Implementation of a Self-Stabilized Virtual Element Approach in Abaqus
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This study presents a Self-Stabilized Virtual Element Method (VEM) based on the mixed Hu-Washizu variational principle. Unlike standard displacement-based VEM, which requires empirical stabilization parameters to fix rank deficiencies, this approach achieves stability by enriching the strain field with a higher-order polynomial model. The formulation is implemented in the commercial software Abaqus via a User-Defined Element (UELMAT) subroutine, allowing direct coupling with native material models. Numerical results demonstrate accurate performance on complex 2D polygonal meshes without artificial stabilization. Ongoing work extends this framework to 3D elements and geometric nonlinearities.
