A Unifying Phase Diagram for the Dynamics of Sheared Solids and Granular Materials
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We present a simple unifying model that can be used to analyze, within a single framework, different dynamic regimes of shear deformation of brittle, plastic, and granular materials. The basic dynamic regimes seen in the response of both solids and granular materials to slowly increasing loading are scale-invariant behavior with power law statistics, quasi-periodicity of system size events, and persisting long term mode switching between the former two types of response. The model provides universal analytical mean field results on the statistics of failure events in the different regimes and distributed versus localized spatial responses. The results are summarized in a phase diagram spanned by three tuning parameters: dynamic strength change (weakening, neutral or strengthening) during slip events, dissipation of stress transfer (related to the void fraction in granular materials and damaged solids), and the ratio of shear rate over healing rate controlling the regaining of cohesion following failures in brittle solids. The mean field scaling predictions agree with experimental, numerical, and observational data on deformation avalanches of solids, granular materials, and earthquake faults. The model provides additional predictions that should be tested with future observation and simulation data.
Keywordsirreversible deformation damaged rocks solid mechanics granular mechanics phase transitions brittle deformation plastic deformation
YBZ acknowledges support from the National Science Foundation (grant EAR-0908903) and the US-Israel Binational Science Foundation (grant number 2008248). KD acknowledges support from NSF DMR 03-25939 (MCC) and thanks the USC Dept. of Earth Sciences and the Kavli Institute of Theoretical Physics at UC Santa Barbara for kind hospitality and support. The manuscript benefited from useful comments by Jay Finberg, Bob Behringer, and Charlie Sammis.
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