.
1974 Perzyna, P., “Internal Variable Description of Plasticity”, in Sawczuk, A.(ed.), Problems of Plasticity, Noordhoff Int. Pub., Leyden, The Nederlands, pp. 145–170.
1975 Martin, J.B., Plasticity: Fundamentals and General Results, The MIT Press, Cambridge, Ma.
1975 Halphen, B. and Nguyen, Q.S., “Sur les Matériaux Standard Géneralisées”, J. de Mécanique 14, 641.
1977 Ainwhorth, R.A., “Bounding Solutions for Creeping Structures Subjected to Load Variations Above the Shakedown Limit”, Int. J. Solids Structures 3, 971.
1977 Chaboche, J.L., “Viscoplastic Constitutive Equations for the Description of Cyclic and Anisotropic Behaviour of Metals”, Bull., of the Polish Academy of Sciences, Series Sc and Techn., Vol 25, no.l, pp. 33–42.
1979 Halphen, B., “Steady Cycles and Shakedown in Elastic-Viscoplastic and Plastic Structures”, in Matériaux et Structures Sous Chargement Cyclique, Association Amicale des Ingenieurs Anciens Eléves de E.N.P.C., Paris, pp. 203–230.
1980 Ainsworth, R.A., Goodall, I.W. and Walters, D.J., “Cyclic Loading in the Creep Range”, Proc. Int. Conf. on Engineering Aspects of Creep, I. Mech. E/ASME, Sheffield, C215/80, pp. 153–160.
1980 Gokhfeld, D.A. and Cherniavsky, D.F., “Limit Analysis of Structures at Thermal Cycling”, Sijthoff & Noordhoff, Alphen aan der Rijn, The Netherlands.
1983 Ponter, A.R.S., Shakedown and Ratchetting Below the Creep Range, Report EUR 8702EN, Commission of European Communities, Brussels.
1985 Lemaitre J. and Chaboche, J.L., Mécanique des Matériaux Solides, Dunod, Paris.
1985a Ponter, A.R.S. and Karadeniz, S., “An Extended Shakedown Theory for Structures that Suffer Cyclic Thermal Loadings, Part 1: Theory”, J. Appl. Mech. 52, 877.
1985b Ponter, A.R.S., and Karadeniz, S., “An Extended Shakedown Theory for Structures that Suffer Cyclic Thermal Toadings, Part 2: Applications”, J. Appl. Mech. 52, 883.
1987 KÖNig, J.A., Shakedown of Elastic-Plastic Structures, PWN-Polish Scientific Publishers, Warsaw, and Elsevier, Amsterdam.
1987 Maier, G.,“A Generalization to Nonlinear Hardening of the First Shakedown Theorem for Discrete Elastic-Plastic Models”, Atti Acc. Lincei, Rend. Fis. 8, LXXX, 161.
1987 Maier, G., and Novati, G., “Deformation Bounds for Elastic-Plastic Structures with Piecewise Linear Yield Laws and Nonlinear Hardening”, in Owen, D.R.J., Hinton, E. and Onate, E., (eds.), Computational Plasticity, Pine-ridge Press, Swansea, UK., pp. 17–31.
1988 Panzeca, T. and Polizzotto, C., “On Shakedown of Elastic-Plastic Solids”, Meccanica 23, 94.
1990 Lubliner, J., Plasticity Theory, Macmillan Publishing Co., New York.
1990 Polizzotto, C., Borino, G., and Fuschi, P., “On the Steady-State Response of Elastic Perfectly Plastic Solids to Cyclic Loads”, in Kleiber, M. and KÖNig, J.A.(eds.), Inelastic Solids and Structures, Pineridge Press, Swansea, U.K., pp. 473–488.
1990 Ponter, A.R.S., Karadeniz, S. and Carter, K.F., “Extended Upper Bound Shakedown Theory and Finite Element Method for Axisymmetric Thin Shells”, in Kleiber, M. and KÖnig, J.A.(eds.), Inelastic Solids and Structures, Pineridge Press, Swansea, U.K., pp. 433–449.
1993a Polizzotto, C., “A Study on Plastic Shakedown of Structures. Part I: Basic Properties”, J. Appl. Mech. 60, 318.
1993b Polizzotto, C., “A Study on Plastic Shakedown of Structures. Part II: Theorems”, J. Appl. Mech. 60, 324.
1993c Polizzotto, C., “The Assessment of the Residual Post-Transient Stresses”, Rend. Mat. Acc. Lincei S.9, 4, 133.
1993d Polizzotto, C., “Steady States and Sensitivity Analysis in Elastic-Plastic Structures Subjected to Cyclic Loads”, J. Solids Struct. (being printed).
1993 Fuschi, P. and Polizzotto, C., “The Shakedown Load Boundary of an Elastic-Plastic Structure Under Combined Cyclic/Steady Loads”, Meccanica, (submitted for publication).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1995 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Polizzotto, C. (1995). Elastic-Viscoplastic Solids Subjected to Thermal and Loading Cycles. In: Mróz, Z., Weichert, D., Dorosz, S. (eds) Inelastic Behaviour of Structures under Variable Loads. Solid Mechanics and Its Applications, vol 36. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-0271-1_6
Download citation
DOI: https://doi.org/10.1007/978-94-011-0271-1_6
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-4120-1
Online ISBN: 978-94-011-0271-1
eBook Packages: Springer Book Archive