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Thermal Stress Analysis of Multi-layer Thin Films and Coatings by an Advanced Boundary Element Method

Xiaolin Chen, Yijun Liu1

Department of Mechanical Engineering, University of Cincinnati, P.O. Box 210072 Cincinnati, Ohio 45221-0072, U.S.A. E-mail:

Computer Modeling in Engineering & Sciences 2001, 2(3), 337-350.


An advanced boundary element method (BEM) is developed in this paper for analyzing thin layered structures, such as thin films and coatings, under the thermal loading. The boundary integral equation (BIE) formulation for steady-state thermoelasticity is reviewed and a special case, that is, the BIE for a uniform distribution of the temperature change, is presented. The new nearly-singular integrals arising from the applications of the BIE/BEM to thin layered structures under thermal loading are treated in the same way as developed earlier for thin structures under the mechanical loading. Three 2-D test problems involving layered thin films and coatings on an elastic body are studied using the developed thermal BEM and a commercial FEM software. Numerical results for displacements and interfacial stresses demonstrate that the developed BIE/BEM remains to be very accurate, efficient in modeling, and surprisingly stable, for thin elastic materials with the thickness-to-length ratios down to 10-9 (the nano-scale). This thermal BEM capability can be employed to investigate other more important and realistic thin film and coating problems, such as residual stresses, interfacial crack initiation and propagation (peeling-off), in electronic packaging or other engineering applications.

Cite This Article

Chen, X., Liu, Y. (2001). Thermal Stress Analysis of Multi-layer Thin Films and Coatings by an Advanced Boundary Element Method. CMES-Computer Modeling in Engineering & Sciences, 2(3), 337–350.

cc This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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