Homogenization of interlocking masonry structures using a generalized differential expansion technique

In this paper a micromorphic continuum is derived for the homogenization of masonry structures with interlocking blocks. This is done by constructing a continuum which maps exactly the kinematics of the corresponding discrete masonry structure and has the same internal and kinetic energy for any ‘virtual’ translational- and rotational-field. The obtained continuum is an anisotropic micromorphic continuum of second order. The enriched kinematics of micromorphic continua allows to model microelement systems undergoing both translations and rotations. The homogenization technique applied here excludes averaging and keeps all the necessary information of the discrete structure. Therefore, all the dispersion curves of the discrete system are reproduced in the continuum model.