On the treatment of non-reciprocal rate-independent kinetics via thermodynamic extremal principles
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In: Journal of the mechanics and physics of solids, Vol. 145, 104149, 12.2020, p. 104149-1-7.
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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 -