Shakedown/Ratcheting Boundary Determination Using Iterative Linear Elastic Schemes

This paper presents a robust non-cyclic method to identify the boundary between the shakedown and ratcheting domains (ratchet boundary) directly without the need for cyclic analysis. The solution can be obtained using only linear-elastic FEA. The method is based on lower bound formulation in shakedown theory, which is safe for design. It offers an attractive alternative to cyclic elastic-plastic analysis since it is simple, and requires considerably less computational effort and computer storage space. Another attractive feature is that the method provides a go/no go criterion for the ratchet boundary, whereas the results of a cyclic elastic-plastic analysis are often difficult to interpret near the ratchet boundary. The proposed method is applied to a number of configurations that include two-dimensional and three-dimensional effects.