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Comparison of second-order serendipity and Lagrange tetrahedral elements for nonlinear explicit methods

机译：用于非线性明确方法的二阶序列和拉格朗日四面体元素的比较

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This paper evaluates the performances of second-order finite elements for nodal lumped-mass explicit methods in nonlinear solid dynamics, with a particular emphasis on 10-node "serendipity" and 15-node "Lagrange" tetrahedral elements. Historically, many nonlinear explicit finite element codes have exclusively used first-order elements, until a fairly recent flurry of activity that has resulted in higher-order elements becoming available in explicit codes including the authors' in-house one, ParaAble, and the production software EPIC, IMPETUS, LS-DYNA, and Abaqus. A major attractiveness of tetrahedrons is their ease in meshing and higher-order elements can facilitate the avoidance of severe volumetric locking with unstructured C-0 meshes, which are generally used with these codes for the discontinuities of inelasticity, contact, etc. They also can improve modeling of flexure and curved shapes as well as eliminate spurious modes without artificial stabilization. The inclusion of face and body centroid nodes with Lagrange interpolants, including the 15-node tetrahedron, has proven to provide robust overall performance with lumped-mass explicit methods and with contact. Nevertheless, versions of the 10-node tetrahedron have also emerged in lumped-mass explicit software. In contrast to hexahedrons, an important observation about tetrahedrons is that the 10-node serendipity version uses about four times fewer quadrature points and a larger time increment than their 15-node Lagrange counterpart, which could result in tremendous computational differences. Serendipity elements, however, notoriously do not nodal mass lump well and tetrahedron versions have not been rigorously evaluated/documented for their effectiveness, as will be done herein with comparisons of those using 15-node tetrahedrons. Using row-summation lumping for Lagrange elements and the ad hoc HRZ scheme for serendipity ones, performances are assessed in common benchmark problems and practical applications using various elastic and inelastic material models and involving large strains/deformations/rotations and severe distortions. Whereas the 10-node tetrahedrons were found to perform much better than their 20-node serendipity hexahedral counterparts, specifically with substantial computational reductions and reasonable predictions, they are not generally quite as accurate or robust as the 15-node tetrahedral elements. The results thus indicate benefits of including both 10- and 15-node tetrahedrons in an explicit code's element library.
机译：本文评估了非线性实体动力学中节点集成质量明确方法的二阶有限元的性能，特别强调了10节点“串联”和15节点“拉格朗日”四面体元件。从历史上看，许多非线性明确的有限元代码专门使用了一阶元素，直到最近导致更高阶元素的速度变得更加秩序，这些活动在包括作者内部的内部内部，可再次和生产的明确代码中提供软件史诗，动力，LS-DYNA和ABAQUS。四边形的主要吸引力是它们的易于啮合，高阶元件可以促进避免使用非结构化C-0网格的严重容量锁定，这通常与这些码用于不连续性，接触等。它们也可以改善弯曲和弯曲形状的建模，并消除没有人造稳定的虚假模式。使用Lagrange Interpolants包含脸部和身体质心，包括包括15个节点四面体的嵌就，已经证明是以集成质量明确的方法和接触提供强大的整体性能。然而，10节点四面体的版本也出现在集群质量显式软件中。与六边形相比，关于四边形的重要观察是10节点偶联版本使用比其15节点拉格朗日对应物较少的正交点减少四倍，并且可以导致巨大的计算差异。然而，偶然的元素令人惊奇地没有节点质量肿块，并且还没有严格评估/记录四面体版本的效果，如本文将与使用15节点四边形的人的比较。利用拉格朗日元件的行总结集团和诸如偶联的临时HOC HRZ方案，使用各种弹性和非弹性材料模型的共同基准问题和实际应用进行了性能，并涉及大菌株/变形/旋转和严重扭曲。虽然发现10节点四边体比其20节点偶联六面对面对应物更好，具体而言，专门具有实质性计算的减少和合理的预测，但它们通常与15节点四面体元素完全不准确或稳健。因此，结果表明包括在显式代码库库中包括10个和15节点Tetrahedrons的益处。

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