Homogenization of heterogeneous materials for aerospace applications

The lecture discusses the micromechanical analysis of heterogeneous can be effectively carried out using the variational asymptotic method (VAM) unit cell homogenization technique. The governing equations obtained by adopting this technique can be solved using numerical methods by conformal discretization of the domain. In the case of heterogeneous materials, conformal discretization of the domain becomes difficult and time-consuming. It is preferable to have a non-conformal discretization procedure for problems involving complex geometries, for example, woven composites. A novel numerical framework for the micromechanical analysis of heterogeneous materials based on VAM is proposed, where the level-set method is used to define the interface as well as to decompose the domain into voxel regions of inclusions and matrix. The point interpolation method (PIM) is used to connect these voxel regions. The PIM-VOXEL framework thus developed is validated using examples having complex geometries taken from open literature for predicting elastic, thermal, thermo-elastic, and visco-elastic properties. The proposed methodology alleviates the requirement for conformal meshing without compromising the accuracy and is capable of automation for homogenization and localization applications. Finally, the application of the numerical framework to capture damage initiation and progression in woven composites is demonstrated.