Locking-Free Mixed Finite Element Methods and Their Spurious Hourglassing Patterns

We present the five field mixed finite element formulation introduced by Armero and extend it to 3D problems. It combines the nonlinear mixed pressure element with an enhanced assumed strain (EAS) method based on the transposed Wilson modes. The well-known mixed pressure element arises from a Hu-Washizu-like variational principle, where dilatation and pressure are independent variables. This functional is further modified using the EAS framework to get the mixed formulation presented in this work. The element is compared to several mixed pressure and EAS element formulations showing its great performance in alleviating volumetric and shear locking in large deformation problems. The main focus of the present work is spurious hourglassing of mixed finite elements that arise in hyperelastic and elasto-plastic simulations.