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An internal variable treatment of evolutive problems in hardening plasticity and viscoplasticity with singularities

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Abstract

In the present paper, evolutive problems in hardening plasticity and viscoplasticity are analyzed by means of an internal variable formulation. The treatment is developed by taking advantage of the proper tools to deal with singularities and non-smooth functions and within the framework of the generalized standard material model. In fact, many physical phenomena pertinent to plasticity and viscoplasticity problems are represented by functions characterized by singularities such as for instance non-smooth yield criteria or non-smooth phase-transformation functions. A complete formulation of subdifferential evolutive laws and constitutive relations is presented herein for hardening plasticity and viscoplasticity by considering a framework which is adequate to deal with singularities of functions and non-smooth yield criteria. The Lagrangian of the plastic and viscoplastic constitutive problem with hardening is adopted herein in a form usually not considered. Accordingly, by enforcing the optimality conditions of the Lagrangian different equivalent expressions are illustrated for the flow laws, the evolutive laws of the internal variables and the complementarity conditions. Equivalent formulations of the evolutive laws and of the complementarity conditions are suitably derived and discussed. The proposed approach shows to be advantageous since it gives a proper geometrical framework to the maximum dissipation principle in non-smooth plasticity and viscoplasticity problems with hardening. In addition, the proposed formulation results to be useful for broadening the adopted geometrical framework to different types of flow laws and evolutive laws for new and innovative solid materials with plastic and viscoplastic constitutive behavior with hardening.

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Acknowledgements

This research is supported by the Italian Ministry of University and Research (MUR).

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  1. Department of Structures for Engineering and Architecture, University of Naples Federico II, via Claudio 21, 80125, Naples, Italy

    Fabio De Angelis

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  1. Fabio De Angelis
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De Angelis, F. An internal variable treatment of evolutive problems in hardening plasticity and viscoplasticity with singularities. Continuum Mech. Thermodyn. 35, 1807–1819 (2023). https://doi.org/10.1007/s00161-023-01227-7

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