Micromorphic continua: Application to the homogenization of diatomic masonry columns
Résumé
In the frame of continuum mechanics, the theory of general micromorphic continua is a key element for modeling mechanical systems of discrete building blocks such as masonry structures. This stems from the fact that the kinematics of the particle, in the terminology of Germain (Germain, P., The Method of Virtual Power in Continuum Mechanics, Part 2: Microstructure. SIAM J. Appl. Math., vol. 25, pp. 556-575, 1973), is quite rich to cover the various degrees of freedom of the discrete microstructure. In the present paper, we derive a third-order micromorphic continuum for modeling diatomic masonry columns. Our analysis is extended to the dynamic regime. For linear elastic interfaces, the derived continuum is compared with the discrete model in terms of the dispersion curves. It is shown that the continuum approximates well the discrete structure for wavelengths five to ten times bigger than the size of the elementary cell. Therefore, the presented model may be the base for future engineering applications in the field of cultural heritage assets, because it might be an alternative approach in the mechanical modeling of ancient colonnades, whose study is mostly performed with the discrete element method. As it is well known, continuum models are quite flexible, computationally cheaper, and may give insight to the fundamental properties of the systems at hand.