The main objective of this study is to generate anisotropic membranes stretched in their plane able to endure large deformations. In this perspective, different crenellated membranes were designed with a filled silicone rubber. The aim of this work is to build a constitutive equation which describes the mechanical behavior of such architectured membranes, by means of a simple decompostion of the strain energy. Since a filled silicone is used to make the architectured membrane, some non linear effects influence also the mechanical behavior of the structure. The main phenomenon is the Mullins effect and must be taken into 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 crenellated membrane. Firstly, a constitutive equation is chosen to describe the core of the membrane. Second, this equation is adapted to the behavior of the crenels and thirdly a coupling term describing the interactions between the crenels and the core of the membrane is developed. The implementation of the equivalent constitutive equation into a finite element code is finally validated on experimental data.