Conditions for adaptation of damaged elastic-plastic bodies to cyclic loading

Conditions for adaptation of isotropically damaged elastic-plastic bodies with isotropic strain hardening are investigated in the framework of the energy-based coupled elastic-plastic damage model by Ju. The yield function is assumed to be a homogeneous function of the first order in the stress tensor components. Due to this assumption, the notion of effective yield stress can be introduced. The loading program is supposed to be prescribed. Features of the stress path at the post-adaptation stage are considered, which lead to new necessary shakedown conditions expressed by a set of inequalities, and, in turn, to a problem of mathematical programming whose solution yields lower estimates for the damage and strain-hardening parameters. In the event, if the calculated value of the damage parameter is greater than its critical value, an adaptation to a given loading program is impossible. This condition is also necessary for adaptation in the case if only bounds for applied loads are prescribed. A correction of the constitutive material model is proposed which possibly could be good for ductile damage. The derived shakedown condition is not only necessary, but also sufficient for the plastic adaptation. The developed method is expounded in an example.