Coupled BEM and FEM analysis of functionally graded underfill layers in electronic packages

This study presents the development of a robust general purpose boundary element method (BEM) capable of including functionally graded materials (FGM) in order to capture the correct behavior of the underfill material accurately. BEM requires discretization only along the boundary while satisfying the governing equations exactly within the domain. The BEM is inherently more accurate than the FEM as it treats both displacements and tractions as primary variables while displacements are the only primary variables in the FEM. In order to take advantage of the salient features of both FEM and BEM, this study also couples the BEM solution with the conventional FEM solution while satisfying the continuity of displacements and equilibrium of tractions along the interfaces. The FEM-BEM coupling is demonstrated by using the super-element capability of ANSYS®, a commercially available finite element program.