This brief note describes an alternative approach for the demonstration of the localization criterion. In the new approach, the criterion is not obtained in terms of the gradient jump, but in terms of the plastic multiplier jump. The new demonstration is as simple as the classic criterion in the loading/loading conditions, but much simpler in the loading/unloading case. It is the opinion of the authors that this alternative approach is more convenient for pedagogical purposes.
Issue Section:
Brief Notes
1.
Rudnicki
, J. W.
, and Rice
, J. R.
, 1975
, “Condition for the Localization of Deformation in Pressure-Sensitive Dilatant Materials
,” J. Mech. Phys. Solids
, 23
, pp. 371
–394
.2.
Rice
, J. R.
, and Rudnicki
, J. W.
, 1980
, “A Note on Some Features of the Theory of Localization of Deformation
,” Int. J. Solids Struct.
, 16
, pp. 597
–605
.3.
Ottosen
, N. S.
, and Runeson
, K.
, 1991
, “Properties of Discontinuous Bifurcation Solutions in Elasto-Plasticity
,” Int. J. Solids Struct.
, 27
, pp. 401
–421
.4.
Chambon
, J.
, 1986
, “Bifurcation Par Localisation en Bande de Cisaillement, Une Approache Avec des Lois Incrementalment Non Line´aires
,” J. Mec. Theor. Appl.
, 5
, pp. 277
–298
.5.
Rice, J. R., 1976, “The Localization of Plastic Deformation,” Theoretical and Applied Mechanics, W.T. Koiter, ed., North-Holland, Amsterdam.
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