TY - JOUR

T1 - On the coupling of Hamilton's principle and thermodynamic extremal principles

AU - Hackl, Klaus

AU - Svoboda, Jiri

AU - Fischer, Franz-Dieter

N1 - Publisher Copyright: © 2024

PY - 2024/3/30

Y1 - 2024/3/30

N2 - Extremal principles can generally be divided into two rather distinct classes. There are, on the one hand side, formulations based on the Lagrangian or Hamiltonian mechanics, respectively, dealing with time dependent problems, but essentially resting on conservation of energy and thus being not applicable to dissipative systems in a consistent way. On the other hand, there are formulations based essentially on maximizing the dissipation, working efficiently for the description of dissipative systems, but being not suitable for including inertia effects. Many attempts can be found in the literature to overcome this split into incompatible principles. However, essentially all of them possess an unnatural appearance. In this work, we suggest a solution to this dilemma resting on an additional assumption based on the thermodynamic driving forces involved. Applications to a simple dissipative structure and a material with varying mass demonstrate the capability of the proposed approach.

AB - Extremal principles can generally be divided into two rather distinct classes. There are, on the one hand side, formulations based on the Lagrangian or Hamiltonian mechanics, respectively, dealing with time dependent problems, but essentially resting on conservation of energy and thus being not applicable to dissipative systems in a consistent way. On the other hand, there are formulations based essentially on maximizing the dissipation, working efficiently for the description of dissipative systems, but being not suitable for including inertia effects. Many attempts can be found in the literature to overcome this split into incompatible principles. However, essentially all of them possess an unnatural appearance. In this work, we suggest a solution to this dilemma resting on an additional assumption based on the thermodynamic driving forces involved. Applications to a simple dissipative structure and a material with varying mass demonstrate the capability of the proposed approach.

KW - Dissipative systems

KW - Hamiltonian mechanics

KW - Lagrangian mechanics

KW - Thermodynamic extremal principle

UR - http://www.scopus.com/inward/record.url?scp=85189862347&partnerID=8YFLogxK

U2 - 10.1016/j.jmps.2024.105633

DO - 10.1016/j.jmps.2024.105633

M3 - Article

AN - SCOPUS:85189862347

VL - 187.2024

JO - Journal of the mechanics and physics of solids

JF - Journal of the mechanics and physics of solids

SN - 0022-5096

IS - June

M1 - 105633

ER -