Shakedown static and kinematic theorems for elastic-plastic limited linear kinematic-hardening solids

Shakedown static and kinematic theorems are constructed for variable-loaded elastic-plastic hardening bodies in classical spirit. Prager's linear kinematic hardening is limited by the initial and ultimate yield surfaces. The theorems indicate that the shakedown safety of a structure does not depend on the plastic modulus, but on the initial and ultimate yield stresses. While the ultimate yield strength determines the unbounded incremental collapse pattern, the initial yield stress is responsible for the bounded cyclic plasticity collapse modes. Though the usual yield criteria do not bound the hydrostatic part of the stresses, the restrictions on the hydrostatic stresses are included in a specific way that is appropriate for structures' safety assessment and for completeness of general shakedown analysis.