Reliable second-order hexahedral elements for explicit methods in nonlinear solid dynamics

Second‐order hexahedral elements are common in static and implicit dynamic finite element codes for nonlinear solid mechanics. Although probably not as popular as first‐order elements, they can perform better in many circumstances, particularly for modeling curved shapes and bending without artificial hourglass control or incompatible modes. Nevertheless, second‐order brick elements are not contained in typical explicit solid dynamic programs and unsuccessful attempts to develop reliable ones have been reported. In this paper, 27‐node formulations, one for compressible and one for nearly incompressible materials, are presented and evaluated using non‐uniform row summation mass lumping in a wide range of nonlinear example problems. The performance is assessed in standard benchmark problems and in large practical applications using various hyperelastic and inelastic material models and involving very large strains/deformations, severe distortions, and contact‐impact. Comparisons are also made with several first‐order elements and other second‐order hexahedral formulations. The offered elements are the only second‐order ones that performed satisfactorily in all examples, and performed generally at least as well as mass lumped first‐order bricks. It is shown that the row summation lumping is vital for robust performance and selection of Lagrange over serendipity elements and high‐order quadrature rules are more crucial with explicit than with static/implicit methods. Whereas the reliable performance is frequently attained at significant computational expense compared with some first‐order brick types, these elements are shown to be computationally competitive in flexure and with other first‐order elements. These second‐order elements are shown to be viable for large practical applications, especially using today's parallel computers. Published in 2010 by John Wiley & Sons, Ltd.