Octree-based scaled boundary finite element approach for polycrystal RVEs: A comparison with traditional FE and FFT methods

Abstract

Finite Element Method (FEM) is one of the most widely used numerical techniques for solving partial differential equations. Despite its popularity, FEM faces challenges such as automatic mesh generation, handling stress singularities, and adaptive meshing. The recently developed Scaled Boundary Finite Element Method (SBFEM) overcomes these challenges by utilizing polyhedral elements, such as octree elements. SBFEM, combined with octree meshes, offer significant advantages over FEM, including rapid mesh transition, automatic mesh generation, adaptive meshing, and enhanced computational efficiency. Octree-based SBFEM has been successfully implemented and tested in various applications, such as homogenization, elastoplasticity, and adaptive phase-field fracture. However, its application to polycrystal representative volume elements (RVEs) remains unexplored. In this work, we implemented octree-based SBFEM for polycrystal RVEs and evaluated its performance for elasticity. A detailed algorithm is provided to generate balanced periodic octree meshes for polycrystal RVEs. The homogenized response and local stress fields are compared with those obtained from FEM and fast Fourier transforms (FFT). The results demonstrate that SBFEM closely matches with FEM and FFT while offering the added advantage of computational efficiency over FEM.