Modeling of elastic waves in a block medium based on equations of the Cosserat continuum

Abstract

Based on the equations of the dynamics of piecewise-homogeneous elastic media, parallel computational algorithms are developed to simulate the process of stress and strain wave propagation in a medium consisting of a large number of blocks interacting through compliant interlayers. Computations of waves caused by localized impulsive perturbations show that such a medium can be considered as isotropic only in the case of sufficiently thin interlayers. In the case of relatively thick interlayers, the anisotropy effects are observed which consist in the appearance of elongated wave fronts along the coordinate directions and characteristic oscillations of velocities and stresses because of the rotational motion of blocks. For the description of waves in a block medium with thin interlayers, the equations of the isotropic Cosserat continuum are applicable. As the thickness of interlayers increases, the orthotropic couple-stress continuum theory which takes into account the symmetry of elastic properties relative to the coordinate planes can be applied. By comparing the elastic wave velocities in the framework of piecewise-homogeneous model and continuum model and the compliance coefficients of the material in the special schemes of quasistatic deformation with uniform block rotation and with internal curvature formation due to an inhomogeneous rotation, simple formulas are obtained to estimate the mechanical parameters of the orthotropic Cosserat continuum modeling a block medium.