Details
| Original language | English |
|---|---|
| Article number | 106133 |
| Journal | Journal of the Mechanics and Physics of Solids |
| Volume | 200 |
| Early online date | 7 Apr 2025 |
| Publication status | Published - Jul 2025 |
Abstract
Based on Hamilton's principle of stationary action, we present a holistic variational formulation for material modeling including dissipative evolution. To this end, we recall the definition of the action as path integral of the momentum vector. Reformulation of the action and inserting the 1st and 2nd Law of Thermodynamics yield an extended Hamilton functional. We show that the stationarity conditions yield well-known expressions as well as new conditions in an extended nested time domain. Introducing an asymptotic two-scale approach transforms the expressions in the nested time domain back to the physical time. Hereby, we receive usual differential equations, e.g., heat conductivity equation, diffusion equation, and Biot equation, and the constitutive laws for, e.g., temperature, entropy, and chemical potential, all from one holistic stationarity principle. Moreover, the formulation in the nested time domain produces additional, virtual conditions that naturally lead to the concept of dissipation distances. Due to its variational origin, our approach yields in a consistent manner a coupled space–time formulation.
Keywords
- Coupled processes, dissipation, Hamilton's principle of stationary action, Variational material modeling
ASJC Scopus subject areas
- Physics and Astronomy(all)
- Condensed Matter Physics
- Engineering(all)
- Mechanics of Materials
- Engineering(all)
- Mechanical Engineering
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In: Journal of the Mechanics and Physics of Solids, Vol. 200, 106133, 07.2025.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - On a holistic variational formulation for material modeling including dissipative evolution
AU - Junker, Philipp
AU - Bode, Tobias
AU - Hackl, Klaus
N1 - Publisher Copyright: © 2025 The Authors
PY - 2025/7
Y1 - 2025/7
N2 - Based on Hamilton's principle of stationary action, we present a holistic variational formulation for material modeling including dissipative evolution. To this end, we recall the definition of the action as path integral of the momentum vector. Reformulation of the action and inserting the 1st and 2nd Law of Thermodynamics yield an extended Hamilton functional. We show that the stationarity conditions yield well-known expressions as well as new conditions in an extended nested time domain. Introducing an asymptotic two-scale approach transforms the expressions in the nested time domain back to the physical time. Hereby, we receive usual differential equations, e.g., heat conductivity equation, diffusion equation, and Biot equation, and the constitutive laws for, e.g., temperature, entropy, and chemical potential, all from one holistic stationarity principle. Moreover, the formulation in the nested time domain produces additional, virtual conditions that naturally lead to the concept of dissipation distances. Due to its variational origin, our approach yields in a consistent manner a coupled space–time formulation.
AB - Based on Hamilton's principle of stationary action, we present a holistic variational formulation for material modeling including dissipative evolution. To this end, we recall the definition of the action as path integral of the momentum vector. Reformulation of the action and inserting the 1st and 2nd Law of Thermodynamics yield an extended Hamilton functional. We show that the stationarity conditions yield well-known expressions as well as new conditions in an extended nested time domain. Introducing an asymptotic two-scale approach transforms the expressions in the nested time domain back to the physical time. Hereby, we receive usual differential equations, e.g., heat conductivity equation, diffusion equation, and Biot equation, and the constitutive laws for, e.g., temperature, entropy, and chemical potential, all from one holistic stationarity principle. Moreover, the formulation in the nested time domain produces additional, virtual conditions that naturally lead to the concept of dissipation distances. Due to its variational origin, our approach yields in a consistent manner a coupled space–time formulation.
KW - Coupled processes
KW - dissipation
KW - Hamilton's principle of stationary action
KW - Variational material modeling
UR - http://www.scopus.com/inward/record.url?scp=105002555939&partnerID=8YFLogxK
U2 - 10.1016/j.jmps.2025.106133
DO - 10.1016/j.jmps.2025.106133
M3 - Article
AN - SCOPUS:105002555939
VL - 200
JO - Journal of the Mechanics and Physics of Solids
JF - Journal of the Mechanics and Physics of Solids
SN - 0022-5096
M1 - 106133
ER -