A new polyhedral element for the analysis of hexahedral-dominant finite element models and its application to nonlinear solid mechanics problems

A hexahedral-dominant finite element mesh can be easily constructed by cutting regular hexahedral elements in a simple block with CAD surfaces representing outer surfaces of a geometric model. Polyhedral elements with straight edges but possibly non-planar faces are generated at the domain boundaries, while regular hexahedral elements remain in the interior region. Shape functions for polyhedral elements are derived from moving least square approximation based on a tetrahedral subdivision of polyhedral domains by a centroid-based subdivision technique. The polyhedral shape functions in this study have similar properties to conventional finite element shape functions in terms of continuity and completeness within elements, compatibility across inter-element boundaries and the Kronecker-delta property. Furthermore, the present approach using hexahedral-dominant meshes with polyhedral elements at domain boundaries is successfully applied to solve large deformation problems of hyperelastic and elastic-plastic materials.