Variational modeling adapted to the medium with gradient properties

This study aims to develop a numerical homogenization method that can be applied to a heterogeneous stratified medium. Traditional scale transition methods are inadequate in capturing the essential gradient properties of some materials. Therefore, the focus of this work is to construct a homogenized model that considers the material property gradient. To achieve this, a two-step homogenization scheme is proposed. Firstly, the 3D model is decomposed into multiple 2D heterogeneous layers, and the behavior of each layer is estimated using a micro-mechanical model such as the Hashin–Shtrikman bounds. Secondly, a variational sum method is used to rebuild the behavior of the 3D environment. Finally, the method is applied to homogenize a thin plate with a porosity gradient.