On the treatment of non-reciprocal rate-independent kinetics via thermodynamic extremal principles

K. Hackl, Franz-Dieter Fischer, Jiří Svoboda

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Onsager's Reciprocal Relations between thermodynamic forces and fluxes, for which Onsager was awarded the Nobel Prize, automatically follow from Thermodynamic Extremal Principles. Thus, the principles have been up to now non-applicable for the treatment of experimentally determined or theoretically modeled non-reciprocal systems as e.g. those involving magnetic fields. Recently, we were able to demonstrate that adding of a certain barrier constraint as bilinear form of thermodynamic forces and fluxes accounted by the Thermodynamic Extremal Principles leads to non-reciprocal relations between the thermodynamic forces and fluxes. In this work, we extend this formulation to rate-independent systems possessing non-differentiable dissipation functions. As an application, we show that the non-associated models of pressure dependent plasticity can be obtained in this fashion.

Original languageEnglish
Article number104149
Pages (from-to)104149-1-7
Number of pages7
JournalJournal of the mechanics and physics of solids
Publication statusPublished - Dec 2020


  • Barrier constraints
  • Non-reciprocal
  • Rate-independent
  • Thermodynamic extremal principle
  • Variational calculus

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