Skip Navigation

The Quarterly Journal of Mechanics and Applied Mathematics 1993 46(4):583-599; doi:10.1093/qjmam/46.4.583
© 1993 by Oxford University Press
This Article
Right arrow Full Text (PDF)
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Services
Right arrow Email this article to a friend
Right arrow Similar articles in this journal
Right arrow Alert me to new issues of the journal
Right arrow Add to My Personal Archive
Right arrow Download to citation manager
Right arrowRequest Permissions
Google Scholar
Right arrow Articles by PIPKIN, A. C.
Right arrow Search for Related Content
Social Bookmarking
Add to CiteULike   Add to Connotea   Add to Del.icio.us  
What's this?

SHOCK FORMATION IN NEARLY ELASTIC MATERIALS

A. C. PIPKIN

( Division of Applied Mathematics, Brown University Providence, Rhode Island 02912, USA )

One-dimensional wave propagation in nonlinear viscoelastic materials is discussed by using a nonlinear version of the compliance integral stress-strain relation of linear viscoelasticity theory. The analysis is phrased in terms of longitudinal waves in a stretched string in order to apply most directly to Kolsky's observation of tensile shock waves in stretched natural rubber. The compliance J(t) for a material that is nominally elastic can be approximated by power-law forms J(to)(t/to)2p with very small exponents 2p. By using approximations based on this fact, it is found that viscoelasticity theory gives results that are nearly the same as those that would be obtained from elasticity theory by treating J as constant along characteristies rather than as an absolute constant. Shocks appear as sudden but continuous changes. An initial-value problem with some relevance to Kolsky's experiment is discussed.


Add to CiteULike CiteULike   Add to Connotea Connotea   Add to Del.icio.us Del.icio.us    What's this?




Disclaimer:
Please note that abstracts for content published before 1996 were created through digital scanning and may therefore not exactly replicate the text of the original print issues. All efforts have been made to ensure accuracy, but the Publisher will not be held responsible for any remaining inaccuracies. If you require any further clarification, please contact our Customer Services Department.