Statistical Mesomechanics of Solid, Linking Coupled Multiple Space and Time Scales

This review begins with the description of a new challenge in solid mechanics: multiphysics and multiscale coupling, and its current situations. By taking spallation as an example, it is illustrated that the fundamental difficulty in these multiscale nonequilibrium problems is due to the hierarchy and evolution of microstructures with various physics and rates at various length levels in solids. Then, some distinctive thoughts to pinpoint the obstacles and outcome are outlined. Section 3 highlights some paradigms of statistical averaging and new thoughts to deal with the problems involving multiple space and time scales, in particular the nonequilibrium damage evolution to macroscopic failure. In Sec. 4, several frameworks of mesomechanics linking multiple space and time scales, like dislocation theory, physical mesomechanics, Weibull theory, and stochastic theory, are briefly reviewed and the mechanisms underlying the trans-scale coupling are elucidated. Then we turn to the frameworks mainly concerning damage evolution in Sec. 5, namely, statistical microdamage mechanics and its trans-scale approximation. Based on various trans-scale frameworks, some possible mechanisms governing the trans-scale coupling are reviewed and compared in Sec. 6. Since the insight into the very catastrophic transition at failure is closely related to strong trans-scale coupling, some new concepts on nonequilibrium and strong interaction are discussed in Sec. 7. Finally, this review is concluded with a short summary and some suggestions. “This review article cites 130 references.”