Page 81 - The Combined Finite-Discrete Element Method

64 PROCESSING OF CONTACT INTERACTION

Figure 2.29 Motion sequence of the tetrahedron with initial velocity impacting a fixed tetrahedron
for the penalty term p = 1.0e + 5Pa.

elements. Material damping due to elastic or plastic deformation of discrete elements is
naturally covered by discrete elements being discretised into finite elements.
The properties of the discretised distributed potential contact force algorithm are best
demonstrated using numerical examples. In Figure 2.29, the impact of two identical tetra-
hedra is shown. The geometry of the tetrahedra is defined with three concurrent orthogonal
edges of 2 m in length.
The material of the tetrahedra is assumed linear elastic with a modulus of elasticity
3
E = 100 GPa, ν = 0and ρ = 1500 kg/m . The top tetrahedron moves with initial velocity
of 550 m/s, while the bottom tetrahedron is fixed.
The problem is solved for penalty p = 1e + 5Pa,p = 7e + 5Pa,p = 1e + 6Pa and
p = 1e + 7 Pa. The motion sequences for penalty values of p = 1e + 5Pa,p = 7e +
5Pa,p = 1e + 6Pa and p = 1e + 7 Pa are shown in Figures 2.29–2.32, respectively. The
energy balance for all cases is shown in Figure 2.33. It can be observed that the energy
balance is preserved irrespective of the penalty value, size of penetration or geometry
of contact.

Figure 2.30 Motion sequence of a tetrahedron with initial velocity impacting on a fixed tetrahe-
dron obtained using penalty term p = 7.0e + 5Pa.