This research was undertaken by Dr. Jiansheng Xiang at Imperial College under the direction of Prof. Antonio Munjiza, Dr. J-P Latham, and Prof. Chris Pain.
Prior to 2005, the combined finite-discrete element method was mostly based on linear tetrahedral finite elements in 3D and triangular elements in 2D problems. Locking problems associated with these linear elements for relatively incompressible solids can seriously degrade the accuracy of their simulations. Many complex-shaped polygonal simulations in use were probably not addressing locking. Deformability in general remained a problem for many FEMDEM codes. Rarely were results presented that showed internal stress waves being transmitted through impacted bodies. 3D particulate/structure simulations were often treating the interior as rigid and using a discretization of the skin thickness into finite elements to help formulate more accurate contact forces and motions.
Crucially, the new code, Y3D, addresses this shortcoming and builds upon the many modules necessary for FEMDEM outlined earlier by Munjiza (2004). An efficient 10-noded quadratic element is developed in a format suitable for FEMDEM, the code being written by Dr J Xiang under the direction of Prof. Munjiza. The so called F-bar approach is also 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 (see Xiang et al. 2009). One of these validation test cases is illustrated below where contours of the normal Cauchy stress in the y (vertical) direction Tyy show more complex vibration modes in response to an initial simple shear in the x (to right) direction with a fixed base in a compressible elastic solid.
The implementation of this finite strain finite rotation tetrahedral element into 3D FEMDEM codes has set the scene for numerous applications where internal stress capture in time and space for dynamic multi-body processes can throw new light on poorly understood phenomena. Many are discussed under applications.
Large finite strains
The large strain capabilities combined with contact mechanics are nicely illustrated by the simulation of a sphere being forced at constant velocity through a thin walled cylinder of slightly smaller diameter, the low stiffnesses have been chosen to illustrate the deformation and buckling modes.
Multibody dynamics simulation
The simulation below represents the collisional behaviour of two rocks selected from the shape library together with a sphere and a cube. The four particles are given an initial random velocity with zero gravity acting and the box container has the same low stiffness elastic properties as the four objects. The visualisation is looking down on the top of the box as if the top side is made of transparent material. Each particle (discrete element) is represented by ~ 1000 finite elements. The motion, distortion and dynamic stress wave propagation seen in the movie are simulated with the new 3D FEMDEM code of VGeST recently developed by Dr. Jiansheng Xiang under the direction of Prof. Antonio Munjiza of QMUL.
Xiang, J., Munjiza, A. and Latham, J.-P., 2009. Finite strain, finite rotation quadratic tetrahedral element for the combined finite-discrete element method. International Journal for Numerical Methods in Engineering. 79(8), 946-978. doi: 10.1002/nme.2599‘
Munjiza, A. 2004. The Combined Finite-Discrete Element Method published in 2004 by Wiley and Sons, New York.