Modeling aspects of the dynamic response of heterogeneous materials

In numerical simulations of engineering applications involving heterogeneous materials capturing the local response coming from a distribution of heterogeneities can lead to a very large model thus making simulations difficult. The use of homogenization techniques can reduce the size of the problem but will miss the local effects. Homogenization can also be difficult if the constituents obey different types of constitutive laws. Additional complications arise if inelastic deformation. In such cases a two-scale approach is prefened and tills work addresses these issues in the context of a two-scale Finite Element Method (FEM). Examples of using two-scale FEM approaches are presented