An extended Hu–Washizu formulation for elasticity

A class of new mixed formulations for elasticity is developed and analysed. The formulations are based on the discrete evss method, introduced in the context of incompressible viscoelastic flows by A. Fortin, M. Fortin and co-workers. A key feature is a stabilization term that renders coercive a problem that might not otherwise be so. The focus in this work is on behaviour in the incompressible limit and the goal is that of obtaining formulations that are uniformly stable and convergent. Concrete examples are presented of element choices that lead to unstable formulations in the classical formulation, and which are stable for the formulations introduced here. A selection of numerical results illustrates in a comparative way the behaviour of the elements introduced.