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.
Elastic solution of a polyhedral particle with a polynomial eigenstrain and particle discretization
Abstract The paper extends the recent work (JAM, 88, 061002, 2021) of the Eshelby's tensors for polynomial eigenstrains from a two dimensional (2D) to three dimensional (3D) domain, which provides the solution to the elastic field with continuously distributed eigenstrain on a polyhedral inclusion approximated by the Taylor series of polynomials. Similarly, the polynomial eigenstrain is expanded at the centroid of the polyhedral inclusion with uniform, linear and quadratic order terms, which provides tailorable accuracy of the elastic solutions of polyhedral inhomogeneity by using Eshelby's equivalent inclusion method. However, for both 2D and 3D cases, the stress distribution in the inhomogeneity exhibits a certain discrepancy from the finite element results at the neighborhood of the vertices due to the singularity of Eshelby's tensors, which makes it inaccurate to use the Taylor series of polynomials at the centroid to catch the eigenstrain at the vertices. This paper formulates the domain discretization with tetrahedral elements to accurately solve for eigenstrain distribution and predict the stress field. With the eigenstrain determined at each node, the elastic field can be predicted with the closed-form domain integral of Green's function. The parametric analysis shows the performance difference between the polynomial eigenstrain by the Taylor expansion at the centroid and the 𝐶0 continuous eigenstrain by particle discretization. Because the stress singularity is evaluated by the analytical form of the Eshelby's tensor, the elastic analysis is robust, stable and efficient.
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- NSF-PAR ID:
- 10282844
- Date Published:
- Journal Name:
- Journal of Applied Mechanics
- ISSN:
- 0021-8936
- Page Range / eLocation ID:
- 1 to 35
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1115/1.4051869
