Alleviation techniques for volumetric locking in elements based on the absolute nodal coordinate formulation

Abstract

This study investigates the application of formulations employed by standard Bubnov-Galerkin Finite Elements to alleviate volumetric locking in the context of the Absolute Nodal Coordinate Formulation (ANCF). Volumetric locking is a prevalent phenomenon that occurs when linearly interpolated displacement fields are used to model incompressible phenomena. Although linear interpolations for the displacement field offer computational efficiency, their direct utilization can frequently yield erroneous solutions and slow convergence rates when applied to modeling incompressible materials. Commonly used techniques to reduce volumetric locking in classical finite elements include reduced and selective integration, mixed two/three field variational formulations, and F-bar methods. This study aims to demonstrate the efficacy of these techniques when applied to a two and three-dimensional linear ANCF-based continuum beam elements. Our findings demonstrate that most of the locking alleviation techniques yielded expected results compared to classical finite elements. Nevertheless and contrary to findings in the finite element literature, the mixed two/three field variational formulation, when used with linear ANCF-based continuum beam elements, improved the convergence rate only in the case of uniaxial tensile testing. For the bending mode, mixed ANCF elements significantly overestimated the displacements. While techniques alleviate locking for some deformation modes, the paper concludes that no definitive technique exists to completely resolve volumetric locking effects observed in linear ANCF elements, for all deformation modes.