A mixed displacement-pressure formulation for numerical analysis of plastic failure

Abstract Finite elements used for analysis of plastic failure must admit near incompressible behaviour for meaningful results whenever the plastic flow rule is isochoric. Most of the classical elements based on displacement formulations present problems to a greater or lesser extent when obtaining limit loads and failure mechanisms. Mixed pressure-displacement formulations are a suitable alternative, but not every combination of interpolation functions for pressures and displacements is allowed, since they have to satisfy Babuska-Brezzi conditions or pass a patch test for convergence. This excludes interpolations of the same order for both fields unless special techniques are used. This paper describes the formulation of mixed displacement-pressure elements with the same order of interpolation, and presents application to elastic and contained viscoplastic failure problems. It is shown how such different elements, like the T3P3 (linear displacements and pressures triangle) or the T6P6 (quadratic triangle in both variables), avoid volumetric locking and circumvent above mentioned restrictions. Indeed the formulation allows arbitrary interpolations as all restrictions are removed. However, the proposed formulation does not improve other aspects of element behaviour such as bending, and, therefore, the linear triangle is not recommended. Finally, performance of the quadratic T6P6 triangle is assessed using boundary value problems for which analytical solutions are available. Robustness against distortion is checked, and a good overall performance of this element is found