Application of the Bipotential Theory to a Nonassociated Drucker–Prager Model

Abstract

The bipotential theory allows us to describe nonassociated material laws. In this paper, we propose its application to the Drucker–Prager model. With a new description of the implicit flow rules, we propose dual constitutive cones as well as five forms of the bipotential function: the elastic stage in rate form, the plastic stage in rate form, the elastic stage in incremental form, the plastic stage in incremental form, and the elastoplastic stage in incremental form. By combining these with the finite element method, a numerical strategy that deals with the nonassociated Drucker–Prager model is obtained. Two examples are simulated to verify the accuracy, the stability, and the practicability of the algorithm in civil engineering.