Abstract
One of the mechanisms of instability in geomaterials is associated with the descending branch of stress-strain curve caused by internal fracturing. The descending stress-strain curve can also be produced by negative stiffness elements, one of the mechanisms of negative stiffness being the rotation of non-spherical grains. The presence of negative stiffness elements can cause dynamic instability in the geomaterials. We investigate a simple elastic model of dynamic instability consisting of chains of oscillators some with negative stiffness springs. We show that in a stable chain only one oscillator can have negative stiffness spring and formulate the criterion of stability.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsReferences
Cook NGW (1965) The failure of rock. Int J Rock Mech Min Sci 2(4):389–403
Dyskin AV, Pasternak E (2011) Rock mass instability caused by incipient block rotation. In: Qian Q, Zhou Y (eds) Harmonising rock engineering and the environment. Proceedings of 12th international congress on rock mechanics. CRC Press Balkema 4
Dyskin AV, Pasternak E (2012a) Elastic composite with negative stiffness inclusions in antiplane strain. Int J Eng Sci 58:45–56
Dyskin AV, Pasternak E (2012b) Mechanical effect of rotating non-spherical particles on failure in compression. Phil Mag 92(28–30):3451–3473
Dyskin AV, Pasternak E (2012c) Rock and rock mass instability caused by rotation of non-spherical grains or blocks. Rock engineering and technology for sustainable underground construction. Proceedings of Eurock paper 102P
Dyskin AV, Pasternak E, Sevel G (2014) Chains of oscillators with negative stiffness elements. J Sound Vibr 333(24):6676–6687
Pasternak E, Dyskin AV (2013) Instability and failure of particulate materials caused by rolling of non-spherical particles. In: Proceedings of 13th international conference on fracture, Beijing. Paper S09-002
Rudnicki JW, Rice JR (1975) Conditions for the localization of deformation in pressure-sensitive dilatant materials. J Mech Phys Solids 23(6):371–394
Salamon MDG (1970) Stability, instability and design of pillar workings. Int J Rock Mech Min Sci 7(6):613–631
Tarasov BG, Dyskin AV (2005) The phenomenon of anomalous rock embrittlement. In: Potvin Y, Hudyma M (eds) Sixth international symposium rockburst and seismicity in mines. ACG, Australia, pp 311–317
Turcotte DL (1992) Fractals and chaos in geology and geophysics. Cambridge University Press, Cambridge
Acknowledgments
The authors acknowledge the financial support through ARC Discovery Grant DP120102434.
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
Pasternak, E., Dyskin, A. (2015). Dynamic Instability in Geomaterials Associated with the Presence of Negative Stiffness Elements. In: Chau, KT., Zhao, J. (eds) Bifurcation and Degradation of Geomaterials in the New Millennium. IWBDG 2014. Springer Series in Geomechanics and Geoengineering. Springer, Cham. https://doi.org/10.1007/978-3-319-13506-9_23
Download citation
DOI: https://doi.org/10.1007/978-3-319-13506-9_23
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-13505-2
Online ISBN: 978-3-319-13506-9
eBook Packages: EngineeringEngineering (R0)