An homogenization iterative process for nonlinear materials applied to compacted clays

In previous works an homogenization iterative approach has been successfully proposed to predict the linear behavior of reinforced and porous materials. This homogenization process consists to construct the Representative Elementary Volume of the heterogeneous media, by adding gradually to the matrix, low heterogeneity proportions until reaching the final rate of heterogeneity of the material following a process closed to the differential scheme method [

1

]. At any intermediate step of this process, an homogenization is carried out by any classical explicit method and the obtained effective behavior becomes the matrix of the following step. The equivalent homogeneous behavior is reached after convergence of the succession of intermediate homogeneous media. A significant result shows that the application of this iterative process to different homogenization approaches like dilute approximation, Hashin’s bound, self consistent method, and even the morphological representative pattern leads to the same behavior even for significant rates of heterogeneities or porosities [

2

].

In this work we extend this homogenization iterative approach in the nonlinear domain. After a secant linearization of the celular problem the iterative process is coupled to the “comparison linear material” with the classical and modified secant homogenization methods [

3

]. We show that these two methods coupled to any explicit homogenization and iterative process lead to the same behavior for all rates of heterogeneities or porosities. This approach is here applied to study the hydro-elastoplastic behavior of compacted clays. The model parameters quantification is based on oedometric experimental results for different clays [

4

].