Echelon-Mode Formation

  • Kiyohiro Ikeda
  • Kazuo Murota
Part of the Applied Mathematical Sciences book series (AMS, volume 149)


The mechanism of the deformation pattern change of cylindrical soil specimens at the later stage has been presented in Chapter 12. In this chapter, we move on to investigate pattern formation at the earlier stage. Photo 13.1 displays:
  1. (a)

    a diamond pattern;

  2. (b)

    an oblique stripe pattern; and

  3. (c)

    an echelon mode

of cylindrical sand and soil specimens observed at the early stage. In particular, the echelon mode denotes a series of oblique parallel short wrinkles arranged with similar intervals, as depicted at the bottom-right of Photo 13.1. Moreover, patterns appear ubiquitously for materials, as shown in Photos 13.2 and 13.3 for rock and steel, regardless of their shape and deformation size. The echelon mode can, for example, be found in various materials: soils (e.g., Ikeda, Murota, and Nakano, 1994 [92]), rocks (e.g., Pollard, Segal, and Delaney, 1982 [151]; Davis, 1984 [35]; Petit, 1988 [147]), and metals (e.g., Bai and Dodd, 1992 [10]; Duszek—Perzyna and Perzyna, 1993 [42]; Poirier, 1985 [150]).


Irreducible Representation Bifurcation Point Image Simulation Soil Specimen Cylindrical Domain 
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Copyright information

© Springer Science+Business Media New York 2002

Authors and Affiliations

  • Kiyohiro Ikeda
    • 1
  • Kazuo Murota
    • 2
  1. 1.Department of Civil EngineeringTohoku UniversityAoba SendaiJapan
  2. 2.Department of Mathematical InformaticsUniversity of TokyoTokyoJapan

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