Basic Definitions and Results

Abstract

The experimental tests show that many engineering structures subjected to variable repeated loads exhibit plastic strains. Above a critical value α ^a of the load factor, they collapse by ratchet or alternating plasticity. On the contrary, below α ^a, the plastic deformations are stabilized and the dissipation is bounded in time. We say that the structure shakes down. Firstly, the standard plasticity model is briefly recalled. Next, we define the basic tools of the fictitious elastic and residual fields. The statical approach due to Melan allows to characterize the shakedown. The kinematical approach due to Halphen gives a description of the collapses. The end of the lecture is devoted to useful concepts of mathematical programming and non smooth mechanics