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

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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