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

2026-06-08

AI Summary

This work addresses the instability and low integration efficiency of the virtual element method in large-deformation nonlinear problems by proposing a stabilized approach that combines scaled boundary parameterization with reduced integration. By performing a Taylor expansion of constitutive quantities about the cross-sectional centroid, the weak form is analytically integrated, requiring only a single integration point per cross-section. This strategy drastically reduces the number of integration points while effectively handling hyperelastic anisotropic and elastoplastic large-deformation scenarios. Numerical experiments demonstrate that the method accurately captures structural responses and inelastic behavior across various materials and loading conditions, exhibiting particularly superior performance when physical elements closely resemble their reference configurations.

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.

Problem

• virtual element method
• finite strains
• stabilization
• patch test
• elasto-plasticity

Innovation

• virtual element method
• reduced integration
• scaled boundary parametrization
• finite strains
• Taylor series expansion