A Note on Scale-Coupling Mechanics

After two decades of rapid growth, multiscale research is currently undergoing a transition from an initial surge of excitement to a more rational stage. The major hindrance in multiscale modeling is continuous use of classical scale-separation theories in conflict with scale-coupling phenomena, and often a price to pay is we end up with some physically inconsistent models or parameters, e.g. non-local theory in damage mechanics, negative mass or moduli in elastodynamics. In this note we propose development of new scale-coupling theories as the most important direction of multiscale research. In Sect. 2, a conceptual distinction is made between scale-separation and scale-coupling strategies. In Sect. 3, a scale-coupling mechanics theory is introduced in a format that leads to derivation of non-local and gradient theories. Conclusion is made at the end.