On adaptation (shakedown) of a class of damaged elastic plastic bodies to cyclic loading

The objective of the presentation is to develop conditions for plastic adaptation of damaged strain-hardening elastic plastic bodies to cyclic loading. The energy based model of isotropically damaged elastic plastic strain hardening bodies by Ju is taken. A necessary condition for adaptation is considered. It is demonstrated that if there exists a time independent field of residual stresses which is in the interior of all current yield surfaces the plastic strain rates and the damage rate tend to zero. This is Melan's theorem generalized to damaged bodies with strain hardening. There exists a class of strain hardening bodies for which the above condition is fulfilled for t > t₀ if it is fulfilled for t = t₀ . Bodies with isotropic strain hardening belong to this class. The Koiter inequality extended to the case under consideration results in the conclusion that, if the conditions of theorem are satisfied, the total plastic dissipation is bounded from above.