On adaptation of elastic plastic anisotropic damage structures to cyclic loading

Conditions for adaptation (shakedown) of structures of elastic plastic materials with anisotropic damage and strain hardening as subjected to cyclic loading are in question. The nature of damage is assumed ductile, so that the damage process ceases along with the cessation of plastic deformation process. The consideration is based on a material model of classical type. The demand of thermodynamical admissibility of deformation processes results in the conclusion: the quadratic form sigma : L : sigma has to be positive where L denotes the current value of the elastic compliance tensor. This inequality makes it possible to show that the rate of plastic deformation tensor tends to zero, and the total plastic dissipation is bounded, if the classical Melan condition of shakedown holds for the initial state of the material.