Elastic plastic transition in shells and tubes under pressure

Abstract

Elastic-plastic transition is obtained in current literature with the help of a semi-empirical yield condition like that of Tresca or Von Mises. The stresses are obtained from the elastic solution and then substituted in the yield condition to get the transition surface. The possibility of treating it as a transition or turning point phenomenon in finite deformation has not been explored. When the plastic state tends to set in, the stressstrain relations undergo a change. This should be reflected in our equations. The linear classical theory cannot do it. If we adopt the theory of finite deformation, the equations of equilibrium give rise to non-linear differential equations whose turning points can give the elastic-plastic transition. The asymptotic solution at these points then give the displacements and the stresses, and no semi-empirical yield condition is necessary. The yield stress can be related to the elastic coefficients in the transition range through the tension-stretch result in finite deformation. This method is applied to the plastic deformation of shells and tubes under pressure.