Accurate shakedown analysis of 2D problems based on stabilization-free hybrid virtual elements

Shakedown analyses require a precise evaluation of pointwise elastic stresses and, at the same time, an accurate representation of the elastoplastic solution for capturing the ratcheting mechanisms effectively. However, existing discretization methods often face a trade-off: techniques that optimize plasticity performance may compromise elastic accuracy, and vice versa. The Hybrid Virtual Element Method (HVEM), based on divergence-free assumed-stresses and polygonal element shapes, has recently proven accuracy in both linear elastic and incremental elastoplastic analyses. For this reason, this work introduces an HVEM-based formulation for shakedown analysis. The proposed approach is based on Melan's static theorem, leveraging the equilibrated stress interpolation of HVEM. Its solution is obtained using a well-established method in which the shakedown multiplier is evaluated through a sequence of safe values, as commonly done in incremental elastoplasticity. The proposed approach is validated in a numerical testing campaign consisting in typical benchmark for shakedown analysis. The results highlight the enhanced computational efficiency of HVEM compared to traditional finite elements, and its high accuracy even with coarse mesh discretizations.