Numerical methods to determine effective elastic properties

Effective elastic properties for heterogeneous materials are widely discussed in the literature. We discuss and review the application range and accuracy of different numerical approaches to determine those effective elastic values from digitized material samples. Recent examples are used for illustration. Whereas the use of most effective-medium theories is restricted to a limited number of geometries the possible application range of numerical methods is much wider. There are two fundamental different numerical methods to extract effective elastic properties from a given microstructure. Both approaches are sensitive to size effects. Static methods can address this problem by applying uniform stress or uniform displacement boundary conditions. For dynamic wave propagation simulations the ratio of the dominant wavelength to the typical inclusion size is the most crucial factor.