Extension of the enhanced assumed strain method based on the structure of polyconvex strain‐energy functions

In this work, two well-known approaches for mixed finite elements are combined to render three novel classes of elements. First, the widely used enhanced assumed strain (EAS) method is considered. Its key idea is to enhance a compatible kinematic field with an incompatible part. The second concept is a framework for mixed elements inspired by polyconvex strain-energy functions, in which the deformation gradient, its cofactor and determinant are three principal kinematic fields. The key idea for the novel elements is to treat enhancement of those three fields separately. This approach leads to a plethora of novel enhancement strategies and promising mixed finite elements. Some key properties of the newly proposed mixed approaches are that they are based on a Hu-Washizu type variational functional, fulfill the patch test, are frame-invariant, can be constructed completely locking free and show no spurious hourglassing in elasticity. Furthermore, they give additional insight into the mechanisms of standard EAS elements. Extensive numerical investigations are performed to assess the elements' behavior in elastic and elasto-plastic simulations.