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The mechanical behavior of geomaterials is studied using an XFEM (extended finite element method). Usually, the modeling of such heterogeneous material is performed either through an analytical homogenization approach, or numerically, especially for complex microstructures. For comparison, the effective properties are obtained using a classical finite element analysis (through the so-called unit cell method) and an analytical homogenization approach. The use of XFEM proposed here retains the accuracy of the classical finite element approach, allowing one to use meshes that do not necessarily match the physical boundaries of the material constituents. Thanks to such methods, it is then possible to study materials with complex microstructures that have non-simplified assumptions commonly used by other methods, as well as quantify the impact of such simplification. The versatility of XFEM in dealing with complex microstructures, including polycrystalline-like microstructures, is also shown through the role of shape inclusions on the overall effective properties of an argillite rock. Voronoi representation is used to describe the complex microstructure of argillite.

A Comparative Study on Linear Effective Properties Predictions of an Argillite Rock Using XFEM