Progressive plastic deformation is one of the damage mechanisms which can occur in pressure vessels subjected to cyclic loading. For design applications, the main rule proposed by codes against this failure mode is the so-called 3f (or 3Sm) criterion. During the last decade, studies have shown that this condition can be unreliable, and its application should be restricted. In parallel, theoretical developments enabled shakedown analyses to be considered in design methodology, and to be incorporated in codes and standards (EN13445, CODAP) from the early 2000s. This paper gives a review of innovative methods based on shakedown theory, which can be used in the determination of elastic shakedown limits, ratchet limits, or cyclic steady state. These approaches are based on different concepts, such as elastic compensation linear matching method (LMM), Gokhfeld theory (uniform modified yield, load dependent yield modification (LDYM)), or the research of stabilized cycle direct cyclic analysis (DCA). Each method is presented and applied on a Benchmark example in abaqus, and results are compared. A final assessment focuses on computation time, and underlines the benefits that could be expected for industrial applications.

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