Bounding principle for elastic-plastic creeping solids with temperature dependence of yield point stress

In the many consideration of the shakedown theory and idealized elastic perfectly plastic model of structural material has been employed (Koenig 1986). By restricting the cyclic loading to the shakedown limit, the designer is assured that after initial plastic deformation further deformations are in the elastic range, the possibilities of incremental collapse or reversed plasticity are thus avoided. The residual stress distribution which allows completely reversible behaviour in shakedown in the case of the elastic-plastic material model will relax away in time when creep is presented. Both creep and plastic deformation may increase indefinitely at loads less than the shakedown limits. Such problems are in general very difficult to solve, even numerical solutions present considerable problems. Therefore various types of bounding techniques on the total dissipation work and on the displacement have been studied and developed. These techniques have been revieved in (Leckie 1974, Ponter 1981). The bounding method lead to considerable simplifications in the analysis particulary for components subjected to many cycles of loading where the alternative approach of full inelastic analysis by finite element method is cumbersome to use. (orig./GL)