Development of a mixed displacement-stress formulation for the analysis of elastoplastic structures under small strains: Application to a locking-free, NURBS-based solid-shell element

In this paper, we develop a general framework for the extension of mixed displacement-stress types of formulations to elastoplastic problems under small strains. The difficulty with such formulations is that, contrary to the more usual mixed methods used for incompressible materials, plasticity (which involves the deviatoric part of the stress) is affected by the static unknown. Thus, the plastic flow is not governed by displacement-induced strains alone. The approach followed in this paper consists in choosing the total elastic stress as the static unknown of the mixed formulation. Then, one determines a strain field which is used as input for the plastic projection. We applied this formalism to the mixed NURBS-based solid-shell element of Bouclier et al. (2013, 2015), which led to an efficient extension of the element into the elastoplastic domain. We were able to verify the ability of this element to overcome shell locking problems through several test cases involving a plastic flow rule with linear isotropic strain hardening.