B. Druyanov et I. Roman, ON ADAPTATION (SHAKEDOWN) OF A CLASS OF DAMAGED ELASTIC-PLASTIC BODIES TO CYCLIC LOADING, European journal of mechanics. A, Solids, 17(1), 1998, pp. 71-78
The objective of the presentation is to develop conditions for plastic
adaptation of damaged strain-hardening elastic plastic bodies to cycl
ic loading. The energy based model of isotropically damaged elastic pl
astic strain hardening bodies by Ju is taken. A necessary condition fo
r adaptation is considered. It is demonstrated that if there exists a
time independent field of residual stresses which is in the interior o
f all current yield surfaces the plastic strain rates and the damage r
ate tend to zero. This is Melan's theorem generalized to damaged bodie
s with strain hardening. There exists a class of strain hardening bodi
es for which the above condition is fulfilled for t > t(0) if it is fu
lfilled for t = t(0). Bodies with isotropic strain hardening belong to
this class. The Koiter inequality extended to the case under consider
ation results in the conclusion that, if the conditions of theorem are
satisfied, the total plastic dissipation is bounded from above. (C) E
lsevier, Paris.