Overcoming paradoxes of Drucker–Prager theory for unconsolidated granular matter

Drucker–Prager model of granular matter contradicts to experiments in several aspects some of which are quite “annoying”, like, for example, the steady shear paradox: in a steady simple shear flow the continuum extends indefinitely in the direction normal to the flow. In this paper we discuss modifications of Drucker–Prager model, which eliminate most obvious paradoxes while the most essential feature of the model, its simple variational structure, is preserved.