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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. 

The inclusion-based boundary element method (iBEM) is developed to calculate the elastic fields of a bi-layered composite with inhomogeneities in one layer. The bi-material Green’s function has been applied to obtain the elastic field caused by the domain integral of the source fields on inclusions and the boundary integral of the applied loads on the surface. Using Eshelby’s equivalent inclusion method (EIM), the material mismatch between the particle and matrix phases is simulated with a continuously distributed source field, namely eigenstrain, on inhomogeneities so that the iBEM can calculate the local field. The stress singularity along the interface leads to the delamination of the bimaterials under a certain load. The crack’s energy release rate (  J) is obtained through the J-integral, which predicts the stability of the delamination. When the stiffness of one layer increases, the J-integral increases with a higher gradient, leading to lower stability. Particularly, the effect of the boundary and inhomogeneity on the J-integral is illustrated by changing the crack length and inhomogeneity configuration, which shows the crack is stable at the beginning stage and becomes unstable when the crack tip approaches the boundary; a stiffer inhomogeneity in the neighborhood of a crack tip decreases J and improves the fracture resistance. For the stable cracking phase, the J-integral increases with the volume fraction of inhomogeneity are evaluated. The model is applied to a dual-glass solar module with air bubbles in the encapsulant layer. The stress distribution is evaluated with the iBEM, and the J-integral is evaluated to predict the delamination process with the energy release rate, which shows that the bubbles significantly increase the J-integral. The effect of the bubble size, location, and number on the J-integral is also investigated. The present method provides a powerful tool for the design and analysis of layered materials and structures.