Abstract
In this note, a generalization of the endochronic theory of plasticity is proposed. The basic idea is the introduction of several distinct intrinsic times instead of the unique one characterizing the standard theory. It follows that endochronic models without elastic domain and multi-layer plasticity models, presenting multi-linear hysteresis loops, can be described by means of a common theoretical framework. Moreover, a new model can be defined, able to produce, for uniaxial loading, closed hysteresis loops for small amplitudes and open loops for larger amplitudes.
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References
Valanis, K.C.: A theory of viscoplasticity without a yield surface. Part I: general theory. Arch. Mech. 23(4), 517–533 (1971)
Valanis, K.C.: On the foundations of the endochronic theory of plasticity. Arch. Mech. 27, 857 (1976)
Bouc, R.: Forced vibrations of a mechanical system with hysteresis. In: Proc. 4th Conf. Nonlinear Oscillations, Prague(1967)
Bouc, R.: Modèle mathématiques d’hystérésis. Acustica 24, 16–25 (1971) (in French)
Volterra, V.: Sur la théorie mathématique des phénomènes héréditaires. J. Math. Pure. Appl. 7, 249 (1928) (in French)
Baber, T.T., Wen, Y.K.: Random vibrations of hysteretic, degrading systems. J. Eng. Mech. Div. ASCE 107(6), 1069–1087 (1981)
Casciati, F.: Stochastic dynamics of hysteretic media. Struct. Safety 6, 259–269 (1989)
Karray, M.A., Bouc, R.: Etude dynamique d’un système d’isolation antisismique. Ann. ENIT 3(1), 43–60 (1989) (in French)
Wen, Y.K.: Method for random vibration of hysteretic systems. J. Eng. Mech. Div. ASCE 102, 249–263 (1976)
Erlicher, S., Point, N.: Thermodynamic admissibility of Bouc-Wen type models. C. R. Acad. Sci. Mechanique 332(1), 51–57 (2004)
Sivaselvan, M.V., Reinhorm, A.M.: Hysteretic models for deteriorating inelastic structures. J. Eng. Mech. 126(6), 633–640 (2000)
Bazant, Z.P.: Endochronic inelasticity and incremental plasticity. Int. J. Solid. Struct. 14, 691–714 (1978)
Valanis, K.C.: Fundamental consequences of a new intrinsic time measure: plasticity as the limit of the endochronic theory. Arch. Mech. 32, 517–533 (1980)
Watanabe, O., Atluri, S.N.: Internal time, general internal variable, and multi-yield-surface theories of plasticity and creep: A unification of concepts. Int. J. Plast. 2, 37–57 (1986)
Armstrong, P.J., Frederick, C.O.: A mathematical representation of the multiaxial Bauschinger effect. GEGB Report RD/B/N 731 (1966)
Chaboche, J.L., Dang-Van, K., Cordier, G.: Modelization of the strain memory effect on the cyclic hardening of 316 stainless steel. L11/3, Trans SMIRT-5, Berlin (1979)
Chiang, D.Y., Beck, J.L.: A new class of distributed-element models for cyclic plasticity. Int. J. Solid Struct. 31(4), 469–484 (1994)
Iwan, W.D.: A distributed element model for hyteresis and its steady-state dynamic response. J. Appl. Mech. ASME 33(4), 893–900 (1966)
Besseling, J.F.: A theory of elastic, plastic and creep deformation of an initially isotropic material showing anisotropic strain hardening, creep recovery and secondary creep. J. Appl. Mech. ASME 25, 529 (1958)
Schwartz, L.: Méthodes mathématiques pour les sciences physiques. Herrmann, Paris (1965) (in French)
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Point, N., Erlicher, S. (2012). A Generalization of the Endochronic Theory of Plasticity Based on the Introduction of Several Intrinsic Times. In: Frémond, M., Maceri, F. (eds) Mechanics, Models and Methods in Civil Engineering. Lecture Notes in Applied and Computational Mechanics, vol 61. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-24638-8_14
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DOI: https://doi.org/10.1007/978-3-642-24638-8_14
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