Dynamic continualization of masonry-like structured materials

Block-lattice materials featuring periodic planar running-bond tessellation of regular rigid blocks and linear elastic homogeneous isotropic interfaces are considered. The governing equations of the discrete masonry-like Lagrangian model are properly manipulated via the novel enhanced continualization scheme, in such a way as to obtain equivalent integral type non-local continua, whose band structure turns out to be coincident with that of the corresponding discrete models. The formal Taylor series expansion of the integral kernels allows deriving homogeneous generalized micropolar higher-order continuum models, characterized by non-local constitutive and inertial terms. The enhanced continualization exhibits thermodynamic consistency in the definition of the overall non-local constitutive tensors, as well as qualitative agreement and quantitative convergent matching of the complex frequency band structure in the regime of both homogeneous and non-homogeneous Bloch waves. The theoretical findings are effectively validated by studying the dispersion relations and the spatial attenuation properties, as referred to realistic representative cases of masonry-like block-lattice micro-structures.