Hourglassing‐ and locking‐free mesh distortion insensitive Petrov–Galerkin EAS element for large deformation solid mechanics

We present a novel geometrically nonlinear EAS element with several desirable features. First, a Petrov–Galerkin ansatz significantly improves the element's performance in distorted meshes without loosing the simple strain-driven format. Second, the recently proposed mixed integration point strategy is employed to improve the element's robustness in the Newton–Raphson scheme. Finally and most importantly, we enhance the spatial displacement gradient instead of the usually modified deformation gradient. This allows to construct an element without the well-known spurious instabilities in compression and tension as shown numerically and supported by a corresponding hypothesis. All in all, this leads to a robust, stable, locking-free, and mesh distortion insensitive finite element successfully applied in a wide range of examples.