Multiscale Modeling of Imperfect Interfaces and Applications

Modeling interfaces between solids is of great importance in the fields of mechanical and civil engineering. Solid/solid interface behavior at the microscale has a strong influence on the strength of structures at the macroscale, such as gluing, optical systems, aircraft tires, pavement layers and masonry, for instance. In this lecture, a deductive approach is used to derive interface models, i. e. the thickness of the interface is considered as a small parameter and asymptotic techniques are introduced. A family of imperfect interface models is presented taking into account cracks at microscale. The proposed models combine homogenization techniques for microcracked media both in three-dimensional and two-dimensional cases, which leads to a cracked orthotropic material, and matched asymptotic method. In particular, it is shown that the Kachanov type theory leads to soft interface models and, alternatively, that Goidescu et al. theory leads to stiff interface models. A fully nonlinear variant of the model is also proposed, derived from the St. Venant-Kirchhoff constitutive equations. Some applications to elementary masonry structures are presented.