The Local Conditions of Uniqueness and Plastic Strain Localization Part I: Determination of the Critical Hardening Moduli for Some Elastoplastic Materials

The classical, most frequently cited constitutive equations of elastic—plastic materials with non-associated and associated plastic flow laws are specified. Local sufficient uniqueness conditions for the solution of the boundary-value problem and local necessary conditions of initiation of deformation localization in the form of a Rice—Rudnicki localization plane are derived. We show that sufficient local uniqueness conditions for these constitutive equations with sign (≤) on the right-hand side become local necessary conditions of non-uniqueness of the solution of the boundary-value problem.