A note on the stability of pressure-sensitive non-associated plasticity

Abstract

Stability issues related to non-associated plastic flow still present an often overlooked cause for numerical difficulties in finite element simulations of cohesive-frictional materials. Despite their significance, only few examples with analytical solutions exist that clearly illustrate the nature of the problem. In this note, we extend the existing literature by deriving a novel closed-form analytical solution for the elastoplastic behavior of non-associated Drucker-Prager plasticity subjected to oedometric extension. Moreover, we demonstrate that structural softening can arise even though material softening is not encompassed by the perfectly plastic model. By means of stability analysis based on the acoustic tensor criterion, we show that structural softening is concomitant with the loss of ellipticity of the governing rate equilibrium equations. The obtained results are illustrated through a numerical experiment, which highlights the encountered numerical difficulties, including non-objectivity of the obtained results and snap-back behavior. By means of this strikingly simple example, we aim to raise awareness about the peculiarities of non-associated plasticity among researchers, students and practitioners of geotechnical engineering alike.