Conditions for shakedown of damaged elastic plastic bodies with internal va
riables were investigated The damage was assumed to be brittle and isotropi
c. The damage evolution equation was integrated, so that a relation between
the damage parameter and the damage energy release rate was obtained. The
relation provides an opportunity to transfer from the effective stress tens
or components to the nominal ones in the yield function. The problem of der
iving the plastic adaptation conditions was reduced to a min-max problem of
mathematical programming. The notion of the core of the limit yield surfac
e was introduced. As a result, a lower estimate for limit value of the para
meter was obtained, and necessary conditions for general (plastic and damag
e) adaptation rue formulated. The notion of the effective limit stress was
introduced for the case where the yield function was an homogeneous functio
n of the first order in the stress tensor components, and strain hardening
is isotropic. Lower estimates for the damage parameter and the parameter of
strain hardening were obtained, and necessary conditions for general adapt
ation were derived. A modification of the material model was proposed such
that the damage process ceases along with the process of plastic deformatio
n. The developed method was expounded by an example. (C) Elsevier, Paris.