Improved Singum Model Based on Finite Deformation of Crystals with the Thermodynamic Equation of State
Publication: Journal of Engineering Mechanics
Volume 149, Issue 4
Abstract
The recently published simplified singum model has been improved by using the thermodynamics-based equation of state (EOS) of solids to derive a new interatomic potential based on elastic constants. The finite deformation formulation under hydrostatic load has been used to evaluate the pressure-volume (p-v) relationship for the EOS of a solid. Using the bulk modulus and its derivatives at the free-stress state, one can construct the EOS, from which a new form of interatomic potential is derived for the singum, which exhibits much higher accuracy than the previous one obtained from the Fermi energy and provides a general approach to construct the interatomic potential. The long-range atomic interactions are approximated to be proportional to the pressure. This improved singum model is demonstrated for the face-centered cubic (FCC) lattice of single-crystalline aluminum. The elastic properties at different pressures are subsequently predicted through the bond length change and compared with the available experimental data. The model can be straightforwardly extended to higher-order terms of EOS with better accuracy and other types of lattices.
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Data Availability Statement
All data that support the findings of this study are available from the corresponding author upon reasonable request.
Acknowledgments
This work is sponsored by the National Science Foundation IIP #1738802, IIP #1941244, CMMI #1762891, and US Department of Agriculture NIFA #2021-67021-34201, whose support is gratefully acknowledged. The author thanks Dr. Jeffrey Kysar and Dr. Sinan Keten for the helpful discussion and the sharing of their relevant papers. This work was inspired by Dr. Richard Li’s Ph.D. dissertation, and Junhe Cui has conducted careful reading and found several typos.
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Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 149 • Issue 4 • April 2023
Copyright
© 2023 American Society of Civil Engineers.
History
Received: Jun 29, 2022
Accepted: Oct 16, 2022
Published online: Feb 6, 2023
Published in print: Apr 1, 2023
Discussion open until: Jul 6, 2023
ASCE Technical Topics:
- Continuum mechanics
- Deformation (mechanics)
- Design (by type)
- Elastic analysis
- Engineering fundamentals
- Engineering mechanics
- Equations of state
- Fluid mechanics
- Hydrologic engineering
- Hydrostatics
- Lattices
- Load factors
- Model accuracy
- Models (by type)
- Solid mechanics
- Structural analysis
- Structural design
- Structural engineering
- Structural mechanics
- Structural systems
- Thermodynamics
- Water and water resources
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