Numerical Investigation of High-Order Solid Finite Elements for Anisotropic Finite Strain Problems

Abstract

In this paper, a hierarchic high-order three-dimensional finite element formulation is studied for hyperelastic and anisotropic elastoplastic problems at finite strains. The element formulation allows for anisotropic ansatz spaces supporting efficient discretizations of beam-, plate-, and shell-like structures. Several benchmark examples are investigated and the results of the high-order formulation are compared to analytic solutions and different mixed finite element formulations. Special emphasis will be placed on locking effects, robustness with respect to high aspect ratios and element distortion as well as anisotropies related to the material model. Furthermore, the interplay between the chosen ansatz space for the displacement field and mapping function in the context of geometrically nonlinear problems are studied.