Numerical Modeling of a Block Medium as an Orthotropic Cosserat Continuum
Based on the equations of the dynamics of a piecewise-homogeneous elastic material, 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. For the description of waves in a block medium with thick interlayers the orthotropic couple-stress continuum theory, taking 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, the simple method is obtained to estimate mechanical parameters of an orthotropic Cosserat continuum, modeling a block medium. In two-dimensional formulation of the orthotropic model, the computational algorithm and the program system are worked out for the analysis of propagation of elastic waves. The comparison showed good qualitative agreement between the results of computations of waves, caused by localized impulses, by the model of a block medium with compliant interlayers and the model of an orthotropic Cosserat continuum.
KeywordsDynamics Elasticity Block medium Cosserat continuum Shock-capturing method Parallel computational algorithm
This work was supported by the Russian Foundation for Basic Research (grant no. 14–01–00130) and the Complex Fundamental Research Program no. 18 of the Presidium of RAS.