FETI-based Homogenization of Composites with Perfect Bonding and Debonding of Constituents

The present paper deals with the homogenization of composite materials with periodic microstructure. Emphasis is put on mathematical modeling of imperfect bonding between linearly elastic constituents. Elements of homogenization theory are introduced, together with the Unit Cell problem governing the macroscopic response of the equivalent homogeneous body. Numerical resolution of mathematical and physical problem of homogenization is based on the Finite Element Tearing and Interconnecting (FETI) method, extended to cover both cases of the perfect bonding and debonding of individual constituents. It is demonstrated that FETI allows very efficient treatment of the conventional homogenization problem for composites with the limit zero as well as infinite values of interfacial compliance. Verification of the method is performed using selected data available in open literature.