A novel methodology for determining the elastic shakedown limit loads via computing the plastic work dissipation

Highlights: • Shakedown Limit - Plastic Work Dissipation SD_Lim PWD method is presented. • The SD_Lim PWD method utilizes the PWD to determine the SD limit loads. • The SD_Lim PWD method permits the incorporation of large displacement formulation. • The SD_Lim PWD method is successfully verified against two SD benchmark problems. • The SD_Lim PWD method is successfully validated against experimental test results. A methodology that targets determining the shakedown (SD) limit loads via computing the plastic work dissipation (PWD) is presented. The methodology is termed: Shakedown Limit - Plastic Work Dissipation (${\text{SD}}_{\text{Lim}}-\text{PWD}$) method. Precisely, the ${\text{SD}}_{\text{Lim}}-\text{PWD}$ method performs a fully automated systematic iterative series of elastic-plastic finite element full cyclic loading simulations till the SD limit load is determined via tracking the PWD history of the applied load cycles. Since the ${\text{SD}}_{\text{Lim}}-\text{PWD}$ method is an energy-based approach for determining the SD limit loads; hence, it permits the incorporation of large displacement formulation and/or cyclic plasticity constitutive material models. The ${\text{SD}}_{\text{Lim}}-\text{PWD}$ method is successfully verified against the closed-form solutions of two classical SD benchmark problems. Additionally, it is validated against the test recordings of a full-scale experimental setup conducted at Berkeley Nuclear Laboratories in the UK concerning a large spherical vessel with a thin radial protruding nozzle subjected to pressurization/depressurization cycles.