Summary
This paper gives the definition of a thermodynamic approach of discrete memory type for strictly irreversible processes. The class of the associated constitutive equations is briefly recalled: it describes hysteresis and hardening by expressing the effective stress as the sum of two hereditary contributions, of discrete and continuous memory types respectively. A discrete memory form of Gibbs' equation is presented and a physical meaning is given to a loading-unloading criterion which defines a set of memorized states. For example, a precise formulation is given for the constitutive equations of an elastoviscoplastic material and an elastoplastic material with strain hardening. The results are obtained numerically and are related to simple geometries, including an axisymmetrical thin shell.
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Wack, B., Terriez, J.M. & Guelin, P. A hereditary type, discrete memory, constitutive equation with applications to simple geometries. Acta Mechanica 50, 9–37 (1983). https://doi.org/10.1007/BF01170438
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DOI: https://doi.org/10.1007/BF01170438