TY - JOUR

T1 - On the treatment of non-reciprocal rate-independent kinetics via thermodynamic extremal principles

AU - Hackl, K.

AU - Fischer, Franz-Dieter

AU - Svoboda, Jiří

PY - 2020/12

Y1 - 2020/12

N2 - 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.

AB - 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.

KW - Barrier constraints

KW - Non-reciprocal

KW - Rate-independent

KW - Thermodynamic extremal principle

KW - Variational calculus

UR - http://www.scopus.com/inward/record.url?scp=85090414160&partnerID=8YFLogxK

U2 - 10.1016/j.jmps.2020.104149

DO - 10.1016/j.jmps.2020.104149

M3 - Article

VL - 145

SP - 104149-1-7

JO - Journal of the mechanics and physics of solids

JF - Journal of the mechanics and physics of solids

SN - 0022-5096

M1 - 104149

ER -