Formulation of Drucker‐Prager Cap Model

Abstract

The Drucker‐Prager cap and similar models for the constitutive behavior of geotechnical materials are widely used in finite element stress analysis. They are multisurface plasticity models, used most frequently with an associated flow rule. The cap may harden or soften, and is coupled to the Drucker‐Prager yield surface. As a result of this coupling, plastic deformation in pure shear is possible, after some plastic volume change, for any state of stress on the Drucker‐Prager surface. This suggests that for full coupling the constitutive equations for the model can be found consistently; however, the model exhibits unstable behavior under certain conditions. To suppress this instability, some modification of the coupling must be made. Two examples of such modifications which appear in the literature are given; each leads to an inconsistent formulation. Numerical examples are used to illustrate differences and consequences arising from the different assumptions.