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**Finite strain, finite rotation quadratic tetrahedral element for the combined finite-discrete element method.**
*(English)*
Zbl 1171.74453

Summary: In the past, the combined finite-discrete element was mostly based on linear tetrahedral finite elements. Locking problems associated with this element can seriously degrade the accuracy of their simulations. In this work an efficient ten-noded quadratic element is developed in a format suitable for the combined finite-discrete element method (FEMDEM). The so-called F-bar approach is used to relax volumetric locking and an explicit finite element analysis is employed. A thorough validation of the numerical method is presented including five static and four dynamic examples with different loading, boundary conditions, and materials. The advantages of the new higher-order tetrahedral element are illustrated when brought together with contact detection and contact interaction capability within a new fully 3D FEMDEM formulation. An application comparing stresses generated within two drop experiments involving different unit specimens called Vcross and VRcross is shown. The Vcross and VRcross units of \(3.5 \times 10^{4}\) kg show very different stress generation implying different survivability upon collision with a deformable floor. The test case shows the FEMDEM method has the capability to tackle the dynamics of complex-shaped geometries and massive multi-body granular systems typical of concrete armour and rock armour layers.

### MSC:

74S05 | Finite element methods applied to problems in solid mechanics |

74S30 | Other numerical methods in solid mechanics (MSC2010) |

74B20 | Nonlinear elasticity |

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\textit{J. Xiang} et al., Int. J. Numer. Methods Eng. 79, No. 8, 946--978 (2009; Zbl 1171.74453)

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