Higher-order finite elements for lumped-mass explicit modeling of high-speed impacts

• Published in: International journal of impact engineering Vol. 137; p. 103458
• Main Authors: Browning, Robert, Danielson, Kent, Adley, Mark
• Format: Journal Article
• Language: English
• Published: Oxford Elsevier Ltd 01.03.2020; Elsevier BV
• Subjects: Computer simulation; Explicit time integration; Finite element; Finite element method; Hex-dominant meshing; Higher-order; Incompressibility; Locking; Mathematical analysis; Meshing; Modelling; Projectiles; R&D; Research & development; Second-order; Shape optimization; Visualization; Hex-dominant meshing; Explicit time integration; Higher-order; Second-order; Finite element
• ISSN: 0734-743X; 1879-3509
• DOI: 10.1016/j.ijimpeng.2019.103458

•New 2nd order 19-node pyramid finite element that lumps well for explicit methods.•New pyramid element is compatible with other 2nd order lumped explicit elements.•Pyramid elements facilitates and completes automatic projectile meshing scheme.•Combined Hex/Tet/wedge/pyramid models perform well for high-speed impact. This paper describes recent advances in higher-order finite elements for lumped-mass explicit approaches typically needed for high-rate impact modeling. Topics include benefits of 2nd order tetrahedral, wedge, hexahedral, and new pyramid element formulations to improve modeling and facilitate meshing, including the important class of applications, ogive nose-shaped projectiles impacting concrete at up to 1200 m/s. These 2nd order elements eliminate the need for hourglass control and provide higher resolution with fewer elements, since a single element can inherently capture curvature and flexural modes. Second-order elements can also simplify meshing, since in contrast to certain types of 1st order elements, they are less prone to volumetric locking associated with near incompressibility, such as what occurs in metal plasticity, and thus do not require special structures for these element types. Methods to avoid severe locking are available at the element level so as to permit unstructured meshing, e.g., all-tetrahedral methods or hexahedral-dominant methods. These technologies were developed within the U.S. Army Engineer Research and Development Center Geotechnical and Structures Laboratory (ERDC-GSL) in-house meshing (ProMesher), parallel analysis (ParaAble), and visualization (PenView) codes as well as placed into popular production software for meshing (Cubit), parallel analysis (EPIC), and visualization (ParaView). Examples using all-tetrahedral and hexahedral-dominant meshes demonstrate the ability of an unstructured 2nd order model using all four element types to accurately simulate high-rate impact problems. The benefits for shape optimization and large tradespace analyses are also demonstrated by the ability to automatically generate meshes.