Homogenization approach based on laminates

In this work, a homogenization approach for the modeling of the material behavior of two-phase composites motivated by modeling a thin-layer-type microstructure is presented. The basic idea here is to idealize the thin-layered microstructure as a first-order laminate. In particular, a jump in deformation state across the phase interface is modeled constitutively via a rank-one connection of habit-plane type. In the material framework, the value for the jump as well as its direction remain as independent constitutive variables. However, in the case of laminates and an ideal plain interface, the direction is given and stays in a first approach constant. We assume that their values are determined by mechanical and configurational equilibrium in the two-phase composite at the interface. This yields to a set of implicit equations which lead to the corresponding response of the structure.