A scaled boundary finite element approach for elastoplastic analysis and implementation in ABAQUS

Abstract

In this study, a revised formulation based on the uniform strain method (Flanagan and Belytschko, 1981) and the scaled boundary finite element method (SBFEM) — a numerical method with arbitrarily shaped polyhedral elements — is introduced for three-dimensional elastoplastic analysis. The proposed formulation uses the average strain of each polyhedral element. By employing the octree decomposition algorithm, high-resolution images and complex STL-format geometries are automatically converted to conforming and balanced octree meshes. Furthermore, the formulation is combined with the 144 unique octree cell patterns (Zhang et al., 2021) to streamline the workflow and improve the computational efficiency. The rotating, mirroring, and scaling operations on the octree cell patterns are derived for elastoplastic analysis. Moreover, the present approach is implemented in ABAQUS as a UELMAT user element to utilize the built-in material library. The accuracy, convergence rate, and computational efficiency of the formulation are investigated using four verification examples covering octree- and arbitrary-shaped scaled boundary finite elements. The results show that the proposed formulation does not suffer from volumetric-locking, and it has achieved a 4x speed up in comparison with existing method. It is also shown that its speed is comparable to the built-in elements in the ABAQUS. Lastly, an image-based compression analysis of a steel sample and a contact analysis on a human mouth structure are performed to illustrate the automatic workflow and the improvement in the computational speed.