Reduced integration with scaled boundary parametrization for virtual elements at finite strains

arXiv (Cornell University)

Abstract

This contribution presents an alternative stabilization technique for the virtual element method (VEM) based on reduced integration combined with a scaled boundary parametrization. To this end, a Taylor series expansion of the constitutive quantities with respect to the sectional center is carried out, enabling analytical integration of the weak form and reducing the need for integration points to only one per section. The accuracy of the proposed formulation is shown by several numerical examples, including a non-linear patch test. Different loading, e.g. compression under large deformations, and material conditions, such as hyperelastic anisotropy and elasto-plasticity, are considered. The biquadratic serendipity finite element formulation (Q2) and the low-order finite element formulation with hourglass stabilization (Q1STc+) are used for comparison. While the patch test was not fulfilled using higher order shape functions, the formulation led to good results and was able to capture the structure's response accurately. Furthermore, the formulation performed better when the physical element resembled the pre-assigned parent elements. The example of the asymmetrically notched specimen under elasto-plastic material behavior showed that the proposed formulation is able to capture inelasticities.

Authors 6

1. Njomza Pacolli Aachen Institute of Applied Mechanics

   RWTH Aachen University

   Affiliation as printed

   RWTH Aachen University , Institute of Applied Mechanics

2. Bjorn Sauren Aachen

   RWTH Aachen University

   Affiliation as printed

   RWTH Aachen University , Chair of Structural Analysis and Dynamics Mies-van-der-Rohe-Str. 1 , 52074 Aachen , Germany

3. Jannick Kehls Aachen Institute of Applied Mechanics

   RWTH Aachen University

   Affiliation as printed

   RWTH Aachen University , Institute of Applied Mechanics

4. Sven Klinkel Aachen

   RWTH Aachen University

   Affiliation as printed

   RWTH Aachen University , Chair of Structural Analysis and Dynamics Mies-van-der-Rohe-Str. 1 , 52074 Aachen , Germany

5. Stefanie Reese Aachen Institute of Applied Mechanics

   University of Siegen · RWTH Aachen University

   Affiliation as printed

   RWTH Aachen University , Institute of Applied Mechanics

   University of Siegen , Adolf-Reichwein-Straße 2a , 57076 Siegen , Germany

6. Hagen Holthusen

   Friedrich-Alexander-Universität Erlangen-Nürnberg

   Affiliation as printed

   University of Erlangen-Nuremberg , Institute of Applied Mechanics Egerlandstraße 5 , 91058 Erlangen , Germany