Conditions for equivalence between the Hu–Washizu and related formulations, and computational behavior in the incompressible limit

The relationship of the Hu–Washizu mixed formulation to other mixed and enhanced formulations is examined in detail, in the context of linear elasticity, with a view to presenting a unified framework for such formulations. The Hu–Washizu formulation is considered in both its classical form and in a modified form that is suited to establishing well-posedness in the incompressible limit. Recently established theoretical results on uniform well-posedness are studied computationally by considering a range of numerical examples, which illustrate where appropriate the good behavior predicted by the theory, as well as the locking behavior that is evident in those problems in which the conditions for stability and convergence are not satisfied.