Shakedown in mechanical systems involving friction and plasticity

organizzato dal Dottorato Internazionale "Civil and Environmental Engineering", d'intesa con la Scuola di Dottorato in Ingegneria “Leonardo da Vinci”.

Abstract. In associated plasticity, mechanical systems subjected to cyclic loading are sometimes predicted to shake down, meaning that, after some dissipative cycles, the response goes back to a purely elastic state, where no plastic flow occurs. Frictional ystems show a similar behaviour, in the sense that frictional microslips due to the external loads may cease after some cycles. In the present seminar, it is shown that, for general discrete systems featuring complete contacts with either elastic or elastic-plastic behaviour and Coulomb friction, Melan’s static theorem of limit analysis gives a sufficient condition for the system to shake down, if and only if there is no normal-tangential coupling at the interfaces. A non-linear programming algorithm for calculating shakedown limit load is discussed, along with some illustrative examples related to elastic-plastic solids containing frictional cracks, where both normal-tangential coupling and friction-plasticity coupling are exhibited.