Development of an abaqus user element (uel) subroutine for trimmed hexahedral elements

Recently, polyhedral elements and trimmed hexahedral elements have been developed and applied to structural analysis. A trimmed hexahedral mesh is constructed by cutting a background hexahedral mesh with the surface of an analysis domain. Polyhedral elements are then placed on the structural boundaries, and regular hexahedral elements remain in the interior domain. In this study, an Abaqus user element subroutine (UEL) for trimmed hexahedral elements is developed to analyze hexahedral dominant meshes. The shape functions of trimmed hexahedral elements are explicitly expressed in the Abaqus UEL using the harmonic shape functions on master elements stored in advance, and numerical integration is performed based on a tetrahedral division of trimmed hexahedral elements. In Abaqus a dummy mesh with a user material subroutine (UMAT) is used to visualize the results of trimmed hexahedral meshes. Accuracy and effectiveness of the Abaqus UEL for analyzing trimmed hexahedral meshes are verified through patch tests and numerical examples.