Multiscale Coupling in Complex Mechanical Systems

Multiscale coupling attracts broad interests from mechanics, physics and chemistry to biology. The diversity and coupling of physics at different scales are two essential features of multiscale problems in far-from-equilibrium systems. The two features present fundamental difficulties and are great challenges to multiscale modeling and simulation. The theory of dynamical system and statistical mechanics provide fundamental tools for the multiscale coupling problems. The paper presents some closed multiscale formulations, e.g., the mapping closure approximation, multiscale large-eddy simulation and statistical mesoscopic damage mechanics, for two typical multiscale coupling problems in mechanics, that is, turbulence in fluids and failure in solids. It is pointed that developing a tractable, closed nonequilibrium statistical theory may be an effective approach to deal with the multiscale coupling problems. Some common characteristics of the statistical theory are discussed.