The response of many materials of engineering interest to external loading is influenced by their microstructure. The components of such a microstructure may have different material properties, resulting in an enormous complexity in the response of a material. It is discussed how such dynamical response of advanced materials with an inner structure can be predicted numerically.

Computation of high strain rate processes in real materials and structures with necessary efficiency and accuracy is another important task. Results of numerical simulations by means of a thermodynamically consistent algorithm are demonstrated on examples of wave propagation.

The wave propagation in novel concept in material science termed dynamic materials (DM) is disscussed. DM are not materials in a traditional sense: they are defined as material substances with properties that may change in space and time. Particularly, we may speak about formations assembled from traditional material constituents with space-time variable properties.