Shakedown and steady-state responses of elastic-plastic solids in large displacements (Q1388582)

Elastic-perfectly plastic solids (or structures) subjected to loads quasi-statically varying within a specified domain are addressed in the framework of large displacements and the additive strain decomposition rule. On the ground of Drucker's principle of stability in the large, an appropriate stability requisite (called \(D\)-stability) is formulated as the positive definiteness property of a specific functional, sum of the second variation of the Helmholtz free energy with an additional term depending on higher-order geometry change effects. For a \(D\)-stable structure for which the additive strain decomposition rule is applicable, Melan's and Koiter's theorems of classical shakedown theory are reconsidered and reformulated for large displacements. A few illustrative numerical results are represented.