Vol. 5, No. 3-4, 2017

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Forms of the dissipation function for a class of viscoplastic models

Massimo Cuomo

Vol. 5 (2017), No. 3-4, 217–237
DOI: 10.2140/memocs.2017.5.217

The minimum properties that allow a dissipation functional to describe a behavior of viscoplastic type are analyzed. It is considered a material model based on an internal variable description of the irreversible processes and characterized by the existence of an elastic region. The dissipation functional derived includes the case of time-independent plasticity in the limit. The complementary dissipation functional and the flow rule are also stated. The model analyzed leads naturally to the fulfillment of the maximum dissipation postulate and thus to associative viscoplasticity. A particular class of models is analyzed, and similarities to and differences from diffused viscoplastic formats are given.

dissipation potential, viscoplasticity, convex potentials
Mathematical Subject Classification 2010
Primary: 74A20, 74C10
Received: 6 June 2016
Revised: 16 January 2017
Accepted: 10 March 2017
Published: 7 July 2017

Communicated by Francesco dell'Isola
Massimo Cuomo
Department of Civil Engineering and Architecture
University of Catania
Viale Andrea Doria 6
I-95125 Catania