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    Hodograph transformation for crack-tip fields in hyperelastic sheets: higher order eigenmodes and asymptotic path-independent integrals

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    IsoHodo v04.pdf
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    Description:
    Accepted manuscript
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    Type
    Article
    Authors
    Liu, Yin
    Moran, Brian cc
    KAUST Department
    Physical Science and Engineering (PSE) Division
    Mechanical Engineering Program
    Graduate Affairs
    Date
    2021-05-11
    Embargo End Date
    2022-05-11
    Submitted Date
    2021-02-28
    Permanent link to this record
    http://hdl.handle.net/10754/669216
    
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    Abstract
    Hodograph transformations can be used to linearize a nonlinear partial differential equation by judicious use of physical quantities (e.g. velocities or displacement gradients) as coordinate variables in the hodograph plane. This approach has been found useful for obtaining the leading order terms of eigenproblems that govern asymptotic singular crack fields in nonlinear materials. There is little work on the use of the hodograph transformation for obtaining higher order terms in the asymptotic expansion of the crack tip fields. In this paper, we develop a framework to obtain such higher order terms using the hodograph transformation. The method relies heavily on the representation of physical quantities of interest in terms of hodograph plane variables. We demonstrate the method via application to a generalized neo-Hookean material. In addition, asymptotic path-independent J-integrals are expressed in terms of either physical or hodograph variables and are used to compute the leading-order amplitude coefficients. A relationship between the asymptotic J-integrals and the energy release rate is established for a mixed crack mode. The asymptotic results are compared with numerical results from finite element computation and excellent agreement is obtained.
    Citation
    Liu, Y., & Moran, B. (2021). Hodograph transformation for crack-tip fields in hyperelastic sheets: higher order eigenmodes and asymptotic path-independent integrals. International Journal of Fracture. doi:10.1007/s10704-021-00542-x
    Publisher
    Springer Science and Business Media LLC
    Journal
    International Journal of Fracture
    DOI
    10.1007/s10704-021-00542-x
    Additional Links
    https://link.springer.com/10.1007/s10704-021-00542-x
    ae974a485f413a2113503eed53cd6c53
    10.1007/s10704-021-00542-x
    Scopus Count
    Collections
    Articles; Physical Science and Engineering (PSE) Division; Mechanical Engineering Program

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