Dynamic Cohesive Node Insertion Results

As inidcated earlier, when solving dynamic fracture problems using the CVFE scheme, the conservative approach dictates that cohesive elements or nodes be placed everywhere in the domain at the beginning of the simulation. Although this insures that all possible failures will be captured, the cost of such an implementation is extremely large. An alternative approach is to dynamically insert cohesive elements at any time in the domain. In this way, we can obtain some time savings by not performing complex cohesive calculations, as well as memory savings since fewer nodes will be present in the domain. In this section, we detail a dynamic cohesive node insertion algorithm on simple 1-D beam problems.

Going back to the reference problem described in Figure 3.10, we insert cohesive nodes into the nodes $\char93 12$ through $\char93 20$. In order to avoid cohesive failure, we set the failing stresses of the cohesive elements to be very high. Furthermore, we reduce the critical time step based on the volumetric elements by $1/30th$, to a value of $\Delta t = 0.0025$ $s$, which ensures that any instabilities in the system are a result of the insertion algorithm and not due to the cohesive elements themselves.

Figure 3.10: Nodes 12 through 20 are made cohesive.

The first test is a blind insertion problem where nodes are inserted without any thought to the equilibrium of system. As will be presented in the next section, blind insertion causes some nodal oscillations, which affect the accuracy of the solution. As a result, we attempt to minimize these oscillations through the use of damping. Although this has some favorable results, the implementation of damping is not very efficient, so we instead present a third method of pre- stretching cohesive nodes during insertion. This allows us to minimize the oscillations much more easily while still maintaining an accurate result. Lastly we present the results from combining dynamic insertion with multi-time step nodal subcycling to further increase our computational savings.