THEORETICAL AND COMPUTATIONAL ASPECTS IN THE SHAKEDOWN ANALYSIS OF FINITE ELASTOPLASTICITY

A fully nonlinear shakedown analysis is considered for structures unde rgoing large elastic-plastic strains. The underlying kinematics of fin ite elastoplasticity are based on the multiplicative decomposition of the deformation gradient into elastic and plastic parts. It is shown t hat the notion of a fictitious, self-equilibrated residual stress fiel d of Melan's linear shakedown theorem has to be replaced by the notion of real, self-equilibrated residual state. Path-dependent and path-in dependent shakedown theorems are presented that can be realized in an incremental step-by-step procedure using Finite Element codes. The num erical implementation is considered for highly nonlinear truss structu res undergoing large cyclic deformations with ideal-plastic, isotropic and kinematic hardening material behavior. Path-dependency of the res idual states in the case of non-adaptation and path-independency in th e case of shakedown are shown, and the shakedown domain is determined taking into account also the stability boundaries of the structure.