This work will be focused on the concept of material mixing in dynamics.This concept introduces spatio-temporal composites, i.e. material microstructures assembled and maintained in space-time. Such composites will be investigated in the framework of a Maxwell system for moving dielectrics as well as for the relativistic equations of elastodynamics and acoustics. The relevant set of effective parameters (G-closures) will be explicitly specified for a number of practical examples.
The knowledge of G-closures is crucial for the analysis of material optimization problems that arise in dynamics of moving media, particularly in acoustics and hydroacoustics, as well as in high frequency electronic engineering. Such a knowledge makes many of these problems well-posed when the material coefficients act as the control factors. Physically, this is because the optimal material layouts in space-time generally shape themselves as microstructures. This work is aimed to prepare a conceptual basis for a subsequent investigation of material optimization in dynamics.
