## 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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