13th International Conference on Fracture June 16–21, 2013, Beijing, China -1- Singular Thermo-Elastic Stress Analysis of An Irregular Shaped Inclusion MengCheng Chen1,*, XueCheng Pin2 1School of Civil Engineering, East China Jiaotong University, 330013, Nanchang, P. R. China 2 School of Mechatronics Engineering, East China Jiaotong University, 330013, Nanchang, P. R. China * Corresponding author: mengchengchen2012@yahoo.com.cn Abstract This paper develops a super element that simulates the elastic behavior around an inclusion corner. The super inclusion corner element is finally incorporated with standard four-node hybrid-stress elements to constitute an ad hoc hybrid-stress finite element method for thermo-elastic stress analysis of an irregular inclusion in isotropic materials under thermal and mechanical loadings. In the numerical analysis, generalized stress intensity factors at the inclusion corner are systematically calculated for various material stiffness ratio and dimensions of the inclusion in a plate subjected to thermo-mechanical loadings. Keywords Thermo-mechanical stress, Hybrid finite element, Inclusion, Super inclusion corner element, Stress intensity factor 1. Introduction Much attention has been paid to inclusion problems by many researchers since Eshelby’s first solution to the ellipsoidal inclusion problems. The application background is found in microstructures, composite material structures and others. As the stress intensity at an inclusion corner is governed by the corner surrounding material properties, the corner geometry conditions and loading situations, great mathematical difficulties are usually encountered in analytical solutions. Therefore, most complicated engineering problems of inclusions have to resort to numerical methods such as the finite element method (FEM) and others. Chen [1] used the body force method to calculate stress intensity factors (SIFs). The SIFs for a dissimilar material wedge under mechanical and thermal loads were determined by using the least square method [2-4]. Path-independent conservative line integrals derived from Betti’s reciprocal principle were utilized to evaluate stress intensities at the interface [5-7]. The solutions from the aforementioned methods are strongly dependent on the number of element meshes. Furthermore, it is very difficult to obtain accurate numerical results for singular stress states near the apex in dissimilar materials using the conventional finite element method, even with the help of many finite elements. To improve the accuracy of numerical results for wedge or interface problems in the traditional finite element analysis, the analytical asymptotic solutions near the apex can be used as interpolation functions to construct a stiffness matrix for special elements containing a part or interface of a wedge. Chen [8] developed an enriched element with appropriate interpolation functions to account for the singular behavior at the junction of dissimilar materials subjected to mechanical load. Similar to Chen [8]’s work, enriched finite elements were further developed by Gadi et al. [9] and Pageau and Biggers [10]. However, numerical results with enriched finite elements are still dependent on the special element size, and the convergence of the results is not guaranteed. Therefore, more accurate numerical results require a lot of refined element meshes between the special element and standard elements. For a crack that either follows or is perpendicular to the interface, Tong et al. [11] constructed a special super element for the analysis of plane crack problems. Similarly, Tan and Meguid [12] developed a singular inclusion corner
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