Architectured membranes can be developed in order to mimic living tissues. The main point is to generate anisotropic membranes that can endure large deformations. In this way, crenellated membranes are elaborated with a filled silicone rubber. The aim of this work is to develop a constitutive equation which describes the mechanical behavior of such architectured materials. Membranes with different crenel orientations are elaborated and tested. The architectured membranes endure the same phenomena as the bulk silicone, they are made with, i.e. principally the Mullins effect for this filled silicone. This phenomenon must be taken account in the modeling. An equivalent constitutive equation is built for the architectured membrane by taking into account the mechanical behavior of the silicone and the geometrical parameters of the crenelated membrane. First, a constitutive equation is chosen to describe the core of the membrane. Second, this equation is adapted to the behavior of the crenels and third a coupling term describing the interactions between the crenels and the membrane is developed. Finally, the model is validated on experimental data.