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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 When cylinders are packed and wrapped by the bands around the surface, the effective elastic behavior in the cross section of the assembly, which is of significance to its stability and integrity, can be controlled by the wrapping force in the band. The wrapping force is transferred to the cylinders through the Hertz contact between each pair of neighboring cylinders, which is validated by the experiments. The Singum model is introduced to study the mechanical behaviors of the packed cylinders with two-dimensional (2D) packing lattices, in which an inner cylinder is simulated by a continuum particle of Singum and the inter-cylinder force is governed by the Hertz contact model so as to derive the effective stress-strain relationship. The wrapping force will produce configurational forces given a displacement variation, which significantly changes the effective stiffness of the packed cylinders. The hexagonal packing exhibits isotropic elasticity whereas the square packing is anisotropic. The efficacy of our model is demonstrated by comparing the closed form elasticity against the numerical simulation and the previous models. The explicit form of elasticity can be used for packing design and quality control of cable construction and installation.