A critical comparison of several numerical methods for computing effective properties of highly heterogeneous materials

Modelling transport and long-term creep in concrete materials is a difficult problem when the complexity of the microstructure is taken into account, because it is hard to predict instantaneous elastic responses. In this work, several numerical methods are compared to assess their properties and suitability to model concrete-like microstructures with large phase properties contrast. The methods are classical finite elements, a novel extended finite element method (μ-xfem), an unconstrained heuristic meshing technique (amie), and a locally homogenising preprocessor in combination with various solvers (benhur). The benchmark itself consists of a number of simple and complex microstructures, which are tested with a range of phase contrasts designed to cover the needs of creep and transport modelling in concrete. The calculations are performed assuming linear elasticity and thermal conduction. The methods are compared in term of precision, ease of implementation and appropriateness to the problem type. We find that xfem is the most suitable when the mesh if coarse, and methods based on Cartesian grids are best when a very fine mesh can be used. Finite element methods are good compromises with high flexibility.

► We compare five very different numerical strategies for modelling composite microstructure.
► They are applied to large-scale microstructural problems.
► We study the impact of very high phase contrast on numerical accuracy.
► The benchmark proposed in this paper can be used to determine the causes and nature of the numerical errors.
► We evaluate the practicality of these methods to tackle current material science problems.