Orientation of shear bands for a rigid plastic frictional material in simple shear

Papon, A., Liu, X., Muhlhaus, H. and Gross, L. (2012) Orientation of shear bands for a rigid plastic frictional material in simple shear. Philosophical Magazine, 92 28-30: 3564-3588. doi:10.1080/14786435.2012.704417


Author Papon, A.
Liu, X.
Muhlhaus, H.
Gross, L.
Title Orientation of shear bands for a rigid plastic frictional material in simple shear
Journal name Philosophical Magazine   Check publisher's open access policy
ISSN 1478-6435
1478-6443
Publication date 2012-10
Sub-type Article (original research)
DOI 10.1080/14786435.2012.704417
Volume 92
Issue 28-30
Start page 3564
End page 3588
Total pages 25
Place of publication Essex United Kingdom
Publisher Taylor and Francis
Collection year 2013
Language eng
Formatted abstract
The orientation of shear bands is investigated analytically and numerically for a rigid plastic frictional material in simple shear. The model is based on co-axial flow rule, incompressible deformations and a friction factor which depends on the strain history. Since we are focussing on geological timescales, the influence of elasticity is neglected. Firstly, a linear stability analysis is performed confirming Rice's 1976 assertion [The localization of plastic deformation, in Proceedings of the 14th International Congress on Theoretical and Applied Mechanics, W.T. Koiter, ed., North Holland, Amsterdam, 1976, p.207] that, in the hardening regime, bifurcation is possible at every stage. Orientation of shear bands against the less compressive principal axis lies anywhere between the Roscoe and Coulomb angles, namely between π/4+ψ/2 and π/4+φ/2, where φ and ψ are the mobilised angles of friction and dilatancy, respectively (in our study, we assume ψ=0). The linear stability analysis leaves open the question of which orientation will actually emerge in a boundary value problem that consider all nonlinearities. This question is addressed in a finite element study of simple shear with periodic boundary conditions in the shear direction. Our simulations show temporary inclined shear bands in the hardening regime followed by a persistent horizontal shear band. A sensitivity study with respect to geometric and constitutive parameters indicates that the height of the sample controls the orientation of the inclined shear bands. Finally, we extend our analytical and numerical studies to Cosserat plasticity. It turns out that inclined shear bands are suppressed for large values of the internal length R (narrow bands). The case of a standard continuum is gradually recovered for small R (wide bands).
Keyword Finite element method
Simple Shear
Plasticity
Shear band
Linear stability analysis
Q-Index Code C1
Q-Index Status Confirmed Code
Institutional Status UQ

Document type: Journal Article
Sub-type: Article (original research)
Collections: School of Earth Sciences Publications
Official 2013 Collection
 
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