The Local Conditions of Uniqueness and Plastic Strain Localization Part II: Comparison of the Local Uniqueness Condition with the Rice-Rudnicki Local Plastic Strain Localization

Abstract

Based on previous work of the first author, the local sufficient condition of uniqueness of the solution of the incremental boundary-value problem in generalized elastoplasticity which excludes the possibility of bifurcation state is compared with the local necessary condition for the localization of plastic deformations as a Rice—Rudnicki localization plane. The analytical results of limitations imposed on the isothermal hardening functions (moduli) by the Rice—Rudnicki condition of plastic strain localization are compared with those resulting from the local uniqueness condition. It is shown that the local sufficient condition of uniqueness of the solution of the incremental boundary-value problem with an equals sign becomes a local necessary condition of non-uniqueness or local necessary condition of the possible appearance of a bifurcation state.