Abstract
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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Ayzenberg-Stepanenko, M.V., Slepyan, L.I.: Resonant-frequency primitive waveforms and star waves in lattices. J. Sound Vib. 313(3–5), 812–821 (2008)
Alessandrini, B., Raganelli, V.: The propagation of elastic waves in a discrete medium. Eur. J. Mech., Ser. A: Solids 8(2), 129–160 (1989)
Sadovskii, V.M., Sadovskaya, O.V., Pokhabova, M.A.: Modeling of elastic waves in a block medium based on equations of the Cosserat continuum. Comput. Continuum Mech. 7(1), 52–60 (2014). [in Russian]
Sadovskaya, O.V., Sadovskii, V.M.: Analysis of rotational motion of material microstructure particles by equations of the Cosserat elasticity theory. Acoust. Phys. 56(6), 942–950 (2010)
Sadovskaya, O.V., Sadovskii, V.M.: Mathematical Modeling in Mechanics of Granular Materials. Advanced Structured Materials, vol. 21. Springer, Heidelberg (2012)
Sadovskii, V.M., Sadovskaya, O.V., Varygina, M.P.: Numerical solution of dynamic problems in couple-stressed continuum on multiprocessor computer systems. Int. J. Numer. Anal. Modeling, Ser. B 2(2–3), 215–230 (2011)
Acknowledgements
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.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer International Publishing Switzerland
About this paper
Cite this paper
Sadovskaya, O.V., Sadovskii, V.M., Pokhabova, M.A. (2015). Numerical Modeling of a Block Medium as an Orthotropic Cosserat Continuum. In: Dimov, I., Faragó, I., Vulkov, L. (eds) Finite Difference Methods,Theory and Applications. FDM 2014. Lecture Notes in Computer Science(), vol 9045. Springer, Cham. https://doi.org/10.1007/978-3-319-20239-6_37
Download citation
DOI: https://doi.org/10.1007/978-3-319-20239-6_37
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-20238-9
Online ISBN: 978-3-319-20239-6
eBook Packages: Computer ScienceComputer Science (R0)