A minimization principle for finite strain plasticity: incremental objectivity and immediate implementation

Abstract

SUMMARYA ÿnite strain plasticity formulation is proposed which meets several requirements that often appear contradictory. On a physical ground, it is based on a multiplicative split of the deformation, hyperelasticity for the reversible part of the behaviour and the maximal dissipation principle to deÿne the evolution laws. On a numerical ground, it is incrementally objective and the integration over a time increment can be expressed as a minimization problem, a proper framework to examine the questions of existence and uniqueness of the solutions. Last but not least, the implementation is immediate since it relies on the same equations for ÿnite and inÿnitesimal transformations. Finally, the formulation is applied to von Mises plasticity with isotropic linear hardening and introduced in the ÿnite element software Code Aster J . The numerical computation of a cantilever beam shows that it leads to results in good agreement with those obtain with common approaches.