Open AccessHomogenization and multicontinuum models for high contrast composites
Author(s) -
Grigory Panasenko
Publication year - 2019
Publication title -
iop conference series. materials science and engineering
Language(s) - English
Resource type - Journals
eISSN - 1757-899X
pISSN - 1757-8981
DOI - 10.1088/1757-899x/683/1/012020
Subject(s) - homogenization (climate) , composite number , materials science , composite material , moduli , mathematical analysis , physics , mathematics , biodiversity , ecology , biology , quantum mechanics
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.