• Login
    View Item 
    •   Home
    • Theses & Dissertations
    • 2018 - Mines Theses & Dissertations
    • View Item
    •   Home
    • Theses & Dissertations
    • 2018 - Mines Theses & Dissertations
    • View Item
    JavaScript is disabled for your browser. Some features of this site may not work without it.

    Browse

    All of Mines RepositoryCommunitiesPublication DateAuthorsTitlesSubjectsThis CollectionPublication DateAuthorsTitlesSubjects

    My Account

    Login

    Mines Links

    Arthur Lakes LibraryColorado School of Mines

    Statistics

    Display Statistics

    Unified interpretation of nonlinear elasticity in granular solids, A

    • CSV
    • RefMan
    • EndNote
    • BibTex
    • RefWorks
    Thumbnail
    Name:
    Li_mines_0052N_11511.pdf
    Size:
    3.849Mb
    Format:
    PDF
    Download
    Author
    Li, Xun
    Advisor
    Snieder, Roel, 1958-
    Date issued
    2018
    Keywords
    geomaterials
    resonance experiments
    thermodynamics
    nonlinear elasticity
    duffing oscillation
    slow dynamics
    
    Metadata
    Show full item record
    URI
    https://hdl.handle.net/11124/172339
    Abstract
    Granular solids such as natural rocks and concrete show nonlinear elasticity in response to dynamic deformation with a large strain amplitude. Resonance experiments can measure the nonlinear elasticity using resonance curves which show response amplitudes as a function of driving (oscillation) frequencies. To analyze the nonlinear elasticity observed in resonance experiments, I first simulate a nonlinear oscillation system (i.e., Duffing equation) that involves a cubic term in the equation of state. The simulation illustrates three critical factors, i.e., driving frequency, driving amplitude, and the initial condition of the deformation; these factors control the stable solution that is the sustained amplitude of the Duffing oscillation. I propose a thermodynamics-based model to reproduce the nonlinear resonance features observed in laboratory experiments of rocks and concrete including (a) the log-time recovery of the resonant frequency after the deformation ends (slow dynamics), (b) asymmetric resonance curves in the direction of the driving frequency, (c) the difference between resonance curves when the driving frequency is swept upward and downward, and (d) the presence of a cliff segment to the left of the resonant peak under the condition that the nonlinearity in the oscillation system is strong. This model provides a unified interpretation of nonlinear elasticity. The asymmetry of the resonance curve is caused by softening, which is documented by a reduction of the resonant frequency during the deformation; the cliff segment of the resonance curve is linked to a bifurcation that involves a steep change in the response amplitude when the driving frequency is changed. The simulated Duffing oscillation system shows similar behavior as the resonance simulations. The bifurcation originates from the strong nonlinearity in the oscillation system and is present in both simulations. Extensions of the thermodynamics-based model could include temperature, moisture (pore pressure), and confining pressure. This thesis could contribute to geophysical applications such as monitoring of fracture healing after hydraulic fracturing in unconventional oil and gas reservoirs as well as in enhanced geothermal systems.
    Rights
    Copyright of the original work is retained by the author.
    Collections
    2018 - Mines Theses & Dissertations

    entitlement

     
    DSpace software (copyright © 2002 - 2023)  DuraSpace
    Quick Guide | Contact Us
    Open Repository is a service operated by 
    Atmire NV
     

    Export search results

    The export option will allow you to export the current search results of the entered query to a file. Different formats are available for download. To export the items, click on the button corresponding with the preferred download format.

    By default, clicking on the export buttons will result in a download of the allowed maximum amount of items.

    To select a subset of the search results, click "Selective Export" button and make a selection of the items you want to export. The amount of items that can be exported at once is similarly restricted as the full export.

    After making a selection, click one of the export format buttons. The amount of items that will be exported is indicated in the bubble next to export format.