An advanced numerical method for predicting effective elastic properties of heterogeneous composite materials

• A new method based on XFEM and VAMUCH models is introduced to predict effective properties of composite materials.
• The method is implemented in an in house code, tested, compared with existing methods.
• The microstructure is first generated using a developed algorithm.
• Good agreement was found and many advantages are highlighted.

This paper presents a new numerical methodology for predicting the effective elastic properties of composite materials. The material microstructure was generated in a repeated unit cell, the so-called representative volume elementary (RVE) using a developed microstructure generator. The homogenisation was first performed using the variational asymptotic method for unit cell homogenisation (VAMUCH) and by applying the eXtended Finite Element Method (XFEM) directly. Moreover, we propose a new methodology to introduce the XFEM into the VAMUCH principle. Thus, the obtained new scheme (i.e. the eXtended VAMUCH) uses the Variational Asymptotic Method on nonconforming meshes. All the implemented methods were validated and compared each other using existing benchmarking tests, then more complex microstructures are investigated. The obtained results were globally very well in agreement. The proposed methodology was found efficient to determine accurately the composite properties and showed several advantages.