On a viscoplastic Shanley-like model under constant load (Q1302498)

Throughout this paper, the authors consider a T-shaped rigid rod with initial imperfection on two no-tension viscoplastic springs under constant load. Under fairly general assumptions, a viscoplastic constitutive law is derived as a particular case of Gurtin theory which describes the material behavior under loading. By using a time-rescaling procedure and the extreme retardation, the authors determine the yielding parameter which allows to distinguish between viscoelastic and viscoplastic regimes. For all the rod states, the authors derive explicit expressions for two displacement parameters characterizing the rod evolution. By noting that the failure may occur if the reaction of one spring goes to zero, the authors obtain for all phases sufficient conditions under which no bifurcation and no failure occur, which leads to the determination of the minimum upper bound for load parameter. The new results turn out to depend only on the relaxation surface parameters at equilibrium, irrespective of the behavior under non-zero finite deformation velocities.