Ratcheting and strain ranges in the shakedown state with stress stiffening using the Simplified Theory of Plastic Zones

• Main Authors: Hübel, H. (Author), Vollrath, B. (Author)
• Format: Article
• Language: English
• Published: Elsevier Ltd 2022
• Subjects: Cyclic strain; Cyclic strain accumulation; Elastoplasticity; Plastic deformation; Plastic zones; Post-shakedown quantities; Post-shakedown quantity; Ratcheting; Shakedown; Simplified theory of plastic zone; Simplified theory of plastic zones; Strain; Strain accumulations; Strain ranges; Stress analysis; Stress stiffening
• Online Access: View Fulltext in Publisher

 The behavior of elastic-plastic structures under cyclic loading can be determined by incremental elastic-plastic analyses where a given load histogram is analysed cycle-by-cycle until shakedown is achieved. Many cycles may be required for this, if a ratchet mechanism is causing plastic strains to accumulate in each cycle until either elastic or plastic shakedown is achieved. The complexity of the elastic-plastic response of a structure is further increased if geometric effects are present. It may be very costly to get the accumulated strains and strain ranges in the state of shakedown by incremental analyses so that simplified or direct methods have been developed as an alternative. The Simplified Theory of Plastic Zones (STPZ) has proven itself for estimating the required quantities in the state of elastic and plastic shakedown within the framework of the 1st order theory, i.e., if the equilibrium conditions are satisfied for the undeformed structure. It is shown in this paper, how the STPZ can be expanded to capture 2nd order effects introduced by the equilibrium of the deformed structure. Some examples are used to demonstrate its applicability and the quality of the results, but also its limitations with respect to determining the accumulated strains and elastic-plastic strain ranges. © 2022 The Authors