Contact algorithm

Treatment of contact along the interfaces of different elements is an important issue in finite element modelling. In this research, to avoid penetration at elements’ interface with different

152 Chapter 5: Development and Validation of Numerical Model

material properties and element sizes, the

*CONTACT_AUTOMATIC_SURFACE_TO_SURFACE algorithm was employed to model the interface between (1) the impact head and the specimen’s outer tube, (2) the specimen’s outer tube and the specimen’s concrete core, (3) the specimen’s concrete core and the specimen’s inner tube and (4) the specimen end caps and the specimen end plates. Additionally,

*CONSTRAINED_EXTRA_NODES, which ties the nodes of a deformable surface to a rigid body, was used to connect (1) the specimen end plates to the reaction plates, (2) the specimen end plates to the specimen ends and (3) the specimen end caps to the reaction plates. To tie together the reaction plates to the base plates of the load cells, which both comprised of deformable elements, at their contact area *CONTACT_TIED_NODES_TO_SURFACE was used.

The *CONTACT_AUTOMATIC_SURFACE_TO_SURFACE (Figure 5-5) is a penalty-based contact algorithm which eliminates the penetration by applying a force proportional to the penetration depth when a penetration is found for the parts in contact (Hallquist, 2006). It allows for direct determination of the impact force-time histories. The subroutines that check the slave nodes for penetration, are called for a second time to check the master nodes for penetration through the slave segments. In other words, this treatment is symmetric and the definition of the master and slave surfaces is arbitrary. However, in general, the master surface is defined as the stiffer body or the surface with a coarser mesh if the two surfaces have comparable stiffness (Hallquist, 1999). Checking for penetration on either side of an element is beneficial in impact analysis, since in the impact simulations the orientation of parts relative to each other cannot always be anticipated as the model undergoes large deformations. This sliding contact type only considers the friction interaction between the interfaces. In this study, the dynamic friction coefficient of 0.6 and static friction coefficient of 0.7 were applied to the impact head and outer steel tube interface as well as the specimen end caps and the specimen end plates interface, as recommended in (Sullivan, 1988). For the interface between the outer steel tube and concrete core as well as the inner steel tube and concrete core, the dynamic friction coefficient of 0.45 and static friction coefficient of 0.57 were used, as recommended in (Rabbat & Russell, 1985; Sohel, 2009). Additionally, the contact formulation was invoked by setting SOFT=1 in optional card A. SOFT=1 calculates contact stiffness based on stability considerations taking into account the time step. It is more effective than SOFT=0 when materials with dissimilar stiffness and/or mesh densities come into contact (Hallquist, 2007).

Chapter 5: Development and Validation of Numerical Model 153 The contact damping has been often found beneficial in reducing high-frequency oscillation of

contact forces in impact simulations (Hallquist, 2007). Therefore, to further improve the model stability, the value of 20 was assigned to the viscus damping coefficient.

Figure 5-5: CONTACT_AUTOMATIC_SURFACE_TO_SURFACE

*CONSTRAINED_EXTRA_NODES is a constraint type in LS-DYNA which allows the nodes of a deformable body to be tied to a rigid body. In this way, the nodes of a deformable body are added to a rigid body. Therefore, this constraint type was considered suitable to connect the specimen end plates to the reaction plates at their contact, the specimen end plates to the specimen ends and the specimen end caps to the reaction plates at their contact as they were rigidly tied together in the impact experiments (i.e., the specimen end plates were welded to the reaction plates, the specimen end plates were welded to the specimen ends and the specimen end caps were firmly bolted to the reaction plates.

*CONTACT_TIED_NODES_TO_SURFACE can be used to join the deformable bodies together. In this contact type the slave nodes (reaction plate in this study) are constrained to move with the master surface (base plate of the load cell in this study). At the beginning of the simulation, the closest master segment for each slave node is located based on an orthogonal projection of the slave node to the master segment and then the slave node is moved to the master surface. In this way, the initial geometry may be altered slightly without invoking any stresses. As the simulation progresses, the isoparametric position of the slave node with respect to its master segment is held fixed employing kinematic constraint equations.

The subroutines that check the slave nodes for penetration, are called for a second time to check the master nodes for penetration through the slave segments.

154 Chapter 5: Development and Validation of Numerical Model 5.2.5 Boundary conditions

As mentioned in Section 3.7.3, the specimen’s supporting system served to provide end supports for the specimen in the direction that is parallel and opposite of the lateral impact force. To represent the impact tests’ supports’ condition, the translational displacement of the base plates of the load cells were restrained in the global Y direction (i.e., impact direction) at a line of nodes at their end by defining single point constraints using BOUNDARY_SPC command in LS-DYNA, as highlighted in Figure 5-1. To limit the motion of the impact head to the impacting direction, as in the experiments, its translational displacements were restrained in Global X and Z directions and its rotations were restrained in all global directions using card 2 of *MAT_RIGID. Whilst, each spring was connected at one end to the specimen end cap at the boss location, the other end was restrained, rotationally, in all global directions and, translationally, in all global directions except global X direction, using BOUNDARY_SPC command in LS-DYNA.