On Detecting Elastoplastic Shakedown Using Minimal Digital Image Correlation Results and an Elastic Model: Demonstration for AA6061 Auxetic Sheets

Background. Shakedown occurs in elastoplastic bodies subject to cyclic loading when limited plastic deformation in the early stages of cycling gives rise to residual stresses that arrest the plastic response. As a result, purely elastic behavior is recovered upon further load cycling. Objective. This paper outlines a new procedure for identifying macroscopic shakedown responses using minimal kinematic measurements from digital image correlation and a purely elastic finite element model. Method. In contrast to traditional shakedown detection methods that track the evolution of total or equivalent plastic strains upon cycling, the proposed approach obviates assumptions about the inelastic nature of the constituent material of interest altogether. The proposed approach is inspired by Melan's static lower bound shakedown theorem and it offers advantages in terms of computational and experimental effort, providing robustness against material uncertainties, and flexibility for a variety of applications. Results. The approach is demonstrated on aluminum metamaterial sheets that are auxetic due to their arrangement of periodic perforations. In the demonstration, a set of uniaxial experiments at room temperature are analyzed where a range of cyclic stress amplitudes are imposed at non-zero mean stresses. Conclusions. The proposed shakedown determination protocol was verified by comparing with traditional methods that track the incremental evolution of equivalent plastic strain. The new procedure provides a rapid and robust approach that is suitable for high-throughput experimentation.