Thermodynamically consistent non-local continualization for masonry-like systems

Masonry-like systems composed by modular stiff units bonded by soft connections represent an efficient, versatile and ultimately successful strategy for natural and artificial macro-scale architectures. The static and dynamic behavior of masonry-like materials characterized by a running bond periodic pattern of rigid rectangular blocks and elastic interfaces is described by formulating equivalent nonlocal continuum models. The paper discusses the thermodynamic restrictions limiting the consistency of the standard continualization strategies. The inherent pathologies recognized in the macroscopic quasi-static response and/or in the dynamic dispersion properties of different continuum models motivate the original proposal of an enhanced continualization strategy. Based on the series expansion of the pseudo-differential functions accounting for shift operators and proper downscaling laws, the enhanced continualization scheme allows formulating homogeneous non-local continuum models of increasing orders, analytically featured by characteristic non-local constitutive and inertial terms. The enhanced continualization shows thermodynamic consistency in the definition of the overall elastic moduli, as well as qualitative agreement and convergent matching of the frequency dispersion functions. The theoretical findings are successfully verified though the solution of representative static and dynamic benchmark problems.