Interplay between symmetry and anti-symmetry in the evolution of localized buckle patterns

M. K. Paesold, T. J. Dodwell, G. W. Hunt

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

A model of geological folding comprising a thin elastic beam supported by a nonlinear viscoelastic (Kelvin-Voigt) material is subjected to a slow rate of applied end-shortening. The description reduces to the nonlinear Swift-Hohenberg partial differential equation (PDE), supplemented by a constraint condition. A modified one degree-of-freedom Galerkin description is introduced, built by adopting the evolving modeshapes of the corresponding statical equilibria at the same state of compression. An evolutionary energy landscape is described, formed by plotting total potential energy against the single degree of freedom and the end-shortening. Comparisons of the reduced system with numerical solutions of the full PDE are found to be in good qualitative agreement for slow rates of applied end-shortening.

Original languageEnglish
Title of host publicationBifurcation and Degradation of Geomaterials with Engineering Applications. IWBDG 2017
EditorsE. Papamichos, P. Papanastasiou, E. Pasternak, A. Dyskin
PublisherSpringer
Pages517-527
Number of pages11
ISBN (Print)9783319563961
DOIs
Publication statusPublished - 22 Apr 2017
Event11th International Workshop on Bifurcation and Degradation in Geomaterials, 2017 - Limassol, Cyprus
Duration: 21 May 201725 May 2017

Publication series

NameSpringer Series in Geomechanics and Geoengineering

Conference

Conference11th International Workshop on Bifurcation and Degradation in Geomaterials, 2017
CountryCyprus
CityLimassol
Period21/05/1725/05/17

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ASJC Scopus subject areas

  • Geotechnical Engineering and Engineering Geology
  • Mechanics of Materials

Cite this

Paesold, M. K., Dodwell, T. J., & Hunt, G. W. (2017). Interplay between symmetry and anti-symmetry in the evolution of localized buckle patterns. In E. Papamichos, P. Papanastasiou, E. Pasternak, & A. Dyskin (Eds.), Bifurcation and Degradation of Geomaterials with Engineering Applications. IWBDG 2017 (pp. 517-527). (Springer Series in Geomechanics and Geoengineering). Springer. https://doi.org/10.1007/978-3-319-56397-8_65