A novel framework using point interpolation method with voxels for variational asymptotic method unit cell homogenization of woven composites

Micromechanical analysis of woven composites can be effectively carried out using 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 woven composites 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 like woven composites. A novel numerical framework for micromechanical analysis of woven composites based on VAM is proposed, where level-set method is used to define the interface as well as to decompose the domain into voxel regions of inclusions and matrix. 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.