An Assessment Of The Ls-Dyna Hourglass Formulations Via The 3d: Fill & Download for Free

What is hourglassing?It is essentially a spurious deformation mode of a Finite Element Mesh, resulting from the excitation of zero-energy degrees of freedom. It typically manifests as a patchwork of zig-zag or hourglass like element shapes (Fig.1), where individual elements are severely deformed, while the overall mesh section is undeformed. This happens on hexahedral 3D solid reduced integration elements and on the respective tetrahedral 3D shell elements and 2D solid elements.Fig.1 Typical manifestation of the hourglassing effect (LSDYNA), image source: Hourglassing - ESOCAETWIKIPLUSWhy does hourglassing happen?I believe the following segment from Getting started with Abaqus manual explains it well:Consider a single reduced-integration element modeling a small piece of material subjected to pure bending (Fig.2)Fig. 2 Deformation of a linear element with reduced integration subjected to bending moment M.Neither of the dotted visualization lines has changed in length, and the angle between them is also unchanged, which means that all components of stress at the element's single integration point are zero. This bending mode of deformation is thus a zero-energy mode because no strain energy is generated by this element distortion. The element is unable to resist this type of deformation since it has no stiffness in this mode. In coarse meshes this zero-energy mode can propagate through the mesh, producing meaningless results.The concept of reduced integration elements is explained here [1].How is hourglassing diagnosed?By optical inspection of the mesh deformation, increasing its scale factor of necessary. But most reliably by directly comparing the energy contained in the zero energy modes (hourglass energy) with the internal energy of the system. Hourglass energy should not exceed 5% of internal energy. This is done by plotting the energies from history data.How is hourglassing addressed?By inserting an artificial stiffness to the hourglass deformation modes (the default way utilised in static/quasistatic problems).By inserting an artificial viscosity (preferred for dynamic and high velocity impact problems).By using fully integrated elements.By refining the mesh.The basic hourglass control methodologies have been pioneered by Belytschko and Flanagan since 1981 [2]. Details about the application of hourglass control can be found here [3-7].[1] FAQ: What is reduced integration in the context of finite element analysis?[2] Ted Belytschko, Jame Shau-Jen Ong, Wing Kam Liu, James M. Kennedy, Hourglass control in linear and nonlinear problems, Computer Methods in Applied Mechanics and Engineering, Volume 43, Issue 3, May 1984, Pages 251-276, ISSN 0045-7825, Hourglass control in linear and nonlinear problems. (Hourglass control in linear and nonlinear problems)[3] Presentation by J. Day - LSTC (for LSDYNA) PDF[4] LSDYNA Support page Hourglass - LS-DYNA Support[5] Leonard E. Schwer, Samuel W. Key, Thomas A. Pučik, Lee P. Bindeman, An Assessment of the LS-DYNA Hourglass Formulations via the 3D Patch Test, 5th European LS-DYNA Users Conference PDF[6] Amit H. Varma, Finite Elements in Elasticity, Purdue University CE-595 lecture notes (for ABAQUS) PPT[7] ABAQUS/Explicit Advanced topics seminar, lecture slides, p.31 PDF