Interfacial Micromechanics Assessment of Classical Rheological Models. II: Multiple Interface Sizes and Viscosities

Abstract

© 2015 American Society of Civil Engineers.Whereas the companion paper provided a micromechanical explanation of the spring and dashpot parameters occurring in the rheological models of the Kelvin-Voigt and Maxwell type, we here extend this discussion toward rheological chain models. Therefore, the considered micromechanical system is extended from one interface phase to N interface phases differing in size and viscosity. Elimination schemes allow for deriving differential equations with only overall stresses and strains and their derivatives as unknowns, rather than microstresses and microstrains in case of micromechanics, or spring/dashpot-related stresses and strains in case of the rheological chain models. Comparison of corresponding coefficients reveals a full analogy between the two different types of chain models, and also between the latter and the micromechanics model. For the Kelvin-Voigt chain, this analogy is even identical to the one of the Zener model of companion paper Part I. The Maxwell chain-related analogy is much more complex, and analytical solutions only exist in the case of very few chain units.