Modeling of multi-layered structure containing heterogeneous material layer with randomly distributed particles using infinite element method

Abstract In the electronics industry, filler particles are added to the epoxy to form a composite material in order to adjust the elastic modulus and the coefficient of thermal expansion (CTE). This paper enhances the infinite element method (IEM) for modeling and analyzing a multi-layered structure such as flip–chip assembly containing a heterogeneous material layer reinforced with randomly distributed multiple particles under thermal loading. The proposed method provides a straightforward and efficient means of modeling multiple particles since only one IE stiffness matrix of particle needs to be calculated for all of the other particles. Moreover, in analyzing the material interface problem, the proposed technique could put many number of element layers to measure the high stresses close to the edge of the multi-layered structure, and was easily applied to compare the maximum interfacial stresses near the corner. A series of problems relating to multi-layered structures containing heterogeneous materials are investigated. Initially, this study investigates the effect of varying the volume fraction of randomly arranged particles in the heterogeneous layer on the effective properties of the layer. The results obtained for the effective properties of the heterogeneous material and their influence on the interfacial stress are compared to those obtained from the Mori–Tanaka analytical method. Finally, in addition to equivalent models, three-dimensional finite element models containing multiple randomly distributed particles were built and studied. It is shown that at the free edge the interfacial stresses decrease when the number of particles close to the interface increases.