Study of a stabilized mixed finite element with emphasis on its numerical performance for strain localization problems

Abstract

The numerical performance of a stabilized mixed finite-element formulation based on the pressuregradient- projection method (PGP) using equal-order (linear) interpolation is evaluated by solving solid mechanics problems, such as structural limit load determination and strain localization modelling. All of them present incompressibility kinematical constraints induced by the constitutive behaviour. This work is specially devised to obtain critical conclusions about the use of PGP model when the mechanical response is governed by strain-softening macroscopic mechanisms. In this context, we report some detected limitations in the present formulation due to the existence of pathological mesh bias dependence once the strain localization process becomes dominant, and linear kinematics is used. An additional contribution is the numerical comparative analysis of two different strategies, for solving the complete linear equation system, addressed to a finite-element parallel code. The numerical results are compared with the standard Galerkin formulation and with an alternative stabilized mixed finite-element procedure (pressure stabilizing Petrov–Galerkin scheme).