A stabilization method based on a Taylor series expansion for the virtual element method with application to inelasticities
Please login to view abstract download link
The use of reduced integration for low-order finite element formulations is often employed to overcome locking phenomena, such as shear locking in bending dominated problems or volumetric locking for incompressible materials. Since reduced integration alone yields a rank deficient stiffness matrix, stabilization techniques are employed and often combined with approaches such as enhanced assumed strain formulations to overcome the above-mentioned locking phenomena (EAS) [1]. The virtual element method (VEM) extends the classical finite element method by allowing the use of arbitrary polygonal and polyhedral meshes and providing more flexibility in mesh generation and refinement [2]. Similar to the concept of reduced integration, VEM requires stabilization to avoid rank deficiencies. Several stabilization methods have been proposed to address these challenges, e.g. [3]. In this contribution, a stabilization technique based on reduced integration with a Taylor series expansion is presented, while the focus lies on their application within the framework of the VEM. This has already been explored for regular elements [4] and is now expanded to polygonal meshes.
