Modelling of complex elastic crystals by means of multi-spin micromorphic media

For the microstructural consideration we model the interaction between subparticles as a potential interaction of sufficiently general kind between rigid bodies both of force and torque nature, and calculate the force and the torque acting from the neighbourhood upon a subparticle. We sum the laws of the balance of linear and angular momenta over all subparticles of a cell. To pass from the discrete to the continuum consideration we expand these laws in two space co-ordinates: a “micro”-gradient corresponds to the translations in the neighbourhood of the subparticle, and a “macro”-gradient corresponds to the translation by a basic vector of a crystal lattice.