A direct approach for elastic-plastic analysis and shakedown is presented and its application to a two-dimensional rolling contact problem is demonstrated. The direct approach consists of an operator split technique, which transforms the elastic-plastic problem into a purely elastic problem and a residual problem with prescribed eigenstrains. The eigenstrains are determined using an incremental projection method which is valid for nonproportional loading and both elastic and plastic shakedown. The residual problem is solved analytically and also by using a finite element procedure which can be readily generalized to more difficult problems such as three-dimensional rolling point contact. The direct analysis employs linear-kinematic-hardening plastic behavior and thus either elastic or plastic shakedown is assured, however, the phenomenon of ratchetting which can lead to incremental collapse, cannot be treated within the present framework. Results are compared with full elastic-plastic finite element calculations and a step-by-step numerical scheme for elastic-plastic analysis. Good agreement between the methods is observed. Furthermore, the direct method results in substantial savings in computational effort over full elastic-plastic finite element calculations and is shown to be a straightforward and efficient method for obtaining the steady state (shakedown) solution in the analysis of rolling and/or sliding contact.
Error driven remeshing strategy in an elastic-plastic shakedown problem
