Application de la méthode d’homogénéisation numérique pour la prédiction du comportement élastique d’un empilement de couches minces

Abstract

This work presents a numerical study dedicated to the application of the numerical homogenization method to predict the elastic behavior of a thin-film stack (metallic and dielectric) used in microelectronic and micro-electro-mechanical systems (MEMS), providing an efficient alternative to full heterogeneous modeling which is computationally expensive and time-consuming. The methodology is based on modeling a 5-layer Representative Volume Element (RVE) alternating between conductive materials (AlCu or Platinum Pt) and a dielectric insulator (USG), while including a parametric study on layer thickness variations. Simulations were performed using Abaqus software coupled with the EasyPBC plugin to apply periodic boundary conditions and identify effective elastic constants via virtual tensile and shear tests. To validate the homogenized model, a quantitative comparison was conducted against the reference heterogeneous model under 3-point and 4-point bending loads. The results demonstrate an excellent macroscopic agreement between both models regarding global deflection and stiffness predictions, while showing that increasing the metallic layer thickness enhances structural rigidity but amplifies interfacial stresses. However, despite the drastic computational efficiency of the homogenization method, the study highlights its limitations related to the stress-smoothing effect, which masks local stress concentrations at the material interfaces. Finally, this research opens future perspectives regarding the incorporation of elastoplastic laws for metals, cohesive zone modeling (CZM) for interfacial damage, and the consideration of manufacturing-induced residual thermal stresses.