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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. 

Abstract The Green’s function of a bimaterial infinite domain with a plane interface is applied to thermal analysis of a spherical underground heat storage tank. The heat transfer from a spherical source is derived from the integral of the Green’s function over the spherical domain. Because the thermal conductivity of the tank is generally different from soil, the Eshelby’s equivalent inclusion method (EIM) is used to simulate the thermal conductivity mismatch of the tank from the soil. For simplicity, the ground with an approximately uniform temperature on the surface is simulated by a bimaterial infinite domain, which is perfectly conductive above the ground. The heat conduction in the ground is investigated for two scenarios: First, a steady-state uniform heat flux from surface into the ground is considered, and the heat flux is disturbed by the existence of the tank due to the conductivity mismatch. A prescribed temperature gradient, or an eigen-temperature gradient, is introduced to investigate the local temperature field in the neighborhood of the tank. Second, when a temperature difference exists between the water in the tank and soil, the heat transfer between the tank and soil depends on the tank size, conductivity, and temperature difference, which provide a guideline for heat exchange design for the tank size. The modeling framework can be extended to two-dimensional cases, periodic, or transient heat transfer problems for geothermal well operations. The corresponding Green’s functions are provided for those applications.