Second-order finite elements for Hex-Dominant explicit methods in nonlinear solid dynamics

• Twenty-one node wedges using row summation mass lumping performed satisfactorily.
• Full quadrature is crucial to avoid distortion errors and spurious hourglass modes.
• 2nd order wedge elements were slightly less accurate than 2nd order brick elements.
• 2nd order Hexahedral-Dominant is an effective alternative to all-tetrahedral meshing.

Hexahedral-dominant modeling approaches strike a balance of meshing ease and accuracy/efficiency by exploiting wedge (and/or pyramid) elements to transition from hexahedral elements to volumes filled by other types. Unfortunately, first-order wedges are frequently very poor performers and are the only ones typically contained in explicit solid dynamic programs. The historic preference of first-order elements with explicit methods has frequently been for simplicity and cost, but has also been from the lack of both a satisfactory consistent nodal loading distribution and an acceptable mass lumping technique for serendipity elements. Row summation lumping, for example, produces negative and zero vertex node masses for the popular fifteen and eighteen node wedges, respectively, and zero vertex nodal loads from a uniform traction on the triangular faces. The paper first presents twenty-one node wedge element formulations that produce all positive nodal loads from uniform tractions and row summation mass lumping for this element is shown to produce all positive nodal masses. In addition, they are compatible with other second-order elements applicable to lumped mass explicit methods. Performance is assessed in standard benchmark problems and practical applications using various elastic and elastic-plastic material models and involving very large strains/deformations, severe distortions, and contact-impact. These wedge elements are evaluated on their own as well as part of hexahedral-dominant meshes that use wedges for fill regions and transition from hexahedral to tetrahedral elements. In all cases, these elements performed satisfactorily and thus demonstrate their viability and benefits for practical applications, especially for fill and transition regions of low interest.