Uniqueness and localization—I. Associative and non-associative elastoplasticity

doi:10.1016/0020-7683(91)90205-T

International Journal of Solids and Structures

Volume 28, Issue 2, 1991, Pages 197-213

https://doi.org/10.1016/0020-7683(91)90205-T Get rights and content

Abstract

Localization of deformation into a planar band in the incremental response of elasto-plastic material is studied in the case of small strains and rotations. The critical hardening modulus for localization is given in an explicit form (uncoupled from the band normal) for an arbitrary rate independent non-associative plasticity. Loss of uniqueness of the response is investigated in terms of positiveness of the second order work density. Criteria for loss of second order work positiveness and localization are compared for plane stress and plane strain. In these cases, for the associative flow rule, the threshold for the second order work positiveness coincides with the threshold for shear band formation. This coincidence may not, however, occur if localization into splitting mode is attained.

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Citation Excerpt :
We have presented an analytical strain localization analysis for both isotropic (scalar) and anisotropic (second-order) damage models. We have combined the Bigoni and Hueckel (1990, 1991a, b) resolution method and a further assumption to simplify the analysis in the fully multiaxial case and for anisotropic damage models: the assumption that the constitutive model displays an immediate and sufficiently strong softening right after the elasticity limit, so as to allow for the use of the undamaged elasticity tensor instead of the damaged (effective) one. This approach circumvents the yet unsolved problem of localization analysis in the general (anisotropic) case.
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^†: Visiting Research Associate from the University of Bologna, Bologna, Italy.

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Uniqueness and localization—I. Associative and non-associative elastoplasticity

Abstract

Mech. Res. Commun.

Mech. Res. Commun.

Ing. Arch.

J. Mech. Phys. Solids

J. Mech. Phys. Solids

Int. J. Solids Struct.

J. Appl. Mech.

Int. J. Rock Mech. Min. Sci.

Comp. Mech. Appl. Mech. Engng

Lecture Notes

J. Mech. Phys. Solids

Int. J. Solids Struct.