Octree-based scaled boundary finite element framework for crystal plasticity: An open-source ABAQUS implementation

Understanding the influence of microstructure on micromechanical fields is essential for optimising the mechanical response of metallic materials. In this regard, crystal plasticity (CP)-based polycrystalline simulations provide a powerful framework for resolving microstructure-sensitive deformation behaviour. CP formulations are predominantly implemented using either the finite element method (FEM) or fast Fourier transform (FFT)-based spectral methods. FEM offers geometric flexibility and supports arbitrary boundary conditions, whereas FFT-based methods provide superior computational efficiency but are typically restricted to regular grids and periodic boundary conditions. Despite significant advances in both approaches, a numerical framework that simultaneously achieves the geometric flexibility of FEM and the computational efficiency of FFT-based methods remains an open objective. In this work, the scaled boundary finite element method (SBFEM), coupled with octree-based discretisation, is investigated as a potential alternative for polycrystalline simulations. SBFEM is particularly well-suited for octree meshes, which enable local refinement near grain boundaries and can be generated directly from 3D microstructural images. The proposed framework integrates crystal plasticity within an octree-based SBFEM formulation to simulate elastoplastic deformation in polycrystalline representative volume elements (RVEs). Generalised scaled boundary shape functions are extended to three-dimensional domains to facilitate precomputation of element matrices, while a uniform strain approach is employed for the elastoplastic formulation. Simulations under monotonic and cyclic loading demonstrate that the proposed method accurately predicts both global responses and local fields, comparable to FEM. Furthermore, in fatigue simulations of nickel-based superalloys, the framework achieves a 42% reduction in computational cost relative to the conventional FEM-based CP framework.