Abstract
Various deformation patterns of cylindrical sands were shown to be engendered by recursive bifurcation in Chap. 14. In this chapter, deformation patterns of rectangular parallelepiped steel specimens are investigated by obtaining the rule of recursive bifurcation for that is the direct product of O(2) and two reflection group. Fundamentals of group representation theory in Chap. 7 and group-theoretic bifurcation theory in Chap. 8 are foundations of this chapter.
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Notes
- 1.
- 2.
This chapter is mostly based on Ikeda et al., 2001 [95].
- 3.
The group D2h in the Schoenflies notation was used in Sect. 14.2 to express a partial symmetry of the cylindrical domain. We have the correspondence of σ v = σ x, σ h = σ z, c(π) = σ x σ y, and σ v c(π) = σ y.
- 4.
We set Young’s modulus E = 200 GPa, Poisson’s ratio ν = 0.3333, and initial yield stress σ Y = 400 MPa. For plastic hardening, the following power law is assumed: \( \bar {\sigma } = \sigma _{\mathrm {Y}} ( 1 + {{e}^{\,\mathrm {p}}}/{e_{\mathrm {Y}}})^{0.0625}\), where e Y = σ Y∕E = 1∕500 and e p is the effective plastic strain. A tensile force is applied on the surfaces located at x = ±L∕2 and all the other surfaces are free from stress.
References
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Ikeda, K., Murota, K. (2019). Bifurcation of Steel Specimens. In: Imperfect Bifurcation in Structures and Materials. Applied Mathematical Sciences, vol 149. Springer, Cham. https://doi.org/10.1007/978-3-030-21473-9_15
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DOI: https://doi.org/10.1007/978-3-030-21473-9_15
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