On the thermodynamic consistency of the Drucker–Prager Cap model: Modification of the plastic potential and analysis of unloading

Abstract

The Drucker–Prager Cap (DPC) model is widely used to simulate powder compaction, especially in the pharmaceutical field. However, it has long been recognized that the model may predict an excessive dilation during unloading, most notably for small values of cohesion and/or friction angle. In this article, it is shown that this phenomenon is related to an inherent inconsistency between the yield surface and the commonly used plastic potential. As a result, thermodynamically inconsistent results may be obtained for some parameter values. A modified plastic potential is proposed that guarantees thermodynamic consistency. Uniaxial unloading of a homogeneous tablet in a die with constant cross section and negligible friction is considered so that the elastoplastic equations admit exact closed-form analytical solutions. Hence, exact expressions for the dependence of the axial and radial pressure on tablet height during unloading are obtained. These can be used to analyse experimental unloading data.