Some finite element methods for the three-field formulation of elasticity

Abstract: 

We consider a three-field formulation of linear elasticity problem. The standard three-field formulation -- often known as the Hu-Washizu formulation in elasticity -- is the mother of many different finite element methods in engineering computation. We present some modified three-field formulations and their performance in removing locking effect in the nearly incompressible elasticity. The stabilisation of the standard three-field formulation is used to obtain  the stabilised nodal strain formulation or  node-based uniform strain elements. However, we show that standard  or stabilised nodal strain formulation should be modified  to have a uniformly convergent finite element approximation in the nearly incompressible case. We also consider an extension of the three-field formulation to a nonlinear case.