Finite element formulations for 3D convex polyhedra in nonlinear continuum mechanics

In this paper, we present finite element formulations for general three-dimensional convex polyhedra for use in a common finite element framework that are well suited, e.g., for modeling complex granular materials and for mesh refinements. Based on an universally applicable interpolant for any convex polyhedron, different interpolation schemes are investigated in the context of nonlinear elastostatics. The modeling benefits and the numerical performance regarding the mechanical response and the computational cost are analyzed by several examples.