A 2D granular medium with rotating particles

A two-dimensional (2D) model of a granular medium is represented as a square lattice consisting of elastically interacting round particles possessing one rotational and two translational degrees of freedom. The differential equations describing propagation and interaction of waves of various types in such a medium have been derived in the long-wavelength approximation. Accounting for microrotations of the particles and moment interactions between them leads to the consideration of so-called microrotation waves (spin waves). In the absence of microrotations, the governing equations degenerate into 2D Lame´ equations for anisotropic media. A one-to-one correspondence has been established between the microstructure parameters and effective elasticity constants of the second-order. Dependence of elasticity constants on the size of grains has been analyzed. The proposed model is compared in the continuous approximation to the equations of the 2D Cosserat continuum possessing macroscopic anisotropy.