On the treatment of non-reciprocal rate-independent kinetics via thermodynamic extremal principles. (December 2020)

• Record Type: Journal Article
• Authors: Hackl, K.; Fischer, F.D.; Svoboda, J.
• Is Part Of: Journal of the mechanics and physics of solids. Volume 145(2020)
• Publication Date: 2020-12
• Subjects: Non-reciprocal -- Rate-independent -- Variational calculus -- Thermodynamic extremal principle -- Barrier constraints; Mechanics, Applied -- Periodicals; Solids -- Periodicals; Mechanics -- Periodicals; Mécanique appliquée -- Périodiques; Solides -- Périodiques; Mechanics, Applied; Solids; Periodicals; 531.05
• DOI: 10.1016/j.jmps.2020.104149
• Languages: English
• ISSNs: 0022-5096

Abstract

Highlights: A barrier condition may enforce non-reciprocal behavior of thermodynamic systems. The Thermodynamic Extremal Principle is formulated for non-reciprocal systems. The Thermodynamic Extremal Principle is extended to treat rate-independent processes. A thermodynamic consistent derivation of non-associated plasticity is given. This extension allows treating a large family of non-reciprocal physical processes. Abstract: 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.