Modeling of inclusions with interphases in heterogeneous material using the infinite element method

A two-dimensional heterogeneous infinite element method (HIEM) for modeling heterogeneous materials, like imbedded inclusions with surrounding interphases, is proposed in this paper. The special element, called heterogeneous infinite element (HIE), was formulated based on the conventional finite element method (FEM) using the similarity stiffness property and matrix condensing operations. An HIE-FE coupling scheme was also developed and implemented using the commercial software ABAQUS to conduct a complete elastostatic analysis. oposed approach was first validated so that heterogeneous material containing circular inclusions can be studied. The displacement and stress distribution around the inclusions were accurately captured. The approach was then applied to analyze the effective modulus of the single-cell and 2 × 2-cell square models with the presence of interphases. The effects of varying the modulus and thickness of the interphases were also examined. Finally, the influences of the shape and orientation of the inclusions are investigated. Results show that different arrangements in the model can have marked influences on the evaluation of the effective elastic modulus for periodic fiber-reinforced composites.