Reduced integration with scaled boundary parametrization for virtual elements at finite strains
2026-06-08 • Computational Engineering, Finance, and Science
Computational Engineering, Finance, and Science
AI summaryⓘ
The authors present a new way to stabilize the virtual element method (VEM) by using fewer integration points through a Taylor series expansion and scaled boundary parametrization. This approach simplifies calculations while still accurately capturing how materials behave under different loads and conditions, including complex ones like large deformations and plasticity. They tested their method against standard finite element formulations and found it performed well, especially when the elements matched the assumed shape closely. Although some tests with higher order shape functions did not pass perfectly, the method was overall effective in modeling inelastic material behavior.
virtual element methodstabilization techniquereduced integrationTaylor series expansionscaled boundary parametrizationnon-linear patch testhyperelastic anisotropyelasto-plasticityfinite element methodhourglass stabilization
Authors
Njomza Pacolli, Bjorn Sauren, Jannick Kehls, Sven Klinkel, Stefanie Reese, Hagen Holthusen
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.