Reduced Integration‐Based Stabilization for Virtual Elements

PAMM, vol. 25

Abstract

ABSTRACT Stabilization techniques in combination with reduced integration are often employed in numerical methods to address problems of locking while reducing computational costs. In finite elements, concepts such as enhanced assumed strain (EAS) methods are usually employed in combination with stabilization techniques to tackle certain locking phenomena, such as volumetric or shear locking. This combination has been shown to improve the performance of low‐order finite element formulations while addressing the downsides of reduced integration. In recent years, the virtual element method (VEM) has emerged as a numerical approach capable of handling arbitrary polygonal and polyhedral meshes, offering flexibility in mesh generation and refinement. This flexibility makes VEM particularly suitable for a wide range of applications involving distorted, non‐convex, and irregular meshes. Similar to reduced integration, VEM formulations require stabilization to avoid rank deficiencies and ensure numerical consistency. Different stabilization techniques have been employed to overcome this issue. In this contribution, a stabilization technique based on reduced integration is proposed for VEM. The formulation is validated using two numerical examples.

Authors 5

1. Njomza Pacolli corresponding Aachen Institute of Applied Mechanics

   RWTH Aachen University

   Affiliation as printed

   Institute of Applied Mechanics RWTH Aachen University Aachen Germany

2. Jannick Kehls Aachen Institute of Applied Mechanics

   RWTH Aachen University

   Affiliation as printed

   Institute of Applied Mechanics RWTH Aachen University Aachen Germany

3. Mahmoud Sesa Aachen Institute of Applied Mechanics

   RWTH Aachen University

   Affiliation as printed

   Institute of Applied Mechanics RWTH Aachen University Aachen Germany

4. Stefanie Reese Aachen Institute of Applied Mechanics

   University of Siegen · RWTH Aachen University

   Affiliation as printed

   Institute of Applied Mechanics RWTH Aachen University Aachen Germany

   University of Siegen Siegen Germany

5. Hagen Holthusen

   Friedrich-Alexander-Universität Erlangen-Nürnberg

   Affiliation as printed

   Institute of Applied Mechanics University of Erlangen‐Nuremberg Erlangen Germany