Homogenization and multicontinuum models for high contrast composites
Grigory P. Panasenko · IOP Conference Series Materials Science and Engineering · 2019
Abstract We consider the high contrast periodic composite materials having high ratio ω >>1 of physical constants of the components such as the heat conductivity or Young’s moduli. The ratio of the characteristic microscopic size and the characteristic macroscopic size is a small parameter e. If the component having high constants has the shape of small isolated particles then the homogenized (macroscopic, effective) model demonstrates a loss of the effective wave velocity. If the topology of the component having high constants corresponds to several (at least two) connected periodic sets disconnected one from other and if ε2ω>>1 or ε2ω = const then the macroscopic model is described by a multicontinuum, i.e. several continua in each point.