Some general results on the stability and flow failure of rigid viscoplastic structures

The evolution of structures made of materials which obey a rigid viscoplastic constitutive law, conceived as a generalisation of the classical Bingham model, and submitted to several loading parameters, is examined here in connection with the limit analysis (or yield design) theorems. A minimum principle for the velocities is established, from which it is shown in particular that the structure remains motionless as far as the loading belongs to the domain of safe loadings, while flow failure is triggered as soon as it is loaded beyond its limit load. Such a property is illustrated on the example of a uniform layer of Bingham material flowing on an inclined plane, due to the combined action of gravity and surface shear loading, considered as two independent loading parameters.