Hodograph transformation for crack-tip fields in hyperelastic sheets: higher order eigenmodes and asymptotic path-independent integrals
Type
ArticleAuthors
Liu, YinMoran, Brian

KAUST Department
Physical Science and Engineering (PSE) DivisionMechanical Engineering Program
Graduate Affairs
Date
2021-05-11Embargo End Date
2022-05-11Submitted Date
2021-02-28Permanent link to this record
http://hdl.handle.net/10754/669216
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Show full item recordAbstract
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-xPublisher
Springer Science and Business Media LLCAdditional Links
https://link.springer.com/10.1007/s10704-021-00542-xae974a485f413a2113503eed53cd6c53
10.1007/s10704-021-00542-x