Summary
A discussion of uniaxial ratchetting in linear viscoelasticity is given in [1]. The purpose of this paper is to analyse uniaxial ratchetting in the context of rate-independent plasticity laws. The analysis is referred to constitutive models with kinematic hardening, as well as to sawtooth input functions for stress with constant absolute value for the stress rate. For such loading histories some analytical formulas and explicit expressions concerning the model response for a sufficiently large number of cycles are derived. It turns out that an analogy can be drawn between the constitutive models of linear viscoelasticity and those of rate-independent plasticity with kinematic hardening. The analogy is established by a correspondence between the line representing the elasticity law for the equilibrium stress in viscoelasticity and the axis of kinematic hardening for the plasticity models defined in this paper.
Similar content being viewed by others
References
Korzén, M., Tsakmakis, Ch.: Uniaxial ratchetting in linear viscoelasticity. Acta Mech.120, 157–172 (1997).
Chaboche, J. L.: Time-independent constitutive theories for cyclic plasticity. Int. J. Plasticity2, 149–188 (1986).
Chaboche, J. L., Dang-Van, K., Cordier, G.: Modelization of the strain memory effect on the cyclic hardening of 316 stainless steel. Paper L11/3, 5th. SMIRT, Berlin 1979.
Chaboche, J. L.: Constitutive equations for cyclic plasticity and cyclic viscoplasticity. Int. J. Plasticity5, 247–302 (1989).
Chaboche, J. L., Nouailhas, D.: Constitutive modeling of ratchetting effects — Part I: experimental facts and properties of the classical models. Trans. ASME J. Eng. Mat. Techn.111, 384–392 (1989).
Chaboche, J. L., Nouailhas, D.: Constitutive modeling of ratchetting effects — Part II: possibilities of some additional kinematic rules. Trans. ASME, J. Eng. Mat. Techn.111, 409–416 (1989).
Chaboche, J. L.: On some modifications of kinematic hardening to improve the description of ratchetting effects. Int. J. Plasticity7, 661–678 (1991).
Armstrong, P. J., Frederick, C. O.: A mathematical representation of the multiaxial Bauschinger effect. General Electricity Generating Board, Report RD/B/N 731 (1966).
Chaboche, J. L., Rousselier, G.: On the plastic and viscoplastic constitutive equations — Part I: rules developed with internal variable concept. Trans. ASME, J. Pressure Vessel Tech.105, 153–158 (1983).
Chaboche, J. L., Rousselier, G.: On the plastic and viscoplastic constitutive equations — Part II: application of internal variable concepts to the 316 stainless steel. Trans. ASME J. Pressure Vessel Tech.105, 159–164 (1983).
Marquis, D.: Modélisation et identification de l'écrouissage anisotrope des métaux. Thèse, Paris VI (1979).
Tsakmakis, Ch.: Über inkrementelle Materialgleichungen zur Beschreibung großer inelastischer Deformationen. Fortschr.-Ber. VDI Reihe 18, Nr. 36. Düsseldorf: VDI-Verlag 1987.
Lemaitre, J., Chaboche, J. L.: Mechanics of solid materials. Cambridge: Cambridge University Press 1990.
Ohno, N., Wang, J. D.: Transformation of a nonlinear kinematic hardening rule to a multisurface form under isothermal and nonisothermal conditions. Int. J. Plasticity7 879–891 (1992).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Kamlah, M., Korzeń, M. & Tsakmakis, C. Uniaxial ratchetting in rate-independent plasticity laws. Acta Mechanica 120, 173–198 (1997). https://doi.org/10.1007/BF01174323
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01174323