Thermoelastic modeling of cubic lattices from granular materials to atomic crystals

When a cubic lattice is confined by a surface layer, the effective thermoelastic properties can be tailored by the prestress produced by the surface. The thermal expansion coefficient, temperature derivative of elasticity, and the equation of state (EOS) of the solid depend on the potential of each bond and the lattice structure, which can be predicted by the recently developed singum model. This paper first uses a granular lattice confined by a spherical shell to demonstrate singum modeling of the thermoelastic behavior of the cubic lattices and then extends it to atomic crystal lattices by considering the surface tension and long-range interactions. Given the elasticity and the EOS of a cubic crystal, the interatomic potential can be inversely derived. As the bond length changes with thermal expansion and pressure, the singum model predicts the temperature- and pressure-dependent elasticity. Using the orientational average, isotropic elastic constants can be obtained for polycrystals. The case study of copper (Cu) demonstrates the versatility of the model for different cubic lattices and predicts the experimental results of pressure- and temperature-dependent elasticity. The singum model is general for different lattice types and EOS forms and provides clear physical and mechanical meanings to correlate the interatomic potential, EOS, and elasticity in the closed-form formulation, which is very useful in engineering design and analysis of metal structural members in fire, geothermal, and space applications without the needs of large-scale numerical simulations. (c) 2024 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International (CC BY-NC-ND) license (https://creativecommons.org/licenses/by-nc-nd/4.0/).